=x3-2x2+3x-1+4x2-x+2","","Solution: \u003Cbr />\n1. Write down the given polynomials:\u003Cbr />\n- First polynomial: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>g$x$ = x^3 - 2x^2 + 3x - 1\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Second polynomial: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x^2 - x + 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Align and add the polynomials term by term:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>g$x$ = x^3 - 2x^2 + 3x - 1\u003C/math-field>\u003C/math-field>\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x^2 - x + 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Add the corresponding like terms:\u003Cbr />\n- For \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^3\u003C/math-field>\u003C/math-field> terms: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^3\u003C/math-field>\u003C/math-field>\u003Cbr />\n- For \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^2\u003C/math-field>\u003C/math-field> terms: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-2x^2 + 4x^2 = 2x^2\u003C/math-field>\u003C/math-field>\u003Cbr />\n- For \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> terms: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x - x = 2x\u003C/math-field>\u003C/math-field>\u003Cbr />\n- For constant terms: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-1 + 2 = 1\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. The resulting polynomial after addition is:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^3 + 2x^2 + 2x + 1\u003C/math-field>\u003C/math-field>",null,739,148,"add-the-polynomials-g-x-x3-2x2-3x-1-4x2-x-2",{"id":16,"category":7,"text_question":17,"photo_question":9,"text_answer":18,"step_text_answer":11,"step_photo_answer":11,"views":19,"likes":20,"slug":21},538085,"R=3m. Calculate the volume of the sphere. Round to the nearest tenth if necessary","1. The formula for the volume of a sphere is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{4}{3} \\pi R^3 \u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>2. Substitute the given radius \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> R = 3 \\, \\text{m} \u003C/math-field>\u003C/math-field> into the formula:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{4}{3} \\pi $3$^3 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Calculate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 3^3 = 27 \u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>4. Thus, the volume becomes:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{4}{3} \\pi \\times 27 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Simplify the expression:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{4 \\times 27}{3} \\pi = 36 \\pi \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>6. Use the approximation \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\pi \\approx 3.1416 \u003C/math-field>\u003C/math-field> :\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V \\approx 36 \\times 3.1416 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>7. Calculate the approximate volume:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V\\approx113.0973\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>8. Round to the nearest tenth:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V \\approx 113.1 \\, \\text{m}^3 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Therefore, the volume of the sphere is approximately \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 113.1 \\, \\text{m}^3 \u003C/math-field>\u003C/math-field> .",1203,241,"r-3m-calculate-the-volume-of-the-sphere-round-to-the-nearest-tenth-if-necessary",{"id":23,"category":7,"text_question":24,"photo_question":9,"text_answer":25,"step_text_answer":11,"step_photo_answer":11,"views":26,"likes":27,"slug":28},538084,"Width of 12 in. Calculate the volume of the sphere. Round to the nearest tenth if necessary","1. Identify the radius of the sphere. Given the width is 12 inches, the diameter is 12 inches. Therefore, the radius is half of the diameter:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> r = \\frac{12}{2} = 6 \\, \\text{in} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Use the formula for the volume of a sphere:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{4}{3} \\pi r^3 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Substitute the radius into the formula:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{4}{3} \\pi $6$^3 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Calculate:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{4}{3} \\pi \\times 216 = \\frac{864}{3} \\pi = 288 \\pi \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Approximate using \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\pi \\approx 3.1416 \u003C/math-field>\u003C/math-field>:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V \\approx 288 \\times 3.1416 = 904.8 \\, \\text{in}^3 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. The volume of the sphere, rounded to the nearest tenth, is approximately:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 904.8 \\, \\text{in}^3 \u003C/math-field>\u003C/math-field>",278,56,"width-of-12-in-calculate-the-volume-of-the-sphere-round-to-the-nearest-tenth-if-necessary",{"id":30,"category":7,"text_question":31,"photo_question":9,"text_answer":32,"step_text_answer":11,"step_photo_answer":11,"views":33,"likes":34,"slug":35},538083,"Calculate the volume $to the nearest tenth of a cubic centimeter$ of a golf ball whose diameter is 4.267cm","1. The formula for the volume of a sphere is given by \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V = \\frac{4}{3} \\pi r^3\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>2. The diameter of the golf ball is given as 4.267 cm, so the radius is half of that: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r = \\frac{4.267}{2} = 2.1335 \\, \\text{cm}\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>3. Substitute the radius into the volume formula: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V = \\frac{4}{3} \\pi $2.1335$^3\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>4. Calculate the cube of the radius: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>$2.1335$^3 = 9.707432537375\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>5. Substitute this back into the formula: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V=\\frac{4}{3}\\pi\\times9.707432537375\\approx40.7\\,\\text{cm}^3\u003C/math-field>\u003C/math-field> .\u003Cbr>\u003Cbr>6. The volume of the golf ball is approximately \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>40.7\\,\\text{cm}^3\u003C/math-field>\u003C/math-field> .",1440,288,"calculate-the-volume-to-the-nearest-tenth-of-a-cubic-centimeter-of-a-golf-ball-whose-diameter-is-4-267cm",{"id":37,"category":7,"text_question":38,"photo_question":9,"text_answer":39,"step_text_answer":11,"step_photo_answer":11,"views":40,"likes":41,"slug":42},538082,"Find the length of each base edge $to the nearest tenth of a meter$ of the 24m tall glass square pyramids of the Muttart Conservatory in Alberta, Canada, if each contains 5280m^3 of space","1. Volume V of a square pyramid is given by the formula:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V = \\frac{1}{3} B h\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>where B is the area of the base and h is the height of the pyramid.\u003Cbr>\u003Cbr>2. Given that the height h = 24 m and the volume V = 5280 m^3.\u003Cbr>\u003Cbr>3. The base is square, so if the side length of the base is s, then:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>B = s^2\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Substituting into the volume formula:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5280 = \\frac{1}{3} s^2 \\times 24\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Simplify and solve for s^2:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5280 = 8 s^2\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s^2 = \\frac{5280}{8} = 660\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>6. Solve for s:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s = \\sqrt{660} \\approx 25.7\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>7. To find the length of each base edge to the nearest tenth of a meter, compute:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>s \\approx 25.7 \\, \\text{m}\u003C/math-field>\u003C/math-field>",418,84,"find-the-length-of-each-base-edge-to-the-nearest-tenth-of-a-meter-of-the-24m-tall-glass-square-pyramids-of-the-muttart-conservatory-in-alberta-canada-if-each-contains-5280m-3-of-space",{"id":44,"category":7,"text_question":45,"photo_question":9,"text_answer":46,"step_text_answer":11,"step_photo_answer":11,"views":47,"likes":48,"slug":49},538081,"An observer is 150 meters away\n distance of a hot air balloon online\n straight line at ground level. From your position,\n measures an elevation angle of 40° up to\n the base of the balloon. At what height is\n find the hot air balloon?","Solution:\u003Cbr />\n1. Dado:\u003Cbr />\n- Distancia horizontal desde el observador hasta la base del globo: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>d = 150 \\ m\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Ángulo de elevación: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\theta = 40^{\\circ}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Usamos la función tangente para encontrar la altura \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>h\u003C/math-field>\u003C/math-field> del globo aerostático. La tangente de un ángulo en un triángulo rectángulo es la razón entre la altura y la distancia horizontal:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\tan$\\theta$ = \\frac{h}{d}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Sustituimos los valores conocidos en la ecuación:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\tan$40^{\\circ}$ = \\frac{h}{150}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Resolvemos para \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>h\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>h = 150 \\times \\tan$40^{\\circ}$\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Calculamos el valor numérico:\u003Cbr />\n* Usando una calculadora, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\tan$40^{\\circ}$ \\approx 0.8391\u003C/math-field>\u003C/math-field>\u003Cbr />\n* Entonces: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>h \\approx 150 \\times 0.8391 = 125.865 \\ m\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nLa altura del globo aerostático es aproximadamente \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>125.865 \\ m\u003C/math-field>\u003C/math-field>.",667,133,"an-observer-is-150-meters-away-distance-of-a-hot-air-balloon-online-straight-line-at-ground-level-from-your-position-measures-an-elevation-angle-of-40-up-to-the-base-of-the-balloon-at-what-hei",{"id":51,"category":7,"text_question":52,"photo_question":9,"text_answer":53,"step_text_answer":11,"step_photo_answer":11,"views":54,"likes":55,"slug":56},538080,"A plane ticket has gone up 18%, now costing $4,720. How much did it cost before the increase?","\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{Solution:}\u003C/math-field>\u003C/math-field>\u003Cbr />\n1. Define variables:\u003Cbr />\n- Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P\u003C/math-field>\u003C/math-field> be the original price of the plane ticket.\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P\u003C/math-field>\u003C/math-field> increased by 18% means the new price is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P + 0.18P = 1.18P\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n2. Set up the equation based on the problem statement:\u003Cbr />\n- The new price \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 4,720\u003C/math-field>\u003C/math-field>.\u003Cbr />\n- Therefore, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1.18P = 4,720\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n3. Solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P\u003C/math-field>\u003C/math-field>:\u003Cbr />\n- Divide both sides by 1.18 to isolate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P\u003C/math-field>\u003C/math-field>.\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P = \\frac{4,720}{1.18}\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n4. Calculate:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P \\approx 4,000\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{Answer:}\u003C/math-field>\u003C/math-field>\u003Cbr />\n- The original price of the plane ticket was approximately USD 4,000.",726,145,"a-plane-ticket-has-gone-up-18-now-costing-4-720-how-much-did-it-cost-before-the-increase",{"id":58,"category":7,"text_question":59,"photo_question":9,"text_answer":60,"step_text_answer":11,"step_photo_answer":11,"views":61,"likes":62,"slug":63},538078,"H=8mm, r=2mm. Calculate the volume of the cone round to the nearest tenth if necessary","1. Use the formula for the volume of a cone: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{1}{3} \\pi r^2 H \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Substitute the given values: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> H = 8 \\, \\text{mm}, \\, r = 2 \\, \\text{mm} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{1}{3} \\pi (2)^2 (8) \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Calculate \\( (2)^2 \\):\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> (2)^2 = 4 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Substitute and compute:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{1}{3} \\pi (4)(8) \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{1}{3} \\pi (32) \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Calculate the product: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V = \\frac{32}{3} \\pi \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>6. Calculate:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>V\\approx33.51032\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>7. Round to the nearest tenth:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V \\approx 33.5 \\, \\text{mm}^3 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>This is the answer: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> V \\approx 33.5 \\, \\text{mm}^3 \u003C/math-field>\u003C/math-field>",631,126,"h-8mm-r-2mm-calculate-the-volume-of-the-cone-round-to-the-nearest-tenth-if-necessary",{"id":65,"category":7,"text_question":66,"photo_question":9,"text_answer":67,"step_text_answer":11,"step_photo_answer":11,"views":68,"likes":69,"slug":70},538076,"Dividing 218 or 172 by the natural number n, you get a remainder of 11. Dividing n by 11, you get a remainder equal to:","** \u003Cbr>\u003Cbr>1. Since dividing 218 by n gives a remainder of 11, 218 - 11 = 207 is divisible by n : \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>207\\equiv0\\pmod{n}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Similarly, dividing 172 by n gives a remainder of 11, so 172 - 11 = 161 is divisible by n :\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>161\\equiv0\\pmod{n}\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. n must be a common divisor of 207 and 161. Find the greatest common divisor of 207 and 161:\u003Cbr>\u003Cbr>- First, find the difference: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 207 - 161 = 46 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Find the prime factorization of 46:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 46 = 2 \\times 23 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Prime factorization of 161:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 161 = 7 \\times 23 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Common factor is 23.\u003Cbr>\u003Cbr>4. Therefore, the possible value of n should be 23 (since other divisions have factors that don't divide both). Now, divide n = 23 by 11:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 23 \\div 11 = 2 \\, \\text{R} \\, 1 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Thus, the remainder of dividing n by 11 is 1\u003Cbr>\u003Cbr>",1233,247,"dividing-218-or-172-by-the-natural-number-n-you-get-a-remainder-of-11-dividing-n-by-11-you-get-a-remainder-equal-to",{"id":72,"category":7,"text_question":73,"photo_question":9,"text_answer":74,"step_text_answer":11,"step_photo_answer":11,"views":75,"likes":76,"slug":77},538074,"R=24 inches\nCalculate the surface area of the sphere","1. The formula to calculate the surface area of a sphere is given by: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> A = 4 \\pi R^2 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Substitute the value of the radius \\( R = 24 \\) inches into the formula: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> A = 4 \\pi (24)^2 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Calculate the square of the radius:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> (24)^2 = 576 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Multiply by 4:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 4 \\times 576 = 2304 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. The surface area is:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>A=2304\\pi=7238.23\u003C/math-field>\u003C/math-field> square inches \u003Cbr>\u003Cbr>Therefore, the surface area of the sphere is 7238.23 square inches.",923,185,"r-24-inches-calculate-the-surface-area-of-the-sphere",{"id":79,"category":7,"text_question":80,"photo_question":9,"text_answer":81,"step_text_answer":11,"step_photo_answer":11,"views":82,"likes":83,"slug":84},538073,"Andrés's age is three times Quan's.\n plus wins and both ages add up to 69 years. Nillar\n both ages.","Solution:\u003Cbr />\n1. Define variables:\u003Cbr />\n- Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a\u003C/math-field>\u003C/math-field> be the age of Andrés.\u003Cbr />\n- Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>q\u003C/math-field>\u003C/math-field> be the age of Quan.\u003Cbr />\n\u003Cbr />\n2. Set up the equations based on the problem:\u003Cbr />\n- Andrés is three times as old as Quan: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a = 3q\u003C/math-field>\u003C/math-field>\u003Cbr />\n- The sum of their ages is 69: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a + q = 69\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Substitute \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a = 3q\u003C/math-field>\u003C/math-field> into the second equation:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3q + q = 69\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Simplify the equation:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4q = 69\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>q\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>q = \\frac{69}{4}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Compute \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>q\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>q = 17.25\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Find \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a\u003C/math-field>\u003C/math-field> using the equation \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a = 3q\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a = 3 \\times 17.25\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n8. Compute \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a = 51.75\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nTherefore:\u003Cbr />\n- Quan is approximately 17.25 years old.\u003Cbr />\n- Andrés is approximately 51.75 years old.",553,111,"andres-s-age-is-three-times-quan-s-plus-wins-and-both-ages-add-up-to-69-years-nillar-both-ages",{"id":86,"category":7,"text_question":87,"photo_question":9,"text_answer":88,"step_text_answer":11,"step_photo_answer":11,"views":89,"likes":90,"slug":91},538072,"Andrew's age is three times John's plus nine years, and their ages add up to 69 years. Find both ages.","Solution:\u003Cbr />\n1. Define variables:\u003Cbr />\n- Let \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> be Juan's age.\u003Cbr />\n- Andrés' age is then \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x + 9\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n2. Set up the equation for the total age:\u003Cbr />\n- Juan's age \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> plus Andrés' age \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x + 9\u003C/math-field>\u003C/math-field> equals 69.\u003Cbr />\n\u003Cbr />\n3. Equation:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x + (3x + 9) = 69\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Simplify and solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x + 3x + 9 = 69\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x + 9 = 69\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x = 60\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 15\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Find Andrés' age:\u003Cbr />\n- Substitute \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 15\u003C/math-field>\u003C/math-field> into Andrés' age expression:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x + 9 = 3(15) + 9 = 45 + 9 = 54\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Therefore, the ages are:\u003Cbr />\n- Juan: 15 years\u003Cbr />\n- Andrés: 54 years",531,106,"andrew-s-age-is-three-times-john-s-plus-nine-years-and-their-ages-add-up-to-69-years-find-both-ages",{"id":93,"category":7,"text_question":94,"photo_question":9,"text_answer":95,"step_text_answer":11,"step_photo_answer":11,"views":96,"likes":97,"slug":98},538071,"Solve the following linear equations:\n 1) 5x-3= 3X+7","Solution:\u003Cbr />\n1. Given Equation:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5x - 3 = 3x + 7\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Subtract \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x\u003C/math-field>\u003C/math-field> from both sides to simplify:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5x - 3x - 3 = 7\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Combine like terms:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x - 3 = 7\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Add 3 to both sides to isolate the term with the variable:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x = 10\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Divide both sides by 2 to solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 5\u003C/math-field>\u003C/math-field>",1382,276,"solve-the-following-linear-equations-1-5x-3-3x-7",{"id":100,"category":7,"text_question":101,"photo_question":9,"text_answer":102,"step_text_answer":11,"step_photo_answer":11,"views":103,"likes":104,"slug":105},538070,"Solve the following linear equations:\n\n 2) 2x+4- 5x = x+8-5×","1. Start with the original equation: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x + 4 - 5x = x + 8 - 5x\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Combine like terms on both sides:\u003Cbr>\u003Cbr>- Left side: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x - 5x + 4 = -3x + 4\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- Right side: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x - 5x + 8 = -4x + 8\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>So the equation becomes:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-3x + 4 = -4x + 8\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Add \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x\u003C/math-field>\u003C/math-field> to both sides to get:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x + 4 = 8\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Subtract \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4\u003C/math-field>\u003C/math-field> from both sides:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 4\u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>",674,135,"solve-the-following-linear-equations-2-2x-4-5x-x-8-5",{"id":107,"category":7,"text_question":108,"photo_question":9,"text_answer":109,"step_text_answer":11,"step_photo_answer":11,"views":110,"likes":111,"slug":112},538069,"15=75% of ?","\u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$\\frac{x}{15}=\\frac{4}{3}$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$x=20$\u003C/math-field>\n \u003Cbr>\n \u003C/div>",467,93,"15-75-of",{"id":114,"category":7,"text_question":115,"photo_question":9,"text_answer":116,"step_text_answer":11,"step_photo_answer":11,"views":117,"likes":55,"slug":118},538067,"Naria Wants to build a perimeter wall fence around 400 sqm lot. The frontage of the lot is 20 meters. The wall height is 1.2 meters below the ground and 3.8 meters above the ground .\nThe cost of constructing the wall is 750 per square meter. Additionally,she plans to install a 5-meter-wide gate that costs ₱50,000.\nHow much Maria spend in total for the wall and the gate\na. Php 281,250.00\nb. Php 106,250.00\nc. Php 331,250.00\nd. Php 218,250.00","1. Determine the dimensions of the lot. Given the frontage is 20 meters, calculate the other side using the area:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Area} = 20 \\times x = 400 \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = \\frac{400}{20} = 20 \\, \\text{meters} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Calculate the perimeter of the lot:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Perimeter} = 2 \\times (20 + 20) = 80 \\, \\text{meters} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Calculate the total height of the wall:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Total height} = 1.2 + 3.8 = 5 \\, \\text{meters} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Calculate the wall area excluding the gate:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Wall area} = (\\text{Perimeter} - \\text{Gate width}) \\times \\text{Total height} \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Wall area} = (80 - 5) \\times 5 = 75 \\times 5 = 375 \\, \\text{sqm} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Calculate the cost of the wall:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Wall cost} = 375 \\times 750 = 281,250 \\, \\text{PHP} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Calculate total cost including the gate:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Total cost} = \\text{Wall cost} + \\text{Gate cost} \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Total cost} = 281,250 + 50,000 = 331,250 \\, \\text{PHP} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Therefore, the total cost is: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Php} \\, 331,250.00 \u003C/math-field>\u003C/math-field>",727,"naria-wants-to-build-a-perimeter-wall-fence-around-400-sqm-lot-the-frontage-of-the-lot-is-20-meters-the-wall-height-is-1-2-meters-below-the-ground-and-3-8-meters-above-the-ground-the-cost-of-const",{"id":120,"category":7,"text_question":121,"photo_question":9,"text_answer":122,"step_text_answer":11,"step_photo_answer":11,"views":123,"likes":41,"slug":124},538066,"2. A rectangular lot has a\n30 meters.\nallocated along the frontage. What is the gross area\nfrontage of 18 meters and a depth of\nHowever, a public right of way of 3 meters is\nReve\nof\nthe\nlot?\na. 520 sqm\nb. 540 sqm\nC. 560 sqm\nd. 580 sqm\nReV","1. Calculate the area of the rectangular lot without the right of way:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Area}_{\\text{total}} = \\text{frontage} \\times \\text{depth} = 18 \\, \\text{m} \\times 30 \\, \\text{m} = 540 \\, \\text{sqm} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. No need to subtract any area because the problem states that the right of way has already been accounted for in the dimensions provided.\u003Cbr />\n\u003Cbr />\n3. Therefore, the gross area of the lot remains:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 540 \\, \\text{sqm} \u003C/math-field>\u003C/math-field> \u003Cbr />\n \u003Cbr />\nThus, the answer is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>540 \\, \\text{sqm}\u003C/math-field>\u003C/math-field>.",420,"2-a-rectangular-lot-has-a-30-meters-allocated-along-the-frontage-what-is-the-gross-area-frontage-of-18-meters-and-a-depth-of-however-a-public-right-of-way-of-3-meters-is-reve-of-the-lot-a-520-sq",{"id":126,"category":7,"text_question":127,"photo_question":9,"text_answer":128,"step_text_answer":11,"step_photo_answer":11,"views":129,"likes":130,"slug":131},538065,"A triangular lot has a base of 15 meters and heights of 10 meters . What is the total area of the lot ?","1. The formula for the area of a triangle is given by:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> A = \\frac{1}{2} \\times \\text{base} \\times \\text{height} \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n2. Substitute the given values into the formula:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> A = \\frac{1}{2} \\times 15 \\times 10 \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n3. Calculate the area:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> A = \\frac{1}{2} \\times 150 \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n4. Simplify the expression:\u003Cbr />\n\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> A = 75 \u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\nTherefore, the total area of the lot is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>75 \\, \\text{square meters}\u003C/math-field>\u003C/math-field>.",425,85,"a-triangular-lot-has-a-base-of-15-meters-and-heights-of-10-meters-what-is-the-total-area-of-the-lot",{"id":133,"category":7,"text_question":134,"photo_question":9,"text_answer":135,"step_text_answer":11,"step_photo_answer":11,"views":136,"likes":137,"slug":138},538064,"4x+(x-3)=2x-(3x-4)+5","Solution:\u003Cbr />\n1. Simplify both sides of the equation.\u003Cbr />\n- Left side: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4x + (x - 3) = 4x + x - 3 = 5x - 3\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Right side: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x - (3x - 4) + 5 = 2x - 3x + 4 + 5 = -x + 9\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. The equation is now: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5x - 3 = -x + 9\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Add \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field> to both sides to eliminate the \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-x\u003C/math-field>\u003C/math-field> from the right side and simplify:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5x + x - 3 = 9\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Simplify: \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>6x - 3 = 9\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Add 3 to both sides to isolate terms with \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>6x = 9 + 3\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Simplify:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>6x = 12\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Divide both sides by 6 to solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = \\frac{12}{6}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n8. Simplify the fraction:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 2\u003C/math-field>\u003C/math-field>",1332,266,"4x-x-3-2x-3x-4-5",{"id":140,"category":7,"text_question":141,"photo_question":9,"text_answer":142,"step_text_answer":11,"step_photo_answer":11,"views":143,"likes":144,"slug":145},538063,"Determine the number such that if you add half of it, double it, and triple it, you get 55.","Solution:\u003Cbr />\n1. Let the unknown number be \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n2. Calculate the expressions based on the problem's conditions:\u003Cbr />\n * Half of the number: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{x}{2}\u003C/math-field>\u003C/math-field>\u003Cbr />\n * Double of the number: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2x\u003C/math-field>\u003C/math-field>\u003Cbr />\n * Triple of the number: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Set up the equation from the problem statement:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{x}{2} + 2x + 3x = 55\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Combine the like terms:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{x}{2} + 5x = 55\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. To eliminate the fraction, multiply the entire equation by 2:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x + 10x = 110\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Simplify and solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>11x = 110\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 10\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Therefore, the number is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 10\u003C/math-field>\u003C/math-field>.",484,97,"determine-the-number-such-that-if-you-add-half-of-it-double-it-and-triple-it-you-get-55",{"first":147,"last":148,"prev":11,"next":149},1,187,2,{"current_page":147,"from":147,"last_page":148,"links":151,"path":189,"per_page":190,"to":190,"total":191},[152,155,158,161,164,167,170,173,176,179,182,185,187],{"url":147,"label":153,"active":154},"1",true,{"url":149,"label":156,"active":157},"2",false,{"url":159,"label":160,"active":157},3,"3",{"url":162,"label":163,"active":157},4,"4",{"url":165,"label":166,"active":157},5,"5",{"url":168,"label":169,"active":157},6,"6",{"url":171,"label":172,"active":157},7,"7",{"url":174,"label":175,"active":157},8,"8",{"url":177,"label":178,"active":157},9,"9",{"url":180,"label":181,"active":157},10,"10",{"url":183,"label":184,"active":157},186,"186",{"url":148,"label":186,"active":157},"187",{"url":149,"label":188,"active":157},"Next »","https://api.math-master.org/api/question",20,3736,{"data":193},[194,196,198,200,202,204],{"id":147,"title":195,"slug":11},"Algebra",{"id":149,"title":197,"slug":11},"Geometry",{"id":159,"title":199,"slug":11},"Coordinate-geometry",{"id":162,"title":201,"slug":11},"Statistics",{"id":165,"title":203,"slug":11},"Calculus",{"id":168,"title":205,"slug":11},"General",{"data":207},[208,209,210,211,212,213],{"id":147,"title":195,"slug":11},{"id":149,"title":197,"slug":11},{"id":159,"title":199,"slug":11},{"id":162,"title":201,"slug":11},{"id":165,"title":203,"slug":11},{"id":168,"title":205,"slug":11},{"data":215},{"id":216,"category":7,"slug":217,"text_question":218,"photo_question":11,"text_answer":219,"step_text_answer":11,"step_photo_answer":11,"views":220,"likes":221,"expert":222},537718,"k-6-8","K-6>8","\u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba(0, 0, 0, .3);box-shadow: 0 0 0 rgba(0, 0, 0, .2)\n\" read-only>$k>14$\u003C/math-field>\n \u003Cbr>\n \u003C/div>",1141,228,{"id":223,"name":224,"photo":225,"biography":226,"created_at":11,"updated_at":11,"rating":227,"total_answer":90},29,"Eliseo","https://api.math-master.org/img/experts/29/29.webp","In my school days I was not good in Mathematics but there was something which always attracted me towards Mathematics as playing with numbers and doing round of questions of different exercises of workbook was fun for me and as a hobby I inclined to Math's. I never thought of teaching mathematics and making a career out of it but somethings bound to happen.",4.6,{"data":229},{"questions":230},[231,235,239,243,247,251,255,259,263,267,271,275,279,283,287,291,295,299,303,307],{"id":232,"category":7,"text_question":233,"slug":234},533963,"The data set (75, 85, 58, 72, 70, 75) is a random sample from the\nnormal distribution No(µ, σ). Determine a 95% two-sided confidence\ninterval for the mean µ .","the-data-set-75-85-58-72-70-75-is-a-random-sample-from-the-normal-distribution-no-u-determine-a-95-two-sided-confidence-interval-for-the-mean-u",{"id":236,"category":7,"text_question":237,"slug":238},533967,"The bus one way of the road which is 10km is heading with speed of 20km/h ,then the bus the other 10km is heading with speed of 60km/h. The middle speed of the road is it equal with arithmetic speed of the v1 and v2 ?","the-bus-one-way-of-the-road-which-is-10km-is-heading-with-speed-of-20km-h-then-the-bus-the-other-10km-is-heading-with-speed-of-60km-h-the-middle-speed-of-the-road-is-it-equal-with-arithmetic-speed-o",{"id":240,"category":7,"text_question":241,"slug":242},533972,"Find the measures of the sides of ∆KPL and classify each triangle by its sides k (-2,-6), p (-4,0), l (3,-1)","find-the-measures-of-the-sides-of-kpl-and-classify-each-triangle-by-its-sides-k-2-6-p-4-0-l-3-1",{"id":244,"category":7,"text_question":245,"slug":246},534012,"Margin of error E=0.30 populations standard deviation =2.5. Population means with 95% confidence. What I the required sample size (round up to the whole number)","margin-of-error-e-0-30-populations-standard-deviation-2-5-population-means-with-95-confidence-what-i-the-required-sample-size-round-up-to-the-whole-number",{"id":248,"category":7,"text_question":249,"slug":250},534060,"-4y-6(2z-4y)-6","4y-6-2z-4y-6",{"id":252,"category":7,"text_question":253,"slug":254},534092,"Subscribers to the FAME magazine revealed the following preferences for three categories: Fashion 30, Athletics 24 and Business 15. Following these frequencies of observation, compute the chi-square test statistic.\r\nAt the 0.05 level of significance, would you conclude they are similar?","subscribers-to-the-fame-magazine-revealed-the-following-preferences-for-three-categories-fashion-30-athletics-24-and-business-15-following-these-frequencies-of-observation-compute-the-chi-square-t",{"id":256,"category":7,"text_question":257,"slug":258},534100,"Reparameterize the curve r(t)= cos(t)i without (t)j (t)k by the arc length.","reparameterize-the-curve-r-t-cos-t-i-without-t-j-t-k-by-the-arc-length",{"id":260,"category":7,"text_question":261,"slug":262},534168,"I want you to solve this problem as a grade sixth pupil in primary school:\n8 Pigs ate 6 bags of fee in 20 days. How long will it take 10 pigs to eat 15 bags of feed eating at the same rate?","i-want-you-to-solve-this-problem-as-a-grade-sixth-pupil-in-primary-school-8-pigs-ate-6-bags-of-fee-in-20-days-how-long-will-it-take-10-pigs-to-eat-15-bags-of-feed-eating-at-the-same-rate",{"id":264,"category":7,"text_question":265,"slug":266},534214,"Nice's central library building is considered one of the most original in the world, as it is a mix between a sculpture and a work of habitable architecture. It was called La Tête Carrée and is made up of part of a bust that supports a cube divided into five floors.\n It is known that the building has a total height of approximately 30 meters. It admits that the cubic part of the sculpture is parallel to the floor and has a volume of 2744 meters3\n Calculate, in meters, the height of the bust that supports the cube.\n Displays all the calculations you made.","nice-s-central-library-building-is-considered-one-of-the-most-original-in-the-world-as-it-is-a-mix-between-a-sculpture-and-a-work-of-habitable-architecture-it-was-called-la-tete-carree-and-is-made-u",{"id":268,"category":7,"text_question":269,"slug":270},534221,"How many square feet of floor area are there in three two-storey apartment houses, each of which is 38 feet wide and 76 feet long?","how-many-square-feet-of-floor-area-are-there-in-three-two-storey-apartment-houses-each-of-which-is-38-feet-wide-and-76-feet-long",{"id":272,"category":7,"text_question":273,"slug":274},534304,"2)A tourist has 15 pairs of pants in his hotel room closet. Suppose 5 are blue and the rest are black. The tourist leaves his room twice a day. He takes a pair of pants and puts them on, the tourist leaves the first pair of pants in the closet again and takes another one and puts them on. What is the probability that the two pants chosen are black?","2-a-tourist-has-15-pairs-of-pants-in-his-hotel-room-closet-suppose-5-are-blue-and-the-rest-are-black-the-tourist-leaves-his-room-twice-a-day-he-takes-a-pair-of-pants-and-puts-them-on-the-tourist-l",{"id":276,"category":7,"text_question":277,"slug":278},534322,"In a laboratory test, it was found that a certain culture of bacteria develops in a favorable environment, doubling its population every 2 hours. The test started with a population of 100 bacteria. After six hours, it is estimated that the number of bacteria will be:","in-a-laboratory-test-it-was-found-that-a-certain-culture-of-bacteria-develops-in-a-favorable-environment-doubling-its-population-every-2-hours-the-test-started-with-a-population-of-100-bacteria-af",{"id":280,"category":7,"text_question":281,"slug":282},534392,"a survey showed that 3 out of 7 voters would vote in an election. based on this survey, how many people would vote in a city with 25,000 people?","a-survey-showed-that-3-out-of-7-voters-would-vote-in-an-election-based-on-this-survey-how-many-people-would-vote-in-a-city-with-25-000-people",{"id":284,"category":7,"text_question":285,"slug":286},534400,"Write the equation of the line that is parallel to y= 4x-7 and has a y- intercept at (0,5)","write-the-equation-of-the-line-that-is-parallel-to-y-4x-7-and-has-a-y-intercept-at-0-5",{"id":288,"category":7,"text_question":289,"slug":290},534434,"Translate to an equation and solve. Let x be the unknown number: What number is 52% of 81.","translate-to-an-equation-and-solve-let-x-be-the-unknown-number-what-number-is-52-of-81",{"id":292,"category":7,"text_question":293,"slug":294},534576,"Solve the following system of equations using substitution.\ny=-4x- 11.\n3x+7y=-2","solve-the-following-system-of-equations-using-substitution-y-4x-11-3x-7y-2",{"id":296,"category":7,"text_question":297,"slug":298},534621,"5a-3.(a-7)=-3","5a-3-a-7-3",{"id":300,"category":7,"text_question":301,"slug":302},534632,"What is the set-off agreement? Make your own example, describe and put in T accounts how you record transactions.","what-is-the-set-off-agreement-make-your-own-example-describe-and-put-in-t-accounts-how-you-record-transactions",{"id":304,"category":7,"text_question":305,"slug":306},534643,"6(k-7) -2=5","6-k-7-2-5",{"id":308,"category":7,"text_question":309,"slug":310},534675,"23,456 + 3,451","23-456-3-451",{"data":312},{"questions":313},[314,318,322,326,330,334,338,342,346,350,354,358,362,366,370,374,378,382,386,390],{"id":315,"category":7,"text_question":316,"slug":317},532079,"The gross domestic product the gdp for the United States in 2017 was approximately$2.05x10^3. If you wrote this number in standard notation , it would be 205 followed by how many zeros","the-gross-domestic-product-the-gdp-for-the-united-states-in-2017-was-approximately-2-05x10-3-if-you-wrote-this-number-in-standard-notation-it-would-be-205-followed-by-how-many-zeros",{"id":319,"category":7,"text_question":320,"slug":321},533909,"Express the following numbers in decimal system,\n where the subscript indicates the base: 110101 $SUBINDEX=2$","express-the-following-numbers-in-decimal-system-where-the-subscript-indicates-the-base-110101-subindex-2",{"id":323,"category":7,"text_question":324,"slug":325},533927,"The graph of the equation x²= 4py is a parabola with focus F$_,_$ and directrix y=_____ Therefore, the graph of x²=12y is a parabola with focus F$_,_$ and a directrix y=_____","the-graph-of-the-equation-x-4py-is-a-parabola-with-focus-f-and-directrix-y-therefore-the-graph-of-x-12y-is-a-parabola-with-focus-f-and-a-directrix-y",{"id":327,"category":7,"text_question":328,"slug":329},533929,"Determine the equations of the recipes that pass through the following pairs of points\n P1 $2;-1$ and p2 $4;-1$","determine-the-equations-of-the-recipes-that-pass-through-the-following-pairs-of-points-p1-2-1-and-p2-4-1",{"id":331,"category":7,"text_question":332,"slug":333},533931,"Elliot opened a savings account and deposited $5000.00 as principal. The account earns 4% interest, compounded annually. How much interest will he earn after 5 years?\nRound your answer to the nearest cent.","elliot-opened-a-savings-account-and-deposited-5000-00-as-principal-the-account-earns-4-interest-compounded-annually-how-much-interest-will-he-earn-after-5-years-round-your-answer-to-the-nearest",{"id":335,"category":7,"text_question":336,"slug":337},534038,"What is the r.p.m. required to drill a 13/16\" hole in mild steel if the cutting speed is 100 feet per minute?","what-is-the-r-p-m-required-to-drill-a-13-16-hole-in-mild-steel-if-the-cutting-speed-is-100-feet-per-minute",{"id":339,"category":7,"text_question":340,"slug":341},534052,"-0.15/32.6","0-15-32-6",{"id":343,"category":7,"text_question":344,"slug":345},534083,"The sum of two numbers is equal to 58 and the largest exceeds by at least 12. Find the two numbers","the-sum-of-two-numbers-is-equal-to-58-and-the-largest-exceeds-by-at-least-12-find-the-two-numbers",{"id":347,"category":7,"text_question":348,"slug":349},534222,"A circular window has a rubber molding around the edge. If the window has a radius of 250 mm, how long is the piece of molding that is required ? (To the nearest mm)","a-circular-window-has-a-rubber-molding-around-the-edge-if-the-window-has-a-radius-of-250-mm-how-long-is-the-piece-of-molding-that-is-required-to-the-nearest-mm",{"id":351,"category":7,"text_question":352,"slug":353},534246,"How to do 15 x 3304","how-to-do-15-x-3304",{"id":355,"category":7,"text_question":356,"slug":357},534250,"You are the newly appointed transport manager for Super Trucking (Pty) Ltd, which operates as a logistics service provider for various industries throughout southern Africa. One of these vehicles is a 4x2 Rigid Truck and drawbar trailer that covers 48,000 km per year. Use the assumptions below to answer the following questions (show all calculations):\r\n\r\nOverheads\r\n\r\nR 176,200\r\n\r\nCost of capital (% of purchase price per annum)\r\n\r\n11.25%\r\n\r\nAnnual License Fees—Truck\r\n\r\nR 16,100\r\n\r\nDriver Monthly cost\r\n\r\nR 18,700\r\n\r\nAssistant Monthly cost\r\n\r\nR 10,500\r\n\r\nPurchase price: - Truck\r\n\r\nR 1,130,000\r\n\r\nDepreciation: straight line method\r\n\r\n \r\nTruck residual value\r\n\r\n25%\r\n\r\nTruck economic life (years)\r\n\r\n5\r\n\r\nPurchase price: Trailer\r\n\r\nR 370,000\r\n\r\nTyre usage and cost (c/km)\r\n\r\n127\r\n\r\nTrailer residual value\r\n\r\n0%\r\n\r\nTrailer economic life (years)\r\n\r\n10\r\n\r\nAnnual License Fees—Trailer\r\n\r\nR 7,700\r\n\r\nFuel consumption (liters/100km)\r\n\r\n22\r\n\r\nFuel price (c/liter)\r\n\r\n2053\r\n\r\nInsurance (% of cost price)\r\n\r\n7.5%\r\n\r\nMaintenance cost (c/km)\r\n\r\n105\r\n\r\nDistance travelled per year (km)\r\n\r\n48000\r\n\r\nTruck (tyres)\r\n\r\n6\r\n\r\nTrailer (tyres)\r\n\r\n8\r\n\r\nNew tyre price (each)\r\n\r\nR 13,400\r\n\r\nLubricants (% of fuel cost)\r\n\r\n2.5%\r\n\r\nWorking weeks\r\n\r\n50\r\n\r\nWorking days\r\n\r\n5 days / week\r\n\r\nProfit margin\r\n\r\n25%\r\n\r\nVAT\r\n\r\n15%\r\n\r\n\r\n\r\nQ1. Calculate the annual total vehicle costs (TVC)","you-are-the-newly-appointed-transport-manager-for-super-trucking-pty-ltd-which-operates-as-a-logistics-service-provider-for-various-industries-throughout-southern-africa-one-of-these-vehicles-is-a",{"id":359,"category":7,"text_question":360,"slug":361},534302,"The function h(t)=-5t^2+20t+60 models the height in meters of a ball t seconds after it’s thrown .\nWhich describe the intercepts and vertex of this function","the-function-h-t-5t-2-20t-60-models-the-height-in-meters-of-a-ball-t-seconds-after-it-s-thrown-which-describe-the-intercepts-and-vertex-of-this-function",{"id":363,"category":7,"text_question":364,"slug":365},534328,"What is 75 percent less than 60","what-is-75-percent-less-than-60",{"id":367,"category":7,"text_question":368,"slug":369},534342,"Congratulations, you have saved well and are ready to begin your retirement.\nIf you have$1,750,000.00 saved for your retirement and want it to last for 40 years, and will earn 10.8% compounded monthly:\nWhat is the amount of the monthly distribuion? 216.50\nHow much interest is earned in retirement?","congratulations-you-have-saved-well-and-are-ready-to-begin-your-retirement-if-you-have-1-750-000-00-saved-for-your-retirement-and-want-it-to-last-for-40-years-and-will-earn-10-8-compounded-monthl",{"id":371,"category":7,"text_question":372,"slug":373},534488,"7- A printing company found in its investigations that there were an average of 6 errors in 150-page prints. Based on this information, what is the probability of there being 48 errors in a 1200-page job?","7-a-printing-company-found-in-its-investigations-that-there-were-an-average-of-6-errors-in-150-page-prints-based-on-this-information-what-is-the-probability-of-there-being-48-errors-in-a-1200-page",{"id":375,"category":7,"text_question":376,"slug":377},534524,"x²-7x+12=0","x-7x-12-0",{"id":379,"category":7,"text_question":380,"slug":381},534530,"To verify that a 1 kg gold bar is actually made of pure gold, a dynamometer is used to record the weight of the bar submerged in water and out of water.\n\n a) What would be the value of the weight of the ingot recorded by the dynamometer out of the water?\n\n b) What magnitude of thrust does the ingot receive when it is submerged?\n\n c) What would the weight of the ingot have to be when it is submerged?\n\n Data\n Pagua = 1000 kg/m³\n Pagua= 19300 kg/m³","to-verify-that-a-1-kg-gold-bar-is-actually-made-of-pure-gold-a-dynamometer-is-used-to-record-the-weight-of-the-bar-submerged-in-water-and-out-of-water-a-what-would-be-the-value-of-the-weight-of-t",{"id":383,"category":7,"text_question":384,"slug":385},534626,"Let A denote the set of all people who were alive in 2010. Let B denote the set of all\nreal numbers. Let f assign, to each person in A, their weight during the year 2010.\nIs f a function? Explain in complete sentences.","let-a-denote-the-set-of-all-people-who-were-alive-in-2010-let-b-denote-the-set-of-all-real-numbers-let-f-assign-to-each-person-in-a-their-weight-during-the-year-2010-is-f-a-function-explain-in-c",{"id":387,"category":7,"text_question":388,"slug":389},534655,"An export company grants a bonus of $100,000 pesos to distribute among three of its best employees, so that the first receives double the second and the latter receives triple the third. How much did each person receive?","an-export-company-grants-a-bonus-of-100-000-pesos-to-distribute-among-three-of-its-best-employees-so-that-the-first-receives-double-the-second-and-the-latter-receives-triple-the-third-how-much-did",{"id":391,"category":7,"text_question":392,"slug":393},534696,"In a cheese factory, one pie costs 3800 denars. The fixed ones\ncosts are 1,200,000 denars, and variable costs are 2,500 denars per pie. To encounter:\na) income functions. profit and costs;\nb) the break-even point and profit and loss intervals.","in-a-cheese-factory-one-pie-costs-3800-denars-the-fixed-ones-costs-are-1-200-000-denars-and-variable-costs-are-2-500-denars-per-pie-to-encounter-a-income-functions-profit-and-costs-b-the-brea",{"data":395},[396,400,404],{"id":397,"question":398,"answer":399},101510,"What is the product of the complex numbers (2+3i) and (-4-5i)?","The product is (-7-22i).",{"id":401,"question":402,"answer":403},101813,"What is the product of 256 multiplied by 128?","The answer to 256 multiplied by 128 is 32,768.",{"id":405,"question":406,"answer":407},114144,"What is the sum of angles in an isosceles triangle if one angle measures 60 degrees?","The sum of angles in an isosceles triangle is always 180 degrees, so the other two angles would measure 60 degrees each.",{"$sicons":409},{"bxl:facebook-circle":410,"bxl:instagram":414,"mdi:web":416,"la:apple":418,"ph:google-logo-bold":421,"ph:google-logo":424},{"left":411,"top":411,"width":412,"height":412,"rotate":411,"vFlip":157,"hFlip":157,"body":413},0,24,"\u003Cpath fill=\"currentColor\" d=\"M12.001 2.002c-5.522 0-9.999 4.477-9.999 9.999c0 4.99 3.656 9.126 8.437 9.879v-6.988h-2.54v-2.891h2.54V9.798c0-2.508 1.493-3.891 3.776-3.891c1.094 0 2.24.195 2.24.195v2.459h-1.264c-1.24 0-1.628.772-1.628 1.563v1.875h2.771l-.443 2.891h-2.328v6.988C18.344 21.129 22 16.992 22 12.001c0-5.522-4.477-9.999-9.999-9.999\"/>",{"left":411,"top":411,"width":412,"height":412,"rotate":411,"vFlip":157,"hFlip":157,"body":415},"\u003Cpath fill=\"currentColor\" d=\"M11.999 7.377a4.623 4.623 0 1 0 0 9.248a4.623 4.623 0 0 0 0-9.248m0 7.627a3.004 3.004 0 1 1 0-6.008a3.004 3.004 0 0 1 0 6.008\"/>\u003Ccircle cx=\"16.806\" cy=\"7.207\" r=\"1.078\" fill=\"currentColor\"/>\u003Cpath fill=\"currentColor\" d=\"M20.533 6.111A4.6 4.6 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