MATH MADE EASY - MathMaster

. I think the journey of a math teacher is not just about formulas and calculations; it's about fostering a deep love for learning, empowering students to conquer challenges, and illuminating the path to a world of infinite possibilities.",4.5,96,{"data":37},[38,39,40,41,42,43],{"id":6,"title":7,"slug":8},{"id":10,"title":11,"slug":8},{"id":13,"title":14,"slug":8},{"id":16,"title":17,"slug":8},{"id":19,"title":20,"slug":8},{"id":22,"title":23,"slug":8},{"data":45,"links":118,"meta":120},[46,55,62,69,76,83,90,97,104,111],{"id":47,"category":48,"text_question":49,"photo_question":50,"text_answer":51,"step_text_answer":8,"step_photo_answer":8,"views":52,"likes":53,"slug":54},538064,"general","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":56,"category":48,"text_question":57,"photo_question":50,"text_answer":58,"step_text_answer":8,"step_photo_answer":8,"views":59,"likes":60,"slug":61},538050,"A 4.5m tall tree casts a shadow 6m long.\n\n Find the angle of elevation of the sun at that time","Solution:\u003Cbr />\n1. Given:\u003Cbr />\n- The height of the tree is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4.5 \\, \\text{m}\u003C/math-field>\u003C/math-field>.\u003Cbr />\n- The length of the shadow is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>6 \\, \\text{m}\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n2. The angle of elevation of the sun can be found using the tangent function in a right triangle:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{tan}

$\\theta$ = \\frac{\\text{opposite side}}{\\text{adjacent side}}\u003C/math-field>\u003C/math-field>\u003Cbr />\n- In this case, the opposite side is the height of the tree, and the adjacent side is the length of the shadow.\u003Cbr />\n\u003Cbr />\n3. Calculate the tangent of the angle:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{tan}

$\\theta$ = \\frac{4.5}{6} = 0.75\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Find the angle \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\theta\u003C/math-field>\u003C/math-field> using the inverse tangent

$arctan$ function:\u003Cbr />\n- \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\theta = \\arctan

$0.75$ \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Calculate \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\theta\u003C/math-field>\u003C/math-field>:\u003Cbr />\n- Using a calculator, \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\theta \\approx 36.87^\\circ\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n6. Therefore, the angle of elevation of the sun is approximately \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>36.87^\\circ\u003C/math-field>\u003C/math-field>.",593,119,"a-4-5m-tall-tree-casts-a-shadow-6m-long-find-the-angle-of-elevation-of-the-sun-at-that-time",{"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},537983,"What is the value of 6 in 567186524301","1. Write down the number with each digit's place value: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 567186524301 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- 1 is in the ones place,\u003Cbr>\u003Cbr>- 0 is in the tens place,\u003Cbr>\u003Cbr>- 3 is in the hundreds place,\u003Cbr>\u003Cbr>- 4 is in the thousands place,\u003Cbr>\u003Cbr>- 2 is in the ten thousands place,\u003Cbr>\u003Cbr>- 5 is in the hundred thousands place,\u003Cbr>\u003Cbr>- 6

$second occurrence$ is in the millions place,\u003Cbr>\u003Cbr>- 8 is in the ten millions place,\u003Cbr>\u003Cbr>- 1 is in the hundred millions place,\u003Cbr>\u003Cbr>- 7 is in the billions place,\u003Cbr>\u003Cbr>- 6

$first occurrence$ is in the ten billions place,\u003Cbr>\u003Cbr>- 5 is in the hundred billions place.\u003Cbr>\u003Cbr>2. Identify the places of both occurrences of the digit 6:\u003Cbr>\u003Cbr>- The first digit 6 is fifth from the right, so it is in the millions place:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 6 \\cdot 10^6 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>- The second digit 6 is located fourth from the right, so it is in the ten billion place:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 6 \\cdot 10^4 \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>Thus, the place value of the first digit 6 is in the millions place, and the place value of the second digit 6 is in the ten billion place.",827,165,"what-is-the-value-of-6-in-567186524301",{"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},537980,"A dairy products company uses trucks with a load capacity of 250 boxes to sell and distribute milk, each containing 12 liters and the price per liter is

$10. If a supermarket orders 4 loads, how much should it pay to purchase the dairy from the company?","1. Calculamos la cantidad de litros por carga:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>250 \\, \\text{cajas} \\times 12 \\, \\text{litros/caja} = 3000 \\, \\text{litros}\u003C/math-field>\u003C/math-field>\u003Cbr />\n2. Calculamos el total de litros para 4 cargas:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>4 \\, \\text{cargas} \\times 3000 \\, \\text{litros/carga} = 12000 \\, \\text{litros}\u003C/math-field>\u003C/math-field>\u003Cbr />\n3. Calculamos el costo total multiplicando por el precio por litro:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>12000 \\, \\text{litros} \\times 10 \\, \\text{\\$/litro} = 120000 \\, \\text{\\$}\u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Por lo tanto, el supermercado debe pagar: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>120000 \\, \\text{\\$}\u003C/math-field>\u003C/math-field>",1013,203,"a-dairy-products-company-uses-trucks-with-a-load-capacity-of-250-boxes-to-sell-and-distribute-milk-each-containing-12-liters-and-the-price-per-liter-is-10-if-a-supermarket-orders-4-loads-how-much",{"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},537961,"What is the equation of the line? P(-4;2) Q(2;0)","Solution:\u003Cbr />\n1. Given points:\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P(-4, 2)\u003C/math-field>\u003C/math-field> \u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>Q(2, 0)\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Find the slope \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>m\u003C/math-field>\u003C/math-field> of the line using the formula:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>m = \\frac{y_2 - y_1}{x_2 - x_1}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Substituting the coordinates of the points into the formula:\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y_1 = 2, y_2 = 0, x_1 = -4, x_2 = 2\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Calculate the slope:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>m = \\frac{0 - 2}{2 - (-4)} = \\frac{-2}{2 + 4} = \\frac{-2}{6} = -\\frac{1}{3}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Use the point-slope form of a line equation:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y - y_1 = m(x - x_1)\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Substituting one of the points and the slope into the equation:\u003Cbr />\n* Point \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>P(-4, 2)\u003C/math-field>\u003C/math-field>: \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y - 2 = -\\frac{1}{3}(x - (-4))\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. Simplify the equation:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y - 2 = -\\frac{1}{3}(x + 4)\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y - 2 = -\\frac{1}{3}x - \\frac{4}{3}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n8. Add 2 to both sides:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = -\\frac{1}{3}x - \\frac{4}{3} + \\frac{6}{3}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = -\\frac{1}{3}x + \\frac{2}{3}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n9. The equation of the line in slope-intercept form is:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = -\\frac{1}{3}x + \\frac{2}{3}\u003C/math-field>\u003C/math-field>",495,99,"what-is-the-equation-of-the-line-p-4-2-q-2-0",{"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},537832,"The size of an object-oriented programming class is limited to 15 people. If 3 seats are still available to what percent of its capacity is the class filled?","1. Total capacity of class = 15 seats\u003Cbr />\n2. Available seats = 3 \u003Cbr />\n3. Filled seats = \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 15 - 3 = 12 \u003C/math-field>\u003C/math-field>\u003Cbr />\n4. Percentage filled = \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\left( \\frac{12}{15} \\right) \\times 100 \u003C/math-field>\u003C/math-field> \u003Cbr />\n5. Simplify the fraction = \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{12}{15} = 0.8 \u003C/math-field>\u003C/math-field>\u003Cbr />\n6. Find the percentage = \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 0.8 \\times 100 = 80 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nAnswer: 80%",375,75,"the-size-of-an-object-oriented-programming-class-is-limited-to-15-people-if-3-seats-are-still-available-to-what-percent-of-its-capacity-is-the-class-filled",{"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},537804,"Calculate Decile 8 of the following sample:\n 10\n 11\n 12\n 13\n 14\n 15\n 16\n 18\n 18\n 19\n 20\n 20\n 22\n 23\n 25\n 26\n 27\n 28\n 29\n 30","Solution:\u003Cbr />\n1. Given sample data:\u003Cbr />\n* 10, 11, 12, 13, 14, 15, 16, 18, 18, 19, 20, 20, 22, 23, 25, 26, 27, 28, 29, 30\u003Cbr />\n\u003Cbr />\n2. Order the data set (already ordered):\u003Cbr />\n* 10, 11, 12, 13, 14, 15, 16, 18, 18, 19, 20, 20, 22, 23, 25, 26, 27, 28, 29, 30\u003Cbr />\n\u003Cbr />\n3. To find the position of the 8th decile (D8), use the formula:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>D_k = \\left( \\frac{k(n + 1)}{10} \\right)^{th} \\text{ position}\u003C/math-field>\u003C/math-field>\u003Cbr />\nwhere \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>k = 8\u003C/math-field>\u003C/math-field> and \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>n = 20\u003C/math-field>\u003C/math-field> (number of data points).\u003Cbr />\n\u003Cbr />\n4. Calculate the position:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>D_8 = \\left( \\frac{8(20 + 1)}{10} \\right) = \\left( \\frac{168}{10} \\right) = 16.8^{th} \\text{ position}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n5. Since 16.8 isn't a whole number, it means D8 is between the 16th and 17th data points. Using interpolation:\u003Cbr />\n- 16th value is 26 and 17th value is 27.\u003Cbr />\n- Interpolating:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>D_8 = 26 + 0.8(27 - 26)\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>D_8 = 26 + 0.8(1)\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>D_8 = 26.8\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Therefore, the 8th decile (D8) is:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>26.8\u003C/math-field>\u003C/math-field>",881,176,"calculate-decile-8-of-the-following-sample-10-11-12-13-14-15-16-18-18-19-20-20-22-23-25-26-27-28-29-30",{"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},537754,"12/9 - 5","Cancel \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{12}{9}:{\\quad}\\frac{4}{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{4}{3}-5

$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n Convert \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba(0, 0, 0, .3)\">$ -5

$\u003C/math-field>to fraction \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba(0, 0, 0, .3)\">$ :{\\quad}\\frac{-15}{3}

$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba(0, 0, 0, .3)\">$ \\frac{4}{3}+\\frac{-15}{3}=\\frac{-11}{3}

$\u003C/math-field>\n \u003Cbr>\n \u003C/div>\n \n Apply the fraction rule \u003Cmath-field read-only default-mode=\"inline-math\" style=\"padding-left:5px; padding-right:5px; display:inline-block; border-radius:4px; border: 1px solid rgba(0, 0, 0, .3)\">$ \\frac{-a}{b}=-\\frac{a}{b}

$\u003C/math-field>\n \u003Cbr>\n \u003C/div>",461,92,"12-9-5",{"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},537724,"Determine the coefficients a, b and c, respectively, of the equation 4x² +12x – 7 = 0.","1. Identifique a forma geral da equação quadrática: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> ax^2 + bx + c = 0 \u003C/math-field>\u003C/math-field>.\u003Cbr />\n2. Compare os coeficientes da equação fornecida \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 4x^2 + 12x - 7 = 0 \u003C/math-field>\u003C/math-field> com a forma geral para identificar os valores de \$ a \$, \$ b \$ e \$ c \$.\u003Cbr />\n\u003Cbr />\n- Coeficiente \$ a \$ é o número ao lado de \$ x^2 \$: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> a = 4 \u003C/math-field>\u003C/math-field>.\u003Cbr />\n- Coeficiente \$ b \$ é o número ao lado de \$ x \$: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> b = 12 \u003C/math-field>\u003C/math-field>.\u003Cbr />\n- Coeficiente \$ c \$ é o termo constante: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> c = -7 \u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\nResposta: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> a = 4, \\ b = 12, \\ c = -7 \u003C/math-field>\u003C/math-field>.",801,160,"determine-the-coefficients-a-b-and-c-respectively-of-the-equation-4x-12x-7-0",{"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},537706,"How do you find a % decrease?\nExample 15% decrease of$ 997.58","Solution:\u003Cbr />\n1. Identify the values:\u003Cbr />\n- Original value: USD997.58\u003Cbr />\n- Percentage decrease: 15%\u003Cbr />\n\u003Cbr />\n2. Convert the percentage decrease to a decimal:\u003Cbr />\n- Decimal equivalent = 15% = \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\frac{15}{100} = 0.15\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Calculate the decrease amount:\u003Cbr />\n- Decrease amount = Original value \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\times\u003C/math-field>\u003C/math-field> Decimal equivalent\u003Cbr />\n- Decrease amount = USD997.58 \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\times 0.15 = 149.637\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Calculate the new amount after the decrease:\u003Cbr />\n- New amount = Original value \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>-\u003C/math-field>\u003C/math-field> Decrease amount\u003Cbr />\n- New amount = USD997.58 \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>- 149.637 = 847.943\u003C/math-field>\u003C/math-field>",345,69,"how-do-you-find-a-decrease-example-15-decrease-of-997-58",{"first":6,"last":119,"prev":8,"next":10},10,{"current_page":6,"from":6,"last_page":119,"links":121,"path":149,"per_page":119,"to":119,"total":35},[122,125,128,130,132,134,136,139,142,145,147],{"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":119,"label":146,"active":127},"10",{"url":10,"label":148,"active":127},"Next 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