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2 years ago

Help this is really hard

Mathematics

2 answers:

scoundrel [369]2 years ago

4 0

Answer:

x = 18, y = 45

Step-by-step explanation:

4x - 7 + a = 180 (linear pair)

But, a = 6x + 7 (alternate interior angles)

=> 4x - 7 + 6x + 7 = 180

=> 10x = 180

=> x = 18

Now, 3y - 20 = 6x + 7 (vertically opposite angles)

=> 3y - 20 = 6(18) + 7

=> 3y = 108 + 7 + 20

=> 3y = 135

=> y = 45

Hope it helps :)

Please mark my answer as the brainliest

kakasveta [241]2 years ago

3 0

Answer:

x=18, y=45

Step-by-step explanation:

I'm in algebra 2, so i don't remember theorem names anymore. But I think I know how to solve it. M and N are parallel, which means that the angles that form are equal to each other on opposite sides. We also know that a flat line adds up to 180 degrees. 6x+7 + 4x-7 add up to 180. (They are not equal angles) Solve for x. 10x=180 x=18.

Now for the y value. 6x+7 and 3y-20 are equal to each other, because they are opposite angles. 6(18)+7=115. set y equal to 115. 3y-20=115. 3y=135

y=45

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we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form $y/x=k$ or $y=kx$

in this problem we have

the point $(5,12)$ is on the line of direct variation

Find the constant of proportionality k

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the equation is

$y=\frac{12}{5}x$

Remember that

If a point is on the line of direct variation

then

the point must satisfy the equation of direct variation

we're proceeding to verify each point

case A) point $(0,0)$

$x=0\ y=0$

Substitute the value of x and y in the direct variation equation

$0=\frac{12}{5}*0$

$0=0$ -------> is true

therefore

the point $(0,0)$ is on the line of direct variation

case B) point $(2.5,6)$

$x=2.5\ y=6$

Substitute the value of x and y in the direct variation equation

$6=\frac{12}{5}*2.5$

$6=6$ -------> is true

therefore

the point $(2.5,6)$ is on the line of direct variation

case C) point $(3,10)$

$x=3\ y=10$

Substitute the value of x and y in the direct variation equation

$10=\frac{12}{5}*3$

$10=7.2$ -------> is not true

therefore

the point $(3,10)$ is not on the line of direct variation

case D) point $(7.5,18)$

$x=7.5\ y=18$

Substitute the value of x and y in the direct variation equation

$18=\frac{12}{5}*7.5$

$18=18$ -------> is true

therefore

the point $(7.5,18)$ is on the line of direct variation

case E) point $(12.5,24)$

$x=12.5\ y=24$

Substitute the value of x and y in the direct variation equation

$24=\frac{12}{5}*12.5$

$18=30$ -------> is not true

therefore

the point $(12.5,24)$ is not on the line of direct variation

case F) point $(15,36)$

$x=15\ y=36$

Substitute the value of x and y in the direct variation equation

$36=\frac{12}{5}*15$

$36=36$ -------> is true

therefore

the point $(15,36)$ is on the line of direct variation

therefore

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$(2.5,6)$

$(7.5,18)$

$(15,36)$

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