;box-shadow: 0 0 0 rgba$0, 0, 0, .2$\n\" read-only>$=\\frac{\\sin(2x)}{(-\\sin(x)+1)(\\sin(x)+1)}$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba$0, 0, 0, .3$;box-shadow: 0 0 0 rgba$0, 0, 0, .2$\n\" read-only>$=\\frac{\\sin(2x)}{\\cos^{2}(x)}$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba$0, 0, 0, .3$;box-shadow: 0 0 0 rgba$0, 0, 0, .2$\n\" read-only>$=2\\tan(x)$\u003C/math-field>\n \u003Cbr>\n \u003C/div>",770,154,"prove-the-trig-identity-cos-x-1-sinx-cos-x-1-sin-x-2tan-x",{"id":63,"category":48,"text_question":64,"photo_question":50,"text_answer":65,"step_text_answer":8,"step_photo_answer":8,"views":66,"likes":67,"slug":68},538022,"The sum of3x,4y and z","1. Identify the terms: 3 x , 4 y , and z. \u003Cdiv>\u003Cbr>\u003Cbr>2. Add them together: 3x + 4 y + z. \u003C/div>\u003Cdiv>\u003Cbr>\u003Cbr>3. Therefore, the answer is: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x + 4y + z\u003C/math-field>\u003C/math-field> \u003C/div>",933,187,"the-sum-of3x-4y-and-z",{"id":70,"category":48,"text_question":71,"photo_question":50,"text_answer":72,"step_text_answer":8,"step_photo_answer":8,"views":73,"likes":74,"slug":75},538018,"Perform the indicated operation \nX over x2-1 minus 3 over x2-2x+1","Apply the fraction rule \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba$0, 0, 0, .3$\">$\\frac{a}{c}-\\frac{b}{c}=\\frac{a-b}{c}$\u003C/math-field>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba$0, 0, 0, .3$;box-shadow: 0 0 0 rgba$0, 0, 0, .2$\n\" read-only>$=\\frac{x(x-1)-3(x+1)}{(x+1)(x-1)^{2}}$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n Simplify \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba$0, 0, 0, .3$\">$x(x-1)-3(x+1):{\\quad}x^{2}-4x-3$\u003C/math-field>\n \n \u003Cdiv>\n \n \u003Cmath-field style=\"font-size: 16px;padding: 8px;border-radius: 8px;border: 1px solid rgba$0, 0, 0, .3$;box-shadow: 0 0 0 rgba$0, 0, 0, .2$\n\" read-only>$=\\frac{x^{2}-4x-3}{(x+1)(x-1)^{2}}$\u003C/math-field>\n \u003Cbr>\n \u003C/div>",1075,215,"perform-the-indicated-operation-x-over-x2-1-minus-3-over-x2-2x-1",{"id":77,"category":48,"text_question":78,"photo_question":50,"text_answer":79,"step_text_answer":8,"step_photo_answer":8,"views":80,"likes":81,"slug":82},537941,"Calculate the following permutations:\n In how many ways can 5 different diplomas be placed?","Solution:\u003Cbr />\n1. We have 5 different diplomas and we want to find out in how many different ways they can be arranged.\u003Cbr />\n2. The number of arrangements of n different items is given by the permutation formula \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>n!\u003C/math-field>\u003C/math-field> $n factorial$.\u003Cbr />\n3. Calculate factorial of 5:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5! = 5 \\times 4 \\times 3 \\times 2 \\times 1\u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5! = 120\u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Therefore, the diplomas can be arranged in 120 different ways.",567,113,"calculate-the-following-permutations-in-how-many-ways-can-5-different-diplomas-be-placed",{"id":84,"category":48,"text_question":85,"photo_question":50,"text_answer":86,"step_text_answer":8,"step_photo_answer":8,"views":87,"likes":88,"slug":89},537931,"Write an inequality for:\nThe total bill for a lawnmower and 15 drawer pulls was within the family’s $400 budget. If he the lawnmower cost$325, find the maximum cost of each drawer pull","1. Write down the inequality for the total cost: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 325 + 15x \\leq 400 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Subtract the cost of the lawnmower from both sides to isolate the drawer pulls' cost: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 15x \\leq 400 - 325 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 15x \\leq 75 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Divide both sides by 15 to solve for x :\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \\leq \\frac{75}{15} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \\leq 5 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>The maximum cost of each drawer pull is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x \\leq 5 \u003C/math-field>\u003C/math-field> .",900,180,"write-an-inequality-for-the-total-bill-for-a-lawnmower-and-15-drawer-pulls-was-within-the-family-s-400-budget-if-he-the-lawnmower-cost-325-find-the-maximum-cost-of-each-drawer-pull",{"id":91,"category":48,"text_question":92,"photo_question":50,"text_answer":93,"step_text_answer":8,"step_photo_answer":8,"views":94,"likes":95,"slug":96},537928,"in a geometric sequence r=3 a2=12 find a10","1. Identify the given information in the problem:\u003Cbr />\n - Common ratio: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r = 3\u003C/math-field>\u003C/math-field>\u003Cbr />\n - Second term: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a_2 = 12\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Use the formula for the n-th term of a geometric sequence: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a_n = a_1 \\cdot r^{n-1}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Find the first term \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a_1\u003C/math-field>\u003C/math-field> using the second term:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a_2 = a_1 \\cdot r^{1} \\Rightarrow 12 = a_1 \\cdot 3 \\Rightarrow a_1 = \\frac{12}{3} = 4\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Substitute \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a_1\u003C/math-field>\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>r\u003C/math-field>\u003C/math-field> into the formula for the 10th term:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a_{10} = a_1 \\cdot r^{9} = 4 \\cdot 3^{9}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Calculate:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3^9 = 19683\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Multiply to find \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a_{10}\u003C/math-field>\u003C/math-field>:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a_{10} = 4 \\cdot 19683 = 78732\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. The answer is:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>a_{10} = 78732\u003C/math-field>\u003C/math-field>",791,158,"in-a-geometric-sequence-r-3-a2-12-find-a10",{"id":98,"category":48,"text_question":99,"photo_question":50,"text_answer":100,"step_text_answer":8,"step_photo_answer":8,"views":101,"likes":102,"slug":103},537917,"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,"if-30-of-the-students-in-a-class-made-a-b-and-there-were-12-bs-how-many-students-were-in-the-class",{"id":105,"category":48,"text_question":106,"photo_question":50,"text_answer":107,"step_text_answer":8,"step_photo_answer":8,"views":108,"likes":109,"slug":110},537824,"A dog weighs 20% more than it did three months ago. It weighs 36 pounds now. How much did the dog weigh three months.","1. Identify the current weight of the dog: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>36\u003C/math-field>\u003C/math-field> pounds.\u003Cbr />\n\u003Cbr />\n2. Determine the percentage increase in weight: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>20\u003C/math-field>\u003C/math-field>% or \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.2\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n3. Use the formula for the original weight: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Original Weight} = \\frac{36}{1 + 0.2} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Calculate the denominator: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 1 + 0.2 = 1.2 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Calculate the original weight:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Original Weight} = \\frac{36}{1.2} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Perform the division: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\text{Original Weight} = 30 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nTherefore, the dog weighed \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>30\u003C/math-field>\u003C/math-field> pounds three months ago.",765,153,"a-dog-weighs-20-more-than-it-did-three-months-ago-it-weighs-36-pounds-now-how-much-did-the-dog-weigh-three-months",{"id":112,"category":48,"text_question":113,"photo_question":50,"text_answer":114,"step_text_answer":8,"step_photo_answer":8,"views":115,"likes":116,"slug":117},537822,"If the cost of 1 ½ cup of dressing is $3.00, how much would the cost of 3 ½ oz be?","Solution:\u003Cbr />\n1. Given:\u003Cbr />\n- Cost of 1 ½ cups of dressing is USD3.00.\u003Cbr />\n- 1 cup = 8 ounces. Therefore, 1 ½ cups = 12 ounces.\u003Cbr />\n\u003Cbr />\n2. Determine the cost per ounce:\u003Cbr />\n- Cost of 12 ounces = USD3.00.\u003Cbr />\n- Cost per ounce = USD \\\\frac{3.00}{12} = USD0.25.\u003Cbr />\n\u003Cbr />\n3. Calculate the cost for 3 ½ ounces:\u003Cbr />\n- 3 ½ ounces = 3.5 ounces.\u003Cbr />\n- Cost for 3.5 ounces = 3.5 \\times USD0.25 = USD0.875.\u003Cbr />\n\u003Cbr />\n4. Therefore, the cost of 3 ½ oz of dressing is USD0.875.",261,52,"if-the-cost-of-1-cup-of-dressing-is-3-00-how-much-would-the-cost-of-3-oz-be",{"first":6,"last":119,"prev":8,"next":10},11,{"current_page":6,"from":6,"last_page":119,"links":121,"path":152,"per_page":146,"to":146,"total":35},[122,125,128,130,132,134,136,139,142,145,148,150],{"url":6,"label":123,"active":124},"1",true,{"url":10,"label":126,"active":127},"2",false,{"url":13,"label":129,"active":127},"3",{"url":16,"label":131,"active":127},"4",{"url":19,"label":133,"active":127},"5",{"url":22,"label":135,"active":127},"6",{"url":137,"label":138,"active":127},7,"7",{"url":140,"label":141,"active":127},8,"8",{"url":143,"label":144,"active":127},9,"9",{"url":146,"label":147,"active":127},10,"10",{"url":119,"label":149,"active":127},"11",{"url":10,"label":151,"active":127},"Next »","https://api.math-master.org/api/question/expert",{"$sicons":154},{"bxl:facebook-circle":155,"bxl:instagram":159,"mdi:web":161,"la:apple":163,"ph:google-logo-bold":166,"ph:google-logo":169},{"left":156,"top":156,"width":157,"height":157,"rotate":156,"vFlip":127,"hFlip":127,"body":158},0,24,"\u003Cpath fill=\"currentColor\" d=\"M12.001 2.002c-5.522 0-9.999 4.477-9.999 9.999c0 4.99 3.656 9.126 8.437 9.879v-6.988h-2.54v-2.891h2.54V9.798c0-2.508 1.493-3.891 3.776-3.891c1.094 0 2.24.195 2.24.195v2.459h-1.264c-1.24 0-1.628.772-1.628 1.563v1.875h2.771l-.443 2.891h-2.328v6.988C18.344 21.129 22 16.992 22 12.001c0-5.522-4.477-9.999-9.999-9.999\"/>",{"left":156,"top":156,"width":157,"height":157,"rotate":156,"vFlip":127,"hFlip":127,"body":160},"\u003Cpath fill=\"currentColor\" d=\"M11.999 7.377a4.623 4.623 0 1 0 0 9.248a4.623 4.623 0 0 0 0-9.248m0 7.627a3.004 3.004 0 1 1 0-6.008a3.004 3.004 0 0 1 0 6.008\"/>\u003Ccircle cx=\"16.806\" cy=\"7.207\" r=\"1.078\" fill=\"currentColor\"/>\u003Cpath fill=\"currentColor\" d=\"M20.533 6.111A4.6 4.6 0 0 0 17.9 3.479a6.6 6.6 0 0 0-2.186-.42c-.963-.042-1.268-.054-3.71-.054s-2.755 0-3.71.054a6.6 6.6 0 0 0-2.184.42a4.6 4.6 0 0 0-2.633 2.632a6.6 6.6 0 0 0-.419 2.186c-.043.962-.056 1.267-.056 3.71s0 2.753.056 3.71c.015.748.156 1.486.419 2.187a4.6 4.6 0 0 0 2.634 2.632a6.6 6.6 0 0 0 2.185.45c.963.042 1.268.055 3.71.055s2.755 0 3.71-.055a6.6 6.6 0 0 0 2.186-.419a4.6 4.6 0 0 0 2.633-2.633c.263-.7.404-1.438.419-2.186c.043-.962.056-1.267.056-3.71s0-2.753-.056-3.71a6.6 6.6 0 0 0-.421-2.217m-1.218 9.532a5 5 0 0 1-.311 1.688a3 3 0 0 1-1.712 1.711a5 5 0 0 1-1.67.311c-.95.044-1.218.055-3.654.055c-2.438 0-2.687 0-3.655-.055a5 5 0 0 1-1.669-.311a3 3 0 0 1-1.719-1.711a5.1 5.1 0 0 1-.311-1.669c-.043-.95-.053-1.218-.053-3.654s0-2.686.053-3.655a5 5 0 0 1 .311-1.687c.305-.789.93-1.41 1.719-1.712a5 5 0 0 1 1.669-.311c.951-.043 1.218-.055 3.655-.055s2.687 0 3.654.055a5 5 0 0 1 1.67.311a3 3 0 0 1 1.712 1.712a5.1 5.1 0 0 1 .311 1.669c.043.951.054 1.218.054 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