^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 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- Γngulo 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":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?","\u003Cmathβfieldreadβonlydefaultβmode=\"inlineβmath\"class=\"mathβexpression\">\u003Cmathβfieldreadβonly>textSolution:\u003C/mathβfield>\u003C/mathβfield>\u003Cbr/>\n1.Definevariables:\u003Cbr/>\nβLet\u003Cmathβfieldreadβonlydefaultβmode=\"inlineβmath\"class=\"mathβexpression\">\u003Cmathβfieldreadβonly>P\u003C/mathβfield>\u003C/mathβfield>betheoriginalpriceoftheplaneticket.\u003Cbr/>\nβ\u003Cmathβfieldreadβonlydefaultβmode=\"inlineβmath\"class=\"mathβexpression\">\u003Cmathβfieldreadβonly>P\u003C/mathβfield>\u003C/mathβfield>increasedby18\\frac{x}{15}=\\frac{4}{3}\u003C/mathβfield>\n\u003Cbr>\n\u003C/div>\n\n\u003Cdiv>\n\n\u003Cmathβfieldstyle=\"fontβsize:16px;padding:8px;borderβradius:8px;border:1pxsolidrgba(0,0,0,.3);boxβshadow:000rgba(0,0,0,.2)\n\"readβonly>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 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":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},{"id":216,"category":36,"slug":217,"text_question":217,"photo_question":8,"text_answer":218,"step_text_answer":8,"step_photo_answer":8,"views":219,"likes":220,"expert":221},534332,"392929-9","To solve the problem 392929 - 9, simply subtract 9 from 392929.\u003Cbr />\u003Cbr />Step 1: \u003Cbr />392929 - 9 = 392920\u003Cbr /> \u003Cbr />Answer:\\boxed{392920}",1011,202,"id":222,"name":223,"photo":224,"biography":225,"createdat":8,"updatedat":8,"rating":226,"totalanswer":227,23,"Neal","https://api.mathβmaster.org/img/experts/23/23.webp","IamHarveyRossMendoza,studyingmathreallyfascinatesme.Startingprimaryandsecondarylevelofeducation,Ialreadyhavemathasmyfavoritesubject.SolvingMathproblemsisthrillingandchallengingtometothepointthatIβ²lldowhateverittakestojusttolearnandsolveproblems.Inshort,mathhelpsmetobethebestversionofmyself.ItookaBachelorsDegreeinCivilEngineeringasmyjourneygoesonandnow,IamagraduateofBachelorofScienceinCivilEngineeringandalsoaLicensedCivilEngineer.\r\n\r",4.5,101,"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":36,"textquestion":233,"slug":234,532040,"8xΒ²β30xβ10xΒ²+70x=β30x+10xΒ²β20xΒ²","8xβ30xβ10xβ70xβ30xβ10xβ20x","id":236,"category":36,"textquestion":237,"slug":238,533957,"Determinetheabsoluteextremaofthefunctionπ(π₯)=π₯3β18π₯296π₯,ontheinterval[1,10]","determineβtheβabsoluteβextremaβofβtheβfunctionβfβxβx3β18x2β96xβonβtheβintervalβ1β10","id":240,"category":36,"textquestion":241,"slug":242,533976,"Whichofthefollowingistheproductofmultiplyingtwentyβsevenandtwentyβfivehundredthsbynineandtwentyβsevenhundredths?","whichβofβtheβfollowingβisβtheβproductβofβmultiplyingβtwentyβsevenβandβtwentyβfiveβhundredthsβbyβnineβandβtwentyβsevenβhundredths","id":244,"category":36,"textquestion":245,"slug":246,533990,"Alltheliquidcontainedinabarrelisdistributedinto96equalglassesuptoitsmaximumcapacity.\nWewanttopourthesameamountofliquidfromanotherbarrelidenticaltothepreviousoneintoglassesidenticaltothoseused,butonlyupto3/4ofitscapacity.\nHowmanymoreglasseswillbeneededforthis?","allβtheβliquidβcontainedβinβaβbarrelβisβdistributedβintoβ96βequalβglassesβupβtoβitsβmaximumβcapacityβweβwantβtoβpourβtheβsameβamountβofβliquidβfromβanotherβbarrelβidenticalβtoβtheβpreviousβoneβinto","id":248,"category":36,"textquestion":249,"slug":250,534000,"4xβ3y=5;x+2y=4","4xβ3yβ5βxβ2yβ4","id":252,"category":36,"textquestion":253,"slug":254,534003,"Themaincostofa5poundbagofshrimpis47 with a variance of 36 if a sample of 43 bags of shrimp is randomly selected, what is the probability that the sample mean with differ from the true mean by less than 1.4","theβmainβcostβofβaβ5βpoundβbagβofβshrimpβisβ47βwithβaβvarianceβofβ36βifβaβsampleβofβ43βbagsβofβshrimpβisβrandomlyβselectedβwhatβisβtheβprobabilityβthatβtheβsampleβmeanβwithβdifferβfromβtheβtrueβmean","id":256,"category":36,"textquestion":257,"slug":258,534071,"Thereare162studentsenrolledinthebasicmathematicscourse.Ifthenumberofwomenis8timesthenumberofmen,howmanywomenarethereinthebasicmathematicscourse?","thereβareβ162βstudentsβenrolledβinβtheβbasicβmathematicsβcourseβifβtheβnumberβofβwomenβisβ8βtimesβtheβnumberβofβmenβhowβmanyβwomenβareβthereβinβtheβbasicβmathematicsβcourse","id":260,"category":36,"textquestion":261,"slug":262,534130,"solveforx\n50x+120(176βx)=17340","solveβforβxβ50xβ120β176βxβ17340","id":264,"category":36,"textquestion":265,"slug":266,534191,"6β35Arecentstudybyanenvironmentalwatchdogdeterminedthattheamountofcontaminants\ninMinnesotalakes(inpartspermillion)ithasanormaldistributionwithameanof64ppmandvarianceof17.6.Assumethat35lakesarerandomlyselectedandsampled.Findtheprobabilitythatthesampleaverageoftheamountofcontaminantsis\na)Greaterthan72ppm.\nb)Between64and72ppm.\nc)Exactly64ppm.\nd)Greaterthan94ppm.","6β35βaβrecentβstudyβbyβanβenvironmentalβwatchdogβdeterminedβthatβtheβamountβofβcontaminantsβinβminnesotaβlakesβinβpartsβperβmillionβitβhasβaβnormalβdistributionβwithβaβmeanβofβ64βppmβandβvarianceβo","id":268,"category":36,"textquestion":269,"slug":270,534265,"Ifatwoβbranchparallelcurrentdividernetwork,iftheresistanceofonebranchisdoubledwhilekeepingallotherfactorsconstant,whathappenstothecurrentflowthroughthatbranchandtheotherbranch?\n\nSelectone:\n\na.Thecurrentthroughthedoubledresistancebranchremainsunchanged,andthecurrentthroughtheotherbranchdecreases.\n\nb.Thecurrentthroughthedoubledresistancebranchdecreases,andthecurrentthroughtheotherbranchremainsunchanged.\n\nc.Thecurrentthroughthedoubledresistancebranchincreases,andthecurrentthroughtheotherbranchremainsunchanged.\n\nd.Thecurrentthroughbothbranchesremainunchanged.","ifβaβtwoβbranchβparallelβcurrentβdividerβnetworkβifβtheβresistanceβofβoneβbranchβisβdoubledβwhileβkeepingβallβotherβfactorsβconstantβwhatβhappensβtoβtheβcurrentβflowβthroughβthatβbranchβandβtheβothe","id":272,"category":36,"textquestion":273,"slug":274,534345,"On+January+10+2023+the+CONSTRUCTORA+DEL+ORIENTE+SAC+company+acquires+land+to+develop+a+realestate+project250.00 per month and keeps the money in a safe in his own home. At the end of 12\n months, deposit the total saved into the savings account. Consider that, each year, deposits are\n always carried out on the same day and month; the annual yield on the savings account is 7%; and, the yield\n total is obtained by the interest compounding process. So, the amount that Paulo will have in his savings account\n after 3 years, from the moment you started saving part of your money monthly, it will be\n A) R6,644.70.\nB)R 9,210.00.\n C) R9,644.70.\nD)R 10,319.83.\n E) R13,319.83","25βpauloβsavesβrβ250β00βperβmonthβandβkeepsβtheβmoneyβinβaβsafeβinβhisβownβhomeβatβtheβendβofβ12βmonthsβdepositβtheβtotalβsavedβintoβtheβsavingsβaccountβconsiderβthatβeachβyearβdepositsβareβal","id":296,"category":36,"textquestion":297,"slug":298,534538,"A20βyearoldhopestoretirebyage65.Tohelpwithfutureexpenses,theyinvest6 500 today at an interest rate of 6.4% compounded annually. At age 65, what is the difference between the exact accumulated value and the approximate accumulated value usingtheRuleof72?","a-20-year-old-hopes-to-retire-by-age-65-to-help-with-future-expenses-they-invest-6-500-today-at-an-interest-rate-of-6-4-compounded-annually-at-age-65-what-is-the-difference-between-the-exact-acc",{"id":300,"category":36,"text_question":301,"slug":302},534597,"Arturo had hospitalization expenses of 8,300.Yourpolicyformedicalexpenses\nSeniorshaveadeductibleof500 and expenses are paid at a 20% coinsurance.\n These are the first expenses ever this year, how much will Arturo have to pay in\n your bill for hospitalization expenses?","arturo-had-hospitalization-expenses-of-8-300-your-policy-for-medical-expenses-seniors-have-a-deductible-of-500-and-expenses-are-paid-at-a-20-coinsurance-these-are-the-first-expenses-ever-this-y",{"id":304,"category":36,"text_question":305,"slug":306},534640,"8x+4 -4=4x-1","8-x-4-4-4x-1",{"id":308,"category":36,"text_question":309,"slug":310},534656,"A grain silo has a height of 8.8m with a 11.4m diameter.\n\nIf it is filled 0.5% of it's volume, how much grain m3 is stored in the silo? 0decimalplaces","a-grain-silo-has-a-height-of-8-8m-with-a-11-4m-diameter-if-it-is-filled-0-5-of-it-s-volume-how-much-grain-m-3-is-stored-in-the-silo-0-decimal-places",{"data":312},{"questions":313},[314,318,322,326,330,334,337,341,345,349,353,357,361,365,369,373,377,378,382,386],{"id":315,"category":36,"text_question":316,"slug":317},532032,"Let the vectors be u=β1,0,2 , v=0,2,β3 , w=2,2,3 Calculate the following expressions a)\u003Cu,w> b) <2u- 5v,3w>","let-the-vectors-be-u-1-0-2-v-0-2-3-w-2-2-3-calculate-the-following-expressions-a-u-w-b-lt-2u-5v-3w-gt",{"id":319,"category":36,"text_question":320,"slug":321},532088,"1/2x +3 \u003C4x-7","1-2x-3-4x-7",{"id":323,"category":36,"text_question":324,"slug":325},532304,"what is 9% of 307","what-is-9-of-307",{"id":327,"category":36,"text_question":328,"slug":329},533901,"For a temperature range between 177 degrees Celsius to 213 degrees Celsius, what is the temperature range in degrees Fahrenheit.","for-a-temperature-range-between-177-degrees-celsius-to-213-degrees-celsius-what-is-the-temperature-range-in-degrees-fahrenheit",{"id":331,"category":36,"text_question":332,"slug":333},533913,"Use the elimination to find the solution to each linear system.\n\nX+y=43\n2x-y=20","use-the-elimination-to-find-the-solution-to-each-linear-system-x-y-43-2x-y-20",{"id":335,"category":36,"text_question":336,"slug":336},533969,"7273736363-8",{"id":338,"category":36,"text_question":339,"slug":340},533977,"what is the annual rate on β525at0.046β4302 and has been paid by the seller in advance of closing. Using the 30-day month/260-day year method what will be the tax proration entry on the settlement statement round to the nearest dollar for a closing on Oct. 26 if the buyer owns the day of closing?\n\na. 3525credittothebuyerand777 debit to the seller\nb. 777debittothebuyerand3525 debit to the seller\nc. 777credittothebuyerand777 debit to the seller\nd. 3525debittothebuyerand3525 credit to the seller\n\n*Can anyone help with this? I am studying for my real estate exam and am having trouble with some of the calculations :)","the-annual-real-property-tax-liability-for-a-residential-property-is-4302-and-has-been-paid-by-the-seller-in-advance-of-closing-using-the-30-day-month-260-day-year-method-what-will-be-the-tax-prorat",{"id":366,"category":36,"text_question":367,"slug":368},534463,"Calculate the area of the parallelogram with adjacent vertices 1,4,β2, β3,1,6 π¦ 1,β2,3","calculate-the-area-of-the-parallelogram-with-adjacent-vertices-1-4-2-3-1-6-y-1-2-3",{"id":370,"category":36,"text_question":371,"slug":372},534483,"A property sold for 745,000inacoβbrokeredtransaction.Thesellerhasagreedtopaya714,900\n3725\n37250\n18625","a-property-sold-for-745-000-in-a-co-brokered-transaction-the-seller-has-agreed-to-pay-a-7-commission-to-the-listing-firm-the-listing-firm-has-agreed-to-equally-split-the-commission-with-the-sellin",{"id":374,"category":36,"text_question":375,"slug":376},534517,"solve R the following equation 4 x squared - 35 - 9 over x squared is equal to 0","solve-r-the-following-equation-4-x-squared-35-9-over-x-squared-is-equal-to-0",{"id":292,"category":36,"text_question":293,"slug":294},{"id":379,"category":36,"text_question":380,"slug":381},534584,"Emile organizes a community dance to raise funds. In addition to paying 300torenttheroom,shemustrentchairsat2 each. The quantity of chairs rented will be equal to the number of tickets sold. She sells tickets for 7 each. How much should she sell to raise money?","emile-organizes-a-community-dance-to-raise-funds-in-addition-to-paying-300-to-rent-the-room-she-must-rent-chairs-at-2-each-the-quantity-of-chairs-rented-will-be-equal-to-the-number-of-tickets-sol",{"id":383,"category":36,"text_question":384,"slug":385},534621,"5a-3.(a-7)=-3","5a-3-a-7-3",{"id":387,"category":36,"text_question":388,"slug":389},534665,"Let f(x)=-1/2x+5 evaluate f(-6)","let-f-x-1-2x-5-evaluate-f-6",{"data":391},[392,396,400],{"id":393,"question":394,"answer":395},118102,"What is the measure of the angle bisector if angle A measures 40 degrees?","The measure of the angle bisector is 20 degrees. The angle bisector divides an angle into two congruent angles. In this case, since angle A measures 40 degrees, the angle bisector would measure half that, which is 20 degrees.",{"id":397,"question":398,"answer":399},126670,"Find the value of f(5) if f(x) = x.","f(5) = 5. In a linear function, the value of f(x) is equal to the input value x. When we substitute 5 for x in the given function f(x) = x, the output value f(5) will also be 5. This is because the function only contains the variable x, which means any value we substitute for x will be the same as the output value. Thus, f(5) = 5.",{"id":401,"question":402,"answer":403},150658,"What is the value of arccos(cos(Ο/4))?","The value of arccos(cos(Ο/4)) is Ο/4. In general, the inverse trigonometric function arccos(x) returns an angle between 0 and Ο (or 0 and 180 degrees) whose cosine is x. 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