^x+1 +1 describe transformation","","Solution:\u003Cbr />\n1. Given function:\u003Cbr />\n * \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = -24^{x+1} + 1\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Base function:\u003Cbr />\n * \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = 4^x\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Identify transformations step-by-step:\u003Cbr />\n - **Translation horizontally**: The function has \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x+1\u003C/math-field>\u003C/math-field> as the exponent instead of \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>. This indicates a horizontal shift to the left by 1 unit.\u003Cbr />\n - **Vertical stretch and reflection**: The coefficient before \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4\u003C/math-field>\u003C/math-field> is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-2\u003C/math-field>\u003C/math-field>.\u003Cbr />\n - **Vertical stretch**: The factor \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2\u003C/math-field>\u003C/math-field> indicates that the function is stretched vertically by a factor of \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2\u003C/math-field>\u003C/math-field>.\u003Cbr />\n - **Reflection**: The negative sign indicates a reflection across the x-axis.\u003Cbr />\n - **Vertical translation**: The \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>+1\u003C/math-field>\u003C/math-field> outside the function indicates a vertical shift upwards by 1 unit.\u003Cbr />\n\u003Cbr />\n4. Describe the complete transformation:\u003Cbr />\n - The function \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = 4^x\u003C/math-field>\u003C/math-field> undergoes the following transformations: a horizontal shift to the left by 1 unit, a vertical stretch by a factor of 2, reflection across the x-axis, and finally a vertical shift upwards by 1 unit.",1255,251,"y-2-4-x-1-1-describe-transformation",{"id":44,"category":36,"text_question":45,"photo_question":38,"text_answer":46,"step_text_answer":8,"step_photo_answer":8,"views":47,"likes":48,"slug":49},538086,"Add the polynomials gx=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>gx = 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>gx = 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>",739,148,"add-the-polynomials-g-x-x3-2x2-3x-1-4x2-x-2",{"id":51,"category":36,"text_question":52,"photo_question":38,"text_answer":53,"step_text_answer":8,"step_photo_answer":8,"views":54,"likes":55,"slug":56},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":58,"category":36,"text_question":59,"photo_question":38,"text_answer":60,"step_text_answer":8,"step_photo_answer":8,"views":61,"likes":62,"slug":63},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":65,"category":36,"text_question":66,"photo_question":38,"text_answer":67,"step_text_answer":8,"step_photo_answer":8,"views":68,"likes":69,"slug":70},538083,"Calculate the volume tothenearesttenthofacubiccentimeter 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":72,"category":36,"text_question":73,"photo_question":38,"text_answer":74,"step_text_answer":8,"step_photo_answer":8,"views":75,"likes":76,"slug":77},538082,"Find the length of each base edge tothenearesttenthofameter 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":79,"category":36,"text_question":80,"photo_question":38,"text_answer":81,"step_text_answer":8,"step_photo_answer":8,"views":82,"likes":83,"slug":84},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>\\tantheta = \\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>\\tan40circ = \\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 \\tan40circ\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>\\tan40circ \\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":86,"category":36,"text_question":87,"photo_question":38,"text_answer":88,"step_text_answer":8,"step_photo_answer":8,"views":89,"likes":90,"slug":91},538080,"A plane ticket has gone up 18%, now costing 4,720.Howmuchdiditcostbeforetheincrease?","\u003Cmath−fieldread−onlydefault−mode=\"inline−math\"class=\"math−expression\">\u003Cmath−fieldread−only>textSolution:\u003C/math−field>\u003C/math−field>\u003Cbr/>\n1.Definevariables:\u003Cbr/>\n−Let\u003Cmath−fieldread−onlydefault−mode=\"inline−math\"class=\"math−expression\">\u003Cmath−fieldread−only>P\u003C/math−field>\u003C/math−field>betheoriginalpriceoftheplaneticket.\u003Cbr/>\n−\u003Cmath−fieldread−onlydefault−mode=\"inline−math\"class=\"math−expression\">\u003Cmath−fieldread−only>P\u003C/math−field>\u003C/math−field>increasedby18\\frac{x}{15}=\\frac{4}{3}\u003C/math−field>\n\u003Cbr>\n\u003C/div>\n\n\u003Cdiv>\n\n\u003Cmath−fieldstyle=\"font−size:16px;padding:8px;border−radius:8px;border:1pxsolidrgba(0,0,0,.3);box−shadow:000rgba(0,0,0,.2)\n\"read−only>x=20\u003C/math-field>\n \u003Cbr>\n \u003C/div>",467,93,"15-75-of",{"id":149,"category":36,"text_question":150,"photo_question":38,"text_answer":151,"step_text_answer":8,"step_photo_answer":8,"views":152,"likes":90,"slug":153},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":155,"category":36,"text_question":156,"photo_question":38,"text_answer":157,"step_text_answer":8,"step_photo_answer":8,"views":158,"likes":76,"slug":159},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":161,"category":36,"text_question":162,"photo_question":38,"text_answer":163,"step_text_answer":8,"step_photo_answer":8,"views":164,"likes":165,"slug":166},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":168,"category":36,"text_question":169,"photo_question":38,"text_answer":170,"step_text_answer":8,"step_photo_answer":8,"views":171,"likes":172,"slug":173},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",{"first":6,"last":175,"prev":8,"next":10},187,{"current_page":6,"from":6,"last_page":175,"links":177,"path":211,"per_page":212,"to":212,"total":213},[178,181,184,186,188,190,192,195,198,201,204,207,209],{"url":6,"label":179,"active":180},"1",true,{"url":10,"label":182,"active":183},"2",false,{"url":13,"label":185,"active":183},"3",{"url":16,"label":187,"active":183},"4",{"url":19,"label":189,"active":183},"5",{"url":22,"label":191,"active":183},"6",{"url":193,"label":194,"active":183},7,"7",{"url":196,"label":197,"active":183},8,"8",{"url":199,"label":200,"active":183},9,"9",{"url":202,"label":203,"active":183},10,"10",{"url":205,"label":206,"active":183},186,"186",{"url":175,"label":208,"active":183},"187",{"url":10,"label":210,"active":183},"Next »","https://api.math-master.org/api/question",20,3737,{"data":215},{"questions":216},[217,221,225,229,233,237,241,245,249,253,257,261,265,269,273,277,281,285,289,293],{"id":218,"category":36,"text_question":219,"slug":220},532033,"𝑦 = ( 𝑥2 − 3) (𝑥3 + 2 𝑥 + 1)","y-x2-3-x3-2-x-1",{"id":222,"category":36,"text_question":223,"slug":224},532055,"A college believes that 22% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 5 percentage points?","a-college-believes-that-22-of-applicants-to-that-school-have-parents-who-have-remarried-how-large-a-sample-is-needed-to-estimate-the-true-proportion-of-students-who-have-parents-who-have-remarried-t",{"id":226,"category":36,"text_question":227,"slug":228},532308,"90 divided by 40","90-divided-by-40",{"id":230,"category":36,"text_question":231,"slug":232},533948,"Derivative of x squared","derivative-of-x-squared",{"id":234,"category":36,"text_question":235,"slug":236},533991,"An integer is taken at random from the first 40 positive integers. What is the probability that the integer is divisible by 5 or 6?","an-integer-is-taken-at-random-from-the-first-40-positive-integers-what-is-the-probability-that-the-integer-is-divisible-by-5-or-6",{"id":238,"category":36,"text_question":239,"slug":240},534009,"Suppose SAT reading scores are normally distributed with a mean of 496 and a standard deviation of 109. The University plans towards scholarships for students who scores are in the top 7%. What is the minimum score required for the scholarship round your answer to the nearest whole number.","suppose-sat-reading-scores-are-normally-distributed-with-a-mean-of-496-and-a-standard-deviation-of-109-the-university-plans-towards-scholarships-for-students-who-scores-are-in-the-top-7-what-is-the",{"id":242,"category":36,"text_question":243,"slug":244},534105,"A pair of die is thrown and the absolute difference of the two scores is recorded. What is the probability of the absolute difference being 4 or more?","a-pair-of-die-is-thrown-and-the-absolute-difference-of-the-two-scores-is-recorded-what-is-the-probability-of-the-absolute-difference-being-4-or-more",{"id":246,"category":36,"text_question":247,"slug":248},534106,"Find the equation of the line perpendicular to −5𝑥−3𝑦+5=0 passing through the point (0,−2)","find-the-equation-of-the-line-perpendicular-to-5x-3y-5-0-passing-through-the-point-0-2",{"id":250,"category":36,"text_question":251,"slug":252},534110,"-3(-4x+5)=-6(7x-8)+9-10x","3-4x-5-6-7x-8-9-10x",{"id":254,"category":36,"text_question":255,"slug":256},534137,"Emma is on a 50 m high bridge and sees two boats anchored below. From her position, boat A has a bearing of 230° and boat B has a bearing of 120°. Emma estimates the angles of depression to be about 38° for boat A and 35° for boat B. How far apart are the boats to the nearest meter?","emma-is-on-a-50-m-high-bridge-and-sees-two-boats-anchored-below-from-her-position-boat-a-has-a-bearing-of-230-and-boat-b-has-a-bearing-of-120-emma-estimates-the-angles-of-depression-to-be-about-3",{"id":258,"category":36,"text_question":259,"slug":260},534194,"form a key for your lock containing the numbers 2 2 5 8 How many different keys can you form?","form-a-key-for-your-lock-containing-the-numbers-2-2-5-8-how-many-different-keys-can-you-form",{"id":262,"category":36,"text_question":263,"slug":264},534266,"0.1x8.2","0-1x8-2",{"id":266,"category":36,"text_question":267,"slug":268},534298,"30y - y . y = 144","30y-y-y-144",{"id":270,"category":36,"text_question":271,"slug":272},534340,"A bag has 4 green lollipops, 3 white lollipops, and 1 black lollipop. What is the probability of drawing a white lollipop?","a-bag-has-4-green-lollipops-3-white-lollipops-and-1-black-lollipop-what-is-the-probability-of-drawing-a-white-lollipop",{"id":274,"category":36,"text_question":275,"slug":276},534441,"A buyer purchased a North Carolina home for475,250. The seller allowed the buyer to assume his first small mortgage with a loan balance of 110,000.Howmuchistheexcisetaxpaidinthetransaction?\n951\n729.50\n950.50\n221\nnoneoftheabove","a−buyer−purchased−a−north−carolina−home−for−475−250−the−seller−allowed−the−buyer−to−assume−his−first−small−mortgage−with−a−loan−balance−of−110−000−how−much−is−the−excise−tax−paid−in−the−transactio","id":278,"category":36,"textquestion":279,"slug":280,534531,"Theaverageweeklyearningsintheleisureandhospitalityindustrygroupforare‐\r\ncentyearwas273. A random sample of 40 workers showed weekly average ear‐\r\nnings of 285withthepopulationstandarddeviationequalto58.Atthe0.05levelof\r\nsignificancecanitbeconcludedthatthemeandiffersfrom273? Find a 95% con‐\r\nfidence interval for the weekly earnings and show that it supports the results of the\r\nhypothesis test.","the-average-weekly-earnings-in-the-leisure-and-hospitality-industry-group-for-a-re-cent-year-was-273-a-random-sample-of-40-workers-showed-weekly-average-ear-nings-of-285-with-the-population-sta",{"id":282,"category":36,"text_question":283,"slug":284},534537,"2 - 6x = -16x + 28","2-6x-16x-28",{"id":286,"category":36,"text_question":287,"slug":288},534575,"A nondegenerate ideal gas of diatomic molecules with a kilomolar mass of 2 kg/kmol and a characteristic rotational temperature of 86 K is adsorbed on the walls of a container, where the binding energy is 0.02 eV. The adsorbed molecules move freely on the walls, and their rotation is confined to the plane of the walls. Calculate the surface density of adsorbed molecules at 12 K if the gas pressure is 103 Pa! What result would you get at 68 K and the same pressure?","a-nondegenerate-ideal-gas-of-diatomic-molecules-with-a-kilomolar-mass-of-2-kg-kmol-and-a-characteristic-rotational-temperature-of-86-k-is-adsorbed-on-the-walls-of-a-container-where-the-binding-energy",{"id":290,"category":36,"text_question":291,"slug":292},534580,"4m - 3t + 7 = 16","4m-3t-7-16",{"id":294,"category":36,"text_question":295,"slug":296},534652,"A small box measures 10 in. by 4 in. by 6 in. high. Find the volume of the box.","a-small-box-measures-10-in-by-4-in-by-6-in-high-find-the-volume-of-the-box",{"data":298},{"id":299,"category":36,"slug":300,"text_question":301,"photo_question":8,"text_answer":302,"step_text_answer":8,"step_photo_answer":8,"views":303,"likes":104,"expert":304},537533,"f-x-y-3x2-4y2-find-the-directional-derivative-at-the-point-1-1-in-the-direction-of-the-vector-u-3-4","fx,y=3x2−4y2 . Find the directional derivative at the point 1,−1 in the direction of the vector u=3,4","**\u003Cbr />\n\u003Cbr />\n1. **Normalización de \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\mathbf{u}\u003C/math-field>\u003C/math-field>**: \u003Cbr />\n El vector \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\mathbf{u} = 3,4\u003C/math-field>\u003C/math-field> se normaliza de la siguiente forma:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\|\\mathbf{u}\\| = \\sqrt{3^2 + 4^2} = \\sqrt{9 + 16} = \\sqrt{25} = 5\u003C/math-field>\u003C/math-field> \u003Cbr />\n Entonces, el vector unitario es: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\mathbf{\\hat{u}} = \\leftfrac35,frac45right\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n2. **Cálculo del gradiente \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\nabla f\u003C/math-field>\u003C/math-field>**: \u003Cbr />\n - Derivada parcial respecto a \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>\\frac{\\partial f}{\\partial x} = \\frac{\\partial}{\\partial x}3x2−4y2 = 6x\u003C/math-field>\u003C/math-field> \u003Cbr />\n - Derivada parcial respecto a \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y\u003C/math-field>\u003C/math-field>: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{\\partial f}{\\partial y} = \\frac{\\partial}{\\partial y}3x2−4y2 = -8y\u003C/math-field>\u003C/math-field> \u003Cbr />\n Entonces, \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\nabla fx,y = 6x,−8y\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n3. **Evaluación del gradiente en el punto \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1,−1\u003C/math-field>\u003C/math-field>**: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\nabla f1,−1 = 6cdot1,−8cdot(−1) = 6,8\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\n4. **Cálculo de la derivada direccional**: \u003Cbr />\n La derivada direccional en la dirección de \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\mathbf{\\hat{u}}\u003C/math-field>\u003C/math-field> es el producto escalar: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>D_{\\mathbf{\\hat{u}}}f1,−1 = \\nabla f1,−1 \\cdot \\mathbf{\\hat{u}} = 6,8 \\cdot \\leftfrac35,frac45right\u003C/math-field>\u003C/math-field> \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= 6 \\cdot \\frac{3}{5} + 8 \\cdot \\frac{4}{5}\u003C/math-field>\u003C/math-field> \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= \\frac{18}{5} + \\frac{32}{5}\u003C/math-field>\u003C/math-field> \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>= \\frac{50}{5} = 10\u003C/math-field>\u003C/math-field> \u003Cbr />\n\u003Cbr />\nLa derivada direccional es \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>10\u003C/math-field>\u003C/math-field>.",1236,{"id":305,"name":306,"photo":307,"biography":308,"created_at":8,"updated_at":8,"rating":309,"total_answer":310},15,"Miles","https://api.math-master.org/img/experts/15/15.webp","My name is Ali Haider and I hold a bachelor’s degree in Electrical Engineering and I am also certified Math Expert. I have been teaching Mathematics and Physics for the past 6 years at both the high school and college level. My pass rate for Mathematics is 100%.\nIn addition to teaching, I love playing badminton and video games.\n",4.9,108,{"data":312},{"questions":313},[314,318,322,323,327,331,335,339,343,347,351,355,359,363,367,371,375,379,383,387],{"id":315,"category":36,"text_question":316,"slug":317},532022,"Solution to the equation y'' - y' - 6y = 0","solution-to-the-equation-y-39-39-y-39-6y-0",{"id":319,"category":36,"text_question":320,"slug":321},532042,"The patient is prescribed a course of 30 tablets.\nThe tablets are prescribed “1 tablet twice a day”.\nHow many days does a course of medication last?","the-patient-is-prescribed-a-course-of-30-tablets-the-tablets-are-prescribed-1-tablet-twice-a-day-how-many-days-does-a-course-of-medication-last",{"id":230,"category":36,"text_question":231,"slug":232},{"id":324,"category":36,"text_question":325,"slug":326},533949,"Consider numbers from 1 to 2023. We delete 3 consecutive numbers so, that the avarage of the left numbers is a whole number","consider-numbers-from-1-to-2023-we-delete-3-consecutive-numbers-so-that-the-avarage-of-the-left-numbers-is-a-whole-number",{"id":328,"category":36,"text_question":329,"slug":330},534007,"A soft drink machine outputs a mean of 23 ounces per cup. The machines output is normally distributed with a standard deviation of 3 ounces. What is the probability of filling a cup between 26 and 28 ounces round your answer to four decimal places","a-soft-drink-machine-outputs-a-mean-of-23-ounces-per-cup-the-machines-output-is-normally-distributed-with-a-standard-deviation-of-3-ounces-what-is-the-probability-of-filling-a-cup-between-26-and-28",{"id":332,"category":36,"text_question":333,"slug":334},534041,"You are planning to buy a car worth 20,000.Whichofthetwodealsdescribedbelowwouldyouchoose,bothwitha48−monthterm?(NB:estimatethemonthlypaymentofeachoffer).i)thedealerofferstotake1020,000 i.e.,nodiscount at an APR of 3%, monthly compounding.","you-are-planning-to-buy-a-car-worth-20-000-which-of-the-two-deals-described-below-would-you-choose-both-with-a-48-month-term-nb-estimate-the-monthly-payment-of-each-offer-i-the-dealer-offers",{"id":336,"category":36,"text_question":337,"slug":338},534046,"Sean must chose a 6- digit PIN number for his online banking account.Each digit can be chosen from 0 to 9. How many different possible PIN numbers can sean chose.","sean-must-chose-a-6-digit-pin-number-for-his-online-banking-account-each-digit-can-be-chosen-from-0-to-9-how-many-different-possible-pin-numbers-can-sean-chose",{"id":340,"category":36,"text_question":341,"slug":342},534247,"Estimate the quotient for 3.24 ÷ 82","estimate-the-quotient-for-3-24-82",{"id":344,"category":36,"text_question":345,"slug":346},534300,"4+168×10³×d1+36×10³×d2=-12\n-10+36×10³×d1+72×10³×d2=0","4-168-10-d1-36-10-d2-12-10-36-10-d1-72-10-d2-0",{"id":348,"category":36,"text_question":349,"slug":350},534308,"3+7","3-7",{"id":352,"category":36,"text_question":353,"slug":354},534331,"9.25=2pi r solve for r","9-25-2pi-r-solve-for-r",{"id":356,"category":36,"text_question":357,"slug":358},534390,"Derivative of 2x","derivative-of-2x",{"id":360,"category":36,"text_question":361,"slug":362},534429,"How to factorise 5y^2 -7y -52","how-to-factorise-5y-2-7y-52",{"id":364,"category":36,"text_question":365,"slug":366},534487,"Consider mixing 150 ml, 0.1M, HCI with 100 ml, 0.2M, KOH solution.\nDetermine the pH of final solution.","consider-mixing-150-ml-0-1m-hci-with-100-ml-0-2m-koh-solution-determine-the-ph-of-final-solution",{"id":368,"category":36,"text_question":369,"slug":370},534589,"Select a variable and collect at least 50 data values. For example, you may ask the students in the college how many hours they study per week or how old they are, etc.\na. Explain what your target population was.\nb. State how the sample was selected.\nc. Summarise the data by using a frequency table.\nd. Calculate all the descriptive measures for the data and describe the data\nset using the measures.\ne. Present the data in an appropriate way.\nf. Write a paragraph summarizing the data.","select-a-variable-and-collect-at-least-50-data-values-for-example-you-may-ask-the-students-in-the-college-how-many-hours-they-study-per-week-or-how-old-they-are-etc-a-explain-what-your-target-pop",{"id":372,"category":36,"text_question":373,"slug":374},534649,"Hola👋🏻\r\n\r\nToca en \"Crear Nueva Tarea\" para enviar tu problema de matemáticas.\r\n\r\n¡Uno de nuestros expertos comenzará a trabajar en ello de inmediato!","hola-toca-en-crear-nueva-tarea-para-enviar-tu-problema-de-matematicas-uno-de-nuestros-expertos-comenzara-a-trabajar-en-ello-de-inmediato",{"id":376,"category":36,"text_question":377,"slug":378},534650,"A rectangular swimming pool has a length of 14 feet, a width of 26 feet and a depth of 5 feet. Round answers to the nearest hundredth as needed.\n\n\na How many cubic feet of water can the pool hold?\n cubic feet\nb The manufacturer suggests filling the pool to 95% capacity. How many cubic feet of water is this?\n cubic feet","a-rectangular-swimming-pool-has-a-length-of-14-feet-a-width-of-26-feet-and-a-depth-of-5-feet-round-answers-to-the-nearest-hundredth-as-needed-a-how-many-cubic-feet-of-water-can-the-pool-hold",{"id":380,"category":36,"text_question":381,"slug":382},534669,"The company produces a product with a variable cost of 90perunit.Withfixedcostsof150,000 and a selling price of 1,200peritem,howmanyunitsmustbesoldtoachieveaprofitof400,000?","the-company-produces-a-product-with-a-variable-cost-of-90-per-unit-with-fixed-costs-of-150-000-and-a-selling-price-of-1-200-per-item-how-many-units-must-be-sold-to-achieve-a-profit-of-400-000",{"id":384,"category":36,"text_question":385,"slug":386},534686,"To apply a diagnostic test, in how many ways can 14 students be chosen out of 25? if the order does not matter","to-apply-a-diagnostic-test-in-how-many-ways-can-14-students-be-chosen-out-of-25-if-the-order-does-not-matter",{"id":388,"category":36,"text_question":389,"slug":390},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":392},[393,397,401],{"id":394,"question":395,"answer":396},141352,"What is the period and asymmetry of the cotangent function fx = cotx?","The cotangent function has a period of π and no asymmetry; it is symmetric about the y-axis. It repeats its values every π units. The graph of fx = cotx approaches vertical asymptotes at x = nπ, where n is an integer. The range of this function is all real numbers except for 0.",{"id":398,"question":399,"answer":400},138043,"What is the radian measure of a central angle that subtends an arc of length 5 units in a circle of radius 2 units?","To find the radian measure, divide the arc length 5 by the radius 2, obtaining 2.5 radians. The radian measure is 2.5.",{"id":402,"question":403,"answer":404},150413,"What is the value of sin^−11 + cos^−10 - tan^−11 + cot^−1√3 when applied to an angle in the first quadrant?","The value of the given expression is π/2 radians or90degrees. In the first quadrant, sin^−11 is equal to π/2 radians, cos^−10 equals π/2 radians, tan^−11 is π/4 radians, and cot^−1√3 equals π/3 radians. 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