and $-8, -2$\nFind the distance between 2 points","","To find the distance between two points \\((-3,-2)\\) and \\((-8, -2)\\) in a 2D coordinate plane, we use the distance formula:\u003Cbr>\u003Cbr>1. The distance formula is: \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> d = \\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>2. Substitute the given points \\((-3, -2)\\) and \\((-8, -2)\\) into the formula:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> d = \\sqrt{((-8) - (-3))^2 + ((-2) - (-2))^2} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>3. Simplify the expression inside the square root:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> d = \\sqrt{(-8 + 3)^2 + (0)^2} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> d = \\sqrt{(-5)^2 + 0} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>4. Calculate:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> d = \\sqrt{25} \u003C/math-field>\u003C/math-field> \u003Cbr>\u003Cbr>5. Hence, the distance between the points is:\u003Cbr>\u003Cbr>\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>5\u003C/math-field>\u003C/math-field> units",1078,216,"3-2-and-8-2-find-the-distance-between-2-points",{"id":56,"category":48,"text_question":57,"photo_question":50,"text_answer":58,"step_text_answer":20,"step_photo_answer":20,"views":59,"likes":60,"slug":61},537990,"2x+3y=9\n3x-y=8\nSolve by elimination","1. Start with the given equations:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 2x + 3y = 9 \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 3x - y = 8 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. To eliminate \\( y \\), multiply the second equation by 3:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 9x - 3y = 24 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Add the modified second equation to the first equation:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> (2x + 3y) + (9x - 3y) = 9 + 24 \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 11x = 33 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Solve for \\( x \\):\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = \\frac{33}{11} \u003C/math-field>\u003C/math-field>\u003Cbr />\n \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\u003Cbr />\n5. Substitute \\( x = 3 \\) into the second original equation:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 3(3) - y = 8 \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 9 - y = 8 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n6. Solve for \\( y \\):\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> y = 9 - 8 \u003C/math-field>\u003C/math-field>\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> y = 1 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n7. The solution is:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = 3, \\, y = 1 \u003C/math-field>\u003C/math-field>",990,198,"2x-3y-9-3x-y-8-solve-by-elimination",{"id":63,"category":48,"text_question":64,"photo_question":50,"text_answer":65,"step_text_answer":20,"step_photo_answer":20,"views":66,"likes":67,"slug":68},537942,"What is 33.33 % as a decimal","Solution:\u003Cbr />\n1. Given:\u003Cbr />\n- Percentage: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>33.33\\%\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. To convert a percentage to a decimal, divide the percentage by 100:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\text{Decimal} = \\frac{33.33}{100} = 0.3333\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Thus, 33.33% as a decimal is:\u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>0.3333\u003C/math-field>\u003C/math-field>",318,64,"what-is-33-33-as-a-decimal",{"id":70,"category":48,"text_question":71,"photo_question":50,"text_answer":72,"step_text_answer":20,"step_photo_answer":20,"views":73,"likes":74,"slug":75},537913,"show how to do 349-231 in a base 12 system","Solution:\u003Cbr />\n1. Convert the numbers 349 and 231 from base 12 to decimal:\u003Cbr />\n- 349 base 12: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>(3 \\times 12^2) + (4 \\times 12^1) + (9 \\times 12^0) = (3 \\times 144) + (4 \\times 12) + (9 \\times 1) = 432 + 48 + 9 = 489\u003C/math-field>\u003C/math-field>\u003Cbr />\n- 231 base 12: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>(2 \\times 12^2) + (3 \\times 12^1) + (1 \\times 12^0) = (2 \\times 144) + (3 \\times 12) + (1 \\times 1) = 288 + 36 + 1 = 325\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Subtract the converted numbers in decimal:\u003Cbr />\n- Subtraction: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>489 - 325 = 164\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Convert the result back to base 12:\u003Cbr />\n- The highest power of 12 in 164 is \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>12^1\u003C/math-field>\u003C/math-field> (since \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>12^2 = 144\u003C/math-field>\u003C/math-field> is too large).\u003Cbr />\n- Divide 164 by 12: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>164 \\div 12 = 13 \\text{ remainder } 8\u003C/math-field>\u003C/math-field>\u003Cbr />\n- 13 in base 12 is represented as \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>1 \\times 12 + 1\u003C/math-field>\u003C/math-field> remainder is 1.\u003Cbr />\n- Therefore, 164 in base 12 is 118.\u003Cbr />\n\u003Cbr />\n4. Therefore, 349 base 12 minus 231 base 12 equals: \u003Cbr />\n\u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>118\u003C/math-field>\u003C/math-field> base 12.",943,189,"show-how-to-do-349-231-in-a-base-12-system",{"id":77,"category":48,"text_question":78,"photo_question":50,"text_answer":79,"step_text_answer":20,"step_photo_answer":20,"views":80,"likes":67,"slug":81},537809,"The national peanut board estimates it takes about 45 peanuts to make an ounce of peanut butter. How many more peanuts are in a 20 ounce jar than a 12 ounce jar?","1. Find the number of peanuts in a 20-ounce jar:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 20 \\text{ ounces} \\times 45 \\text{ peanuts/ounce} = 900 \\text{ peanuts} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Find the number of peanuts in a 12-ounce jar:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 12 \\text{ ounces} \\times 45 \\text{ peanuts/ounce} = 540 \\text{ peanuts} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Subtract the number of peanuts in the 12-ounce jar from the 20-ounce jar to find out how many more peanuts are in the 20-ounce jar:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 900 - 540 = 360 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\nTherefore, there are \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 360 \u003C/math-field>\u003C/math-field> more peanuts in the 20-ounce jar than in the 12-ounce jar.",320,"the-national-peanut-board-estimates-it-takes-about-45-peanuts-to-make-an-ounce-of-peanut-butter-how-many-more-peanuts-are-in-a-20-ounce-jar-than-a-12-ounce-jar",{"id":83,"category":48,"text_question":84,"photo_question":50,"text_answer":85,"step_text_answer":20,"step_photo_answer":20,"views":86,"likes":87,"slug":88},537773,"Explain Factorization in Mathematics in German","Lösung:\u003Cbr />\n1. Definition: \u003Cbr />\n- Faktorisierung bedeutet, einen mathematischen Ausdruck in ein Produkt von einfacheren Ausdrücken, sogenannten Faktoren, zu zerlegen. Diese Faktoren sind oft Primzahlen oder algebraische Ausdrücke mit geringeren Graden.\u003Cbr />\n\u003Cbr />\n2. Beispiele:\u003Cbr />\n- Faktorisierung von Zahlen: \u003Cbr />\n - Nehmen wir die Zahl \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>12\u003C/math-field>\u003C/math-field>. Die Faktorisierung von \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>12\u003C/math-field>\u003C/math-field> als Produkt von Primzahlen lautet \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2^2 \\times 3\u003C/math-field>\u003C/math-field>.\u003Cbr />\n- Algebraische Faktorisierung:\u003Cbr />\n - Betrachten wir den Ausdruck \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^2 - 5x + 6\u003C/math-field>\u003C/math-field>. Die Faktorisierung lautet \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>(x - 2)(x - 3)\u003C/math-field>\u003C/math-field>.\u003Cbr />\n\u003Cbr />\n3. Zweck:\u003Cbr />\n- Die Hauptziele der Faktorisierung sind die Vereinfachung von Ausdrücken, das Lösen von Gleichungen und die Erleichterung der Multiplikation, Addition oder Subtraktion von Brüchen.\u003Cbr />\n\u003Cbr />\n4. Praktische Anwendung:\u003Cbr />\n- Faktorisierung ist eine wichtige Technik zur Lösung quadratischer Gleichungen: \u003Cbr />\n - Zum Beispiel: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x^2 - 5x + 6 = 0\u003C/math-field>\u003C/math-field> wird durch Faktorisierung zu \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>(x - 2)(x - 3) = 0\u003C/math-field>\u003C/math-field>, was die Lösungen \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 2\u003C/math-field>\u003C/math-field> und \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>x = 3\u003C/math-field>\u003C/math-field> ergibt.",669,134,"explain-factorization-in-mathematics-in-german",{"id":90,"category":48,"text_question":91,"photo_question":50,"text_answer":92,"step_text_answer":20,"step_photo_answer":20,"views":93,"likes":94,"slug":95},537735,"Solve 3x + 2y= 5-y. Solve for y","Solution:\u003Cbr />\n1. Starting equation:\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3x + 2y = 5 - y\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Move all terms involving \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y\u003C/math-field>\u003C/math-field> to one side of the equation:\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>2y + y = 5 - 3x\u003C/math-field>\u003C/math-field>\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>3y = 5 - 3x\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Solve for \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y\u003C/math-field>\u003C/math-field> by dividing both sides by 3:\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = \\frac{5 - 3x}{3}\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Simplify if necessary:\u003Cbr />\n* \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>y = \\frac{5}{3} - x\u003C/math-field>\u003C/math-field>",1399,280,"solve-3x-2y-5-y-solve-for-y",{"id":97,"category":48,"text_question":98,"photo_question":50,"text_answer":99,"step_text_answer":20,"step_photo_answer":20,"views":100,"likes":101,"slug":102},537726,"The manufacturer profit is 146.14\nThe store price is 204.60\nWhat is the profit in percentage","Solution:\u003Cbr />\n1. Given:\u003Cbr />\n- Manufacturer's Profit: USD 146.14\u003Cbr />\n- Store Price: USD 204.60\u003Cbr />\n\u003Cbr />\n2. Calculate the profit percentage using the formula:\u003Cbr />\n- Profit Percentage = \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\left( \\frac{\\text{Profit}}{\\text{Cost Price}} \\right) \\times 100 \\%\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. The store price is taken as the cost price in this context. Thus, the profit percentage is:\u003Cbr />\n- Profit Percentage = \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\left( \\frac{146.14}{204.60} \\right) \\times 100 \\%\u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Simplify and calculate the profit percentage:\u003Cbr />\n- Profit Percentage = \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>\\left( 0.714 \\right) \\times 100 \\%\u003C/math-field>\u003C/math-field>\u003Cbr />\n- Profit Percentage = \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only>71.46 \\%\u003C/math-field>\u003C/math-field>",1408,282,"the-manufacturer-profit-is-146-14-the-store-price-is-204-60-what-is-the-profit-in-percentage",{"id":104,"category":48,"text_question":105,"photo_question":50,"text_answer":106,"step_text_answer":20,"step_photo_answer":20,"views":107,"likes":108,"slug":109},537672,"(3^(-2)×3^5)/3^6","1. Begin with the expression: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{3^{-2} \\times 3^5}{3^6} \u003C/math-field>\u003C/math-field>.\u003Cbr />\n2. Apply the properties of exponents: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 3^{-2} \\times 3^5 = 3^{-2 + 5} = 3^{3} \u003C/math-field>\u003C/math-field>.\u003Cbr />\n3. Substitute back into the expression: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{3^3}{3^6} \u003C/math-field>\u003C/math-field>.\u003Cbr />\n4. Apply the properties of exponents: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{3^3}{3^6} = 3^{3 - 6} = 3^{-3} \u003C/math-field>\u003C/math-field>.\u003Cbr />\n5. Convert to standard form: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> 3^{-3} = \\frac{1}{3^3} = \\frac{1}{27} \u003C/math-field>\u003C/math-field>.\u003Cbr />\n6. Therefore, the final answer is: \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{1}{27} \u003C/math-field>\u003C/math-field>.",361,72,"3-2-3-5-3-6",{"id":111,"category":48,"text_question":112,"photo_question":50,"text_answer":113,"step_text_answer":20,"step_photo_answer":20,"views":114,"likes":115,"slug":116},537664,"Pablo uses 3 bags of pepperoni to make 9 pepperoni pizza. He says he needs 6 bags to make 12 pepperoni pizzas. Is he correct? Explain your reasoning","1. First, we establish the ratio of bags of pepperoni to pizzas based on the information provided: \u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{3 \\text{ bags}}{9 \\text{ pizzas}} = \\frac{1 \\text{ bag}}{3 \\text{ pizzas}} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n2. Using the above ratio, determine how many bags are needed for 12 pizzas:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> \\frac{1 \\text{ bag}}{3 \\text{ pizzas}} = \\frac{x \\text{ bags}}{12 \\text{ pizzas}} \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n3. Solve for \\( x \\) by cross-multiplying and dividing:\u003Cbr />\n \u003Cmath-field read-only default-mode=\"inline-math\" class=\"math-expression\">\u003Cmath-field read-only> x = \\frac{12}{3} = 4 \u003C/math-field>\u003C/math-field>\u003Cbr />\n\u003Cbr />\n4. Compare with Pablo's claim. He said he needs 6 bags, but the calculation shows only 4 bags are necessary. \u003Cbr />\n\u003Cbr />\nAnswer: No, he is not correct.",846,169,"pablo-uses-3-bags-of-pepperoni-to-make-9-pepperoni-pizza-he-says-he-needs-6-bags-to-make-12-pepperoni-pizzas-is-he-correct-explain-your-reasoning",{"first":18,"last":118,"prev":20,"next":22},10,{"current_page":18,"from":18,"last_page":118,"links":120,"path":148,"per_page":118,"to":118,"total":14},[121,124,127,129,131,133,135,138,141,144,146],{"url":18,"label":122,"active":123},"1",true,{"url":22,"label":125,"active":126},"2",false,{"url":25,"label":128,"active":126},"3",{"url":28,"label":130,"active":126},"4",{"url":31,"label":132,"active":126},"5",{"url":34,"label":134,"active":126},"6",{"url":136,"label":137,"active":126},7,"7",{"url":139,"label":140,"active":126},8,"8",{"url":142,"label":143,"active":126},9,"9",{"url":118,"label":145,"active":126},"10",{"url":22,"label":147,"active":126},"Next 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