Loading [MathJax]/jax/output/HTML-CSS/fonts/TeX/fontdata.js
=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":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},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":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},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":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},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":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},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":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},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 40Β° 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 elevaciΓ³n: \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 funciΓ³n 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 aerostΓ‘tico. La tangente de un Γ‘ngulo en un triΓ‘ngulo rectΓ‘ngulo es la razΓ³n 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 ecuaciΓ³n:\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 numΓ©rico:\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 aerostΓ‘tico 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":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},538080,"A plane ticket has gone up 18%, now costing 4,720.Howmuchdiditcostbeforetheincrease?","\u003Cmathβˆ’fieldreadβˆ’onlydefaultβˆ’mode=\"inlineβˆ’math\"class=\"mathβˆ’expression\">\u003Cmathβˆ’fieldreadβˆ’only>textSolution:\u003C/mathβˆ’field>\u003C/mathβˆ’field>\u003Cbr/>\n1.Definevariables:\u003Cbr/>\nβˆ’Let\u003Cmathβˆ’fieldreadβˆ’onlydefaultβˆ’mode=\"inlineβˆ’math\"class=\"mathβˆ’expression\">\u003Cmathβˆ’fieldreadβˆ’only>P\u003C/mathβˆ’field>\u003C/mathβˆ’field>betheoriginalpriceoftheplaneticket.\u003Cbr/>\nβˆ’\u003Cmathβˆ’fieldreadβˆ’onlydefaultβˆ’mode=\"inlineβˆ’math\"class=\"mathβˆ’expression\">\u003Cmathβˆ’fieldreadβˆ’only>P\u003C/mathβˆ’field>\u003C/mathβˆ’field>increasedby18\\frac{x}{15}=\\frac{4}{3}\u003C/mathβˆ’field>\n\u003Cbr>\n\u003C/div>\n\n\u003Cdiv>\n\n\u003Cmathβˆ’fieldstyle=\"fontβˆ’size:16px;padding:8px;borderβˆ’radius:8px;border:1pxsolidrgba(0,0,0,.3);boxβˆ’shadow:000rgba(0,0,0,.2)\n\"readβˆ’only>x=20\u003C/math-field>\n    \u003Cbr>\n  \u003C/div>",467,93,"15-75-of",{"id":142,"category":36,"text_question":143,"photo_question":38,"text_answer":144,"step_text_answer":8,"step_photo_answer":8,"views":145,"likes":83,"slug":146},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 β‚±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":148,"category":36,"text_question":149,"photo_question":38,"text_answer":150,"step_text_answer":8,"step_photo_answer":8,"views":151,"likes":69,"slug":152},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":154,"category":36,"text_question":155,"photo_question":38,"text_answer":156,"step_text_answer":8,"step_photo_answer":8,"views":157,"likes":158,"slug":159},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":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},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":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},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":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",20,3736,{"data":215},{"id":216,"category":36,"slug":217,"text_question":218,"photo_question":8,"text_answer":219,"step_text_answer":8,"step_photo_answer":8,"views":220,"likes":221,"expert":222},537917,"if-30-of-the-students-in-a-class-made-a-b-and-there-were-12-bs-how-many-students-were-in-the-class","If 30% of the students in a class made a B and there were 12 Bs how many students were in the class?","1. Let the total number of students in the class be denoted by \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>.\u003Cbr />\n2. According to the problem, 30% of the students made a B, and this equals 12 students.\u003Cbr />\n3. Set up the equation:\u003Cbr />\n\u003Cbr />\n   \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.30 \\times x = 12\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. To find \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x\u003C/math-field>\u003C/math-field>, divide both sides of the equation by 0.30:\u003Cbr />\n\u003Cbr />\n   \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = \\frac{12}{0.30}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Simplify the right side:\u003Cbr />\n\u003Cbr />\n   \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = \\frac{12}{0.30} = 40\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Therefore, the total number of students in the class is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\boxed{40} \u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\nAnswer: 40 students.",962,192,{"id":223,"name":224,"photo":225,"biography":226,"created_at":8,"updated_at":8,"rating":227,"total_answer":228},21,"Jon","https://api.math-master.org/img/experts/21/21.webp","I passed my matric from Govt.City Muslim school Faisalabad and got first division in school by getting 981/1000 marks.\nAfter matric i got admission in Shiblee Colege Faisalabad and got 883/1100 marks in degree of inter with Math.\nNow currently i'm student of BS Math and running my last semester.",4.6,107,{"data":230},{"questions":231},[232,236,240,244,248,252,256,260,264,268,272,276,280,284,288,292,296,300,304,308],{"id":233,"category":36,"text_question":234,"slug":235},532034,"-442/c+5=26 what is c?","442-c-5-26-what-is-c",{"id":237,"category":36,"text_question":238,"slug":239},532052,"-6n+5=-13","6n-5-13",{"id":241,"category":36,"text_question":242,"slug":243},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":245,"category":36,"text_question":246,"slug":247},532064,"12-6x=4x+2","12-6x-4x-2",{"id":249,"category":36,"text_question":250,"slug":251},534103,"Convert 78 percent to a decimal","convert-78-percent-to-a-decimal",{"id":253,"category":36,"text_question":254,"slug":255},534106,"Find the equation of the line perpendicular to βˆ’5π‘₯βˆ’3𝑦+5=0 passing through the point (0,βˆ’2)","find-the-equation-of-the-line-perpendicular-to-5x-3y-5-0-passing-through-the-point-0-2",{"id":257,"category":36,"text_question":258,"slug":259},534114,"How many anagrams of the word STROMEC there that do not contain STROM, MOST, MOC or CEST as a subword?\nBy subword is meant anything that is created by omitting some letters - for example, the word EMROSCT contains both MOC and MOST as subwords.","how-many-anagrams-of-the-word-stromec-there-that-do-not-contain-strom-most-moc-or-cest-as-a-subword-by-subword-is-meant-anything-that-is-created-by-omitting-some-letters-for-example-the-word-emr",{"id":261,"category":36,"text_question":262,"slug":263},534115,"How many anagrams of the word SROMEC there that do not contain STROM, MOST, MOC or CEST as a subword?\r\nBy subword is meant anything that is created by omitting some letters - for example, the word EMROSCT contains both MOC and MOST as subwords.","how-many-anagrams-of-the-word-sromec-there-that-do-not-contain-strom-most-moc-or-cest-as-a-subword-by-subword-is-meant-anything-that-is-created-by-omitting-some-letters-for-example-the-word-emr",{"id":265,"category":36,"text_question":266,"slug":267},534200,"suppose random variable x follows poisson distribution with expected value 3. what is variance of x?","suppose-random-variable-x-follows-poisson-distribution-with-expected-value-3-what-is-variance-of-x",{"id":269,"category":36,"text_question":270,"slug":271},534216,"It is known that the content of milk that is actually in a bag distributes normally with\n an average of 900 grams and variance 25 square grams. Suppose that the cost in pesos of a bag of milk is given by\n πΆ(π‘₯) = {\n 3800 π‘ π‘– π‘₯ β‰€ 890\n 4500 π‘ π‘– π‘₯ > 890\n Find the expected cost.","it-is-known-that-the-content-of-milk-that-is-actually-in-a-bag-distributes-normally-with-an-average-of-900-grams-and-variance-25-square-grams-suppose-that-the-cost-in-pesos-of-a-bag-of-milk-is-given",{"id":273,"category":36,"text_question":274,"slug":275},534231,"89, Γ· 10","89-10",{"id":277,"category":36,"text_question":278,"slug":279},534253,"If X1 and X2 are independent standard normal variables, find P(X1^2 + X2^2 > 2.41)","if-x1-and-x2-are-independent-standard-normal-variables-find-p-x1-2-x2-2-2-41",{"id":281,"category":36,"text_question":282,"slug":283},534254,"Convert 9/13 to a percent","convert-9-13-to-a-percent",{"id":285,"category":36,"text_question":286,"slug":287},534396,"Give an example of a function defined in R that is continuous in\n all points, except in the set Z of integers.","give-an-example-of-a-function-defined-in-r-that-is-continuous-in-all-points-except-in-the-set-z-of-integers",{"id":289,"category":36,"text_question":290,"slug":291},534407,"How to convert 45 kg into grams","how-to-convert-45-kg-into-grams",{"id":293,"category":36,"text_question":294,"slug":295},534428,"Two particles of electrical charges Q1=3.8Γ—10-⁢C and q,=4.4Γ—10-⁢C are separated in vacuum by a distance of 4.0.10-⁸ m. Since K=9.0.10⁹ N.mΒ²/CΒ², the intensity of the interaction force between them, in newtons, is?","two-particles-of-electrical-charges-q1-3-8-10-c-and-q-4-4-10-c-are-separated-in-vacuum-by-a-distance-of-4-0-10-m-since-k-9-0-10-n-m-c-the-intensity-of-the-interaction-force-between-them-in",{"id":297,"category":36,"text_question":298,"slug":299},534562,"Solve the following \n9x - 9 - 6x = 5 + 8x - 9","solve-the-following-9x-9-6x-5-8x-9",{"id":301,"category":36,"text_question":302,"slug":303},534563,"How much does 7.2 moles of ammonium dichromate weigh? (NH4)2Cr2O7","how-much-does-7-2-moles-of-ammonium-dichromate-weigh-nh4-2cr2o7",{"id":305,"category":36,"text_question":306,"slug":307},534571,"A group of 17 people spent 9 days on vacation and spent R776.34 on barbecue meat and the bill needs to be divided as follows: 6 people stayed for 9 days, 7 people stayed for 4 days, and 2 people stayed for 5 days and 2 people stayed 3 days, how much does each group have to pay for the days they stayed?","a-group-of-17-people-spent-9-days-on-vacation-and-spent-r-776-34-on-barbecue-meat-and-the-bill-needs-to-be-divided-as-follows-6-people-stayed-for-9-days-7-people-stayed-for-4-days-and-2-people-stay",{"id":309,"category":36,"text_question":310,"slug":311},534661,"Dano forgot his computer password. The password was four characters long. Dano remembered only three characters: 3, g, N. The last character was one of the numbers 3, 5, 7, 9. How many possible expansions are there for Dano's password?","dano-forgot-his-computer-password-the-password-was-four-characters-long-dano-remembered-only-three-characters-3-g-n-the-last-character-was-one-of-the-numbers-3-5-7-9-how-many-possible-expans",{"data":313},{"questions":314},[315,319,323,327,331,335,339,343,347,351,355,359,363,367,371,375,379,383,387,391],{"id":316,"category":36,"text_question":317,"slug":318},532029,"reduction method 2x-y=13 x+y=-1","reduction-method-2x-y-13-x-y-1",{"id":320,"category":36,"text_question":321,"slug":322},532053,"Y=-x^2-8x-15 X=-7","y-x-2-8x-15-x-7",{"id":324,"category":36,"text_question":325,"slug":326},532071,"A normally distributed population has a mean of 118 with a standard deviation of 18. What score separates the lowest 72% of the distribution from the rest of the scores?","a-normally-distributed-population-has-a-mean-of-118-with-a-standard-deviation-of-18-what-score-separates-the-lowest-72-of-the-distribution-from-the-rest-of-the-scores",{"id":328,"category":36,"text_question":329,"slug":330},532090,"String x = 5\r\nInt y=2\r\nSystem.out.printlnx+y","string-x-5-int-y-2-system-out-println-x-y",{"id":332,"category":36,"text_question":333,"slug":334},533965,"In a store there are packets of chocolate, strawberry, tutti-frutti, lemon, grape and banana sweets. If a person needs to choose 4 flavors of candy from those available, how many ways can they make that choice?","in-a-store-there-are-packets-of-chocolate-strawberry-tutti-frutti-lemon-grape-and-banana-sweets-if-a-person-needs-to-choose-4-flavors-of-candy-from-those-available-how-many-ways-can-they-make-th",{"id":336,"category":36,"text_question":337,"slug":338},533996,"Suppose 56% of politicians are lawyers if a random sample of size 873 is selected, what is the probability that the proportion of politicians who are lawyers will be less than 55% round your answer to four decimal places","suppose-56-of-politicians-are-lawyers-if-a-random-sample-of-size-873-is-selected-what-is-the-probability-that-the-proportion-of-politicians-who-are-lawyers-will-be-less-than-55-round-your-answer-to",{"id":340,"category":36,"text_question":341,"slug":342},533999,"2x-4y=-6; -4y+4y=-8","2x-4y-6-4y-4y-8",{"id":344,"category":36,"text_question":345,"slug":346},534076,"4. Show that if n is any integer, then n^2 3n 5 is an odd integer","4-show-that-if-n-is-any-integer-then-n-2-3n-5-is-an-odd-integer",{"id":348,"category":36,"text_question":349,"slug":350},534132,"123+7-5","12-3-7-5",{"id":352,"category":36,"text_question":353,"slug":354},534191,"6-35 A recent study by an environmental watchdog determined that the amount of contaminants\n in Minnesota lakes inpartspermillion it has a normal distribution with a mean of 64 ppm and variance of 17.6. Assume that 35 lakes are randomly selected and sampled. Find the probability that the sample average of the amount of contaminants is\n a) Greater than 72 ppm.\n b) Between 64 and 72 ppm.\n c) Exactly 64 ppm.\n d) Greater than 94 ppm.","6-35-a-recent-study-by-an-environmental-watchdog-determined-that-the-amount-of-contaminants-in-minnesota-lakes-in-parts-per-million-it-has-a-normal-distribution-with-a-mean-of-64-ppm-and-variance-o",{"id":356,"category":36,"text_question":357,"slug":358},534258,"Shows two blocks, masses 4.3 kg and 5.4 kg, being pushed across a frictionless surface by a 22.5-N horizontal force applied to the 4.3-kg block.\nA. What is the acceleration of the blocks?\nB. What is the force of the 4.3-kg block on the 5.4 -kg block?\nC. What is the force of the 5.4 -kg block on the 4.3 -kg block?","shows-two-blocks-masses-4-3-kg-and-5-4-kg-being-pushed-across-a-frictionless-surface-by-a-22-5-n-horizontal-force-applied-to-the-4-3-kg-block-a-what-is-the-acceleration-of-the-blocks-b-what-is-t",{"id":360,"category":36,"text_question":361,"slug":362},534352,"You want to study incomes in a large city. You take a simple random sample of 5012 \r\nhouseholds and find that the distribution of household incomes is skewed right. \r\n\nIf you calculate the mean of the 5012 household incomes will the distribution of \r\nmean scores be skewed right as well? Hint: this involves the Central Limit Theorem.","you-want-to-study-incomes-in-a-large-city-you-take-a-simple-random-sample-of-5012-households-and-find-that-the-distribution-of-household-incomes-is-skewed-right-if-you-calculate-the-mean-of-the",{"id":364,"category":36,"text_question":365,"slug":366},534380,"5x+13+7x-10=99","5x-13-7x-10-99",{"id":368,"category":36,"text_question":369,"slug":370},534387,"A hardware bill totals 857.63withdiscountsof55 and sells for 15.Ifthereareanynotsoldbytheendoftheday,theyaresoldtoalargefoodprocessingcompanyfor3 a case. The probability that daily demand will be 100 cases is 0.30, the probability that daily demand will be 200 cases is 0.40, and the probability that daily demand will be 300 cases is 0.30. Farm Grown has a policy of always satisfying customer demands. If its own supply of cases is less than the demand, it buys the necessary vegetables from a competitor. The estimated cost of doing this is 16 per case. (a) Draw a decision table for this problem (b) What do you recommend?","farm-grown-inc-produces-cases-of-perishable-food-products-each-case-contains-an-assortment-of-vegetables-and-other-farm-products-each-case-costs-5-and-sells-for-15-if-there-are-any-not-sold-by",{"id":388,"category":36,"text_question":389,"slug":390},534560,"Identify the slope and y intercept \ny=11+2/3x","identify-the-slope-and-y-intercept-y-11-2-3x",{"id":392,"category":36,"text_question":393,"slug":394},534688,"Matilde knows that, when driving her car from her office to her apartment, she spends a normal time of x minutes. In the last week, you have noticed that when driving at 50 mph (miles per hour), you arrive home 4 minutes earlier than normal, and when driving at 40 mph, you arrive home 5 minutes earlier\n later than normal. If the distance between your office and your apartment is y miles, calculate x + y.","matilde-knows-that-when-driving-her-car-from-her-office-to-her-apartment-she-spends-a-normal-time-of-x-minutes-in-the-last-week-you-have-noticed-that-when-driving-at-50-mph-miles-per-hour-you-a",{"data":396},[397,401,405],{"id":398,"question":399,"answer":400},122031,"What is the equation of an ellipse with vertices at (-3,0) and (3,0), and a major axis length of 10?","The equation of the ellipse is ((x^2)/36) + ((y^2)/25) = 1. It represents an ellipse centered at the origin, with x-vertices at Β±3, y-vertices at Β±5, and foci at (-√11,0) and (√11,0).",{"id":402,"question":403,"answer":404},111699,"What is the dot product of vector A = (3, -2) and vector B = (-4, 5)?","The dot product is calculated by multiplying corresponding components and summing them: (3 * -4) + (-2 * 5) = -12 + (-10) = -22.",{"id":406,"question":407,"answer":408},101757,"What is the product of 497 and 26?","The product of 497 and 26 is 12,922.",{"sicons":410},{"bxl:facebook-circle":411,"bxl:instagram":415,"mdi:web":417,"la:apple":419,"ph:google-logo-bold":422,"ph:google-logo":425},{"left":412,"top":412,"width":413,"height":413,"rotate":412,"vFlip":183,"hFlip":183,"body":414},0,24,"\u003Cpath 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