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3 years ago

Find the midpoint of the segment with the given endpoints. (2, -6) and (9,2)

Mathematics

1 answer:

vitfil [10]3 years ago

4 0

Answer:

(5.5,-2)

Step-by-step explanation:

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3 years ago

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Step-by-step explanation:

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3 years ago

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3 years ago

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3 years ago

55. If 3x = 4y, the value of (x + y)^2 : (x - y)^2 is:

ladessa [460]

Answer:

$\large\boxed{(x+y)^2:(x-y)^2=49}$

Step-by-step explanation:

$3x=4y\qquad\text{subtract}\ 3y\ \text{from both sides}\\\\3x-3y=y\qquad\text{distributive}\\\\3(x-y)=y\qquad\text{divide both sides by 3}\\\\x-y=\dfrac{y}{3}\qquad(*)\\------------------\\3x=4y\qquad\text{add}\ 3y\ \text{to both sides}\\\\3x+3y=7y\qquad\text{distributive}\\\\3(x+y)=7y\qquad\text{divide both sides by 3}\\\\x+y=\dfrac{7y}{3}\qquad(**)\\------------------$

$(x+y)^2:(x-y)^2=\dfrac{(x+y)^2}{(x-y)^2}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\=\left(\dfrac{x+y}{x-y}\right)^2\qquad\text{substitute}\ (*)\ \text{and}\ (**)\\\\=\left(\dfrac{\frac{7y}{3}}{\frac{y}{3}}\right)^2=\left(\dfrac{7y}{3}\cdot\dfrac{3}{y}\right)^2\qquad\text{cancel}\ 3\ \text{and}\ y\\\\=(7)^2=49$

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3 years ago