Mathematics: An athlete trains for 80 min each day for as many days as possible. Write an equation that relates the number of days d that the athlete spends training when the athlete trains for 560 min. Enter an equation where any numbers represent numbers of minutes

Step-by-step explanation:The given expression isWe need to factor each quadratic expressionFirst, we extract the GCF 6:Then, we look for two numbers which product is 14 and which sum is 9, thos numbers are 7 and 2, so the factored expression isWe do the same process,We need to find two numbers which product is 6 and which sum is 5, those numbers are 3 and 2We have to find two numbers which product is 56, and which difference is 1, those numbers are 8 and 7Replacing all factors in the given expression,...

An athlete trains for 80 min each day for as many

Ответ:

modelingavakin

22.04.2020

Mathematics

$\frac{3(x-2)}{2(x-3)}$

Step-by-step explanation:

The given expression is

$\frac{6x^{2} -54x+84}{8x^{2}-40x+48 } \div \frac{x^{2} +x-56}{2x^{2}+12x-32}$

We need to factor each quadratic expression

$6x^{2} -54x+84$

First, we extract the GCF 6:

$6(x^{2}-9x+14 )$

Then, we look for two numbers which product is 14 and which sum is 9, thos numbers are 7 and 2, so the factored expression is

6(x-7)(x-2)

$8x^{2} -40x+48$

We do the same process,

$8(x^{2} -5x+6)$

We need to find two numbers which product is 6 and which sum is 5, those numbers are 3 and 2

8(x-3)(x-2)

$x^{2} +x-56$

We have to find two numbers which product is 56, and which difference is 1, those numbers are 8 and 7

$x^{2} +x-56=(x+8)(x-7)$

$2x^{2} +12x-32=2(x^{2}+6x-16 )=2(x+8)(x-2)$

Replacing all factors in the given expression, we have

$\frac{6(x-7)(x-2)}{8(x-3)(x-2)} \div \frac{(x+8)(x-7)}{2(x+8)(x-2)} \\\frac{3(x-7)}{4(x-3)} \div \frac{(x-7)}{2(x-2)} \\\frac{3(x-7)}{4(x-3)} \times \frac{2(x-2)}{(x-7)} =\frac{3(x-2)}{2(x-3)}$

Therefore, the answer is

$\frac{3(x-2)}{2(x-3)}$

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An athlete trains for 80 min each day for as many days as possible. Write an equation that relates the number of days d that the athlete spends training when the athlete trains for 560 min. Enter an equation where any numbers represent numbers of minutes

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