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Sveta_85 [38]
3 years ago
9

What is the solution for the system of equations? Use the substitution method to solve. y=5−3x5x−4y=−3 Enter your answer in the

boxes.
Mathematics
1 answer:
velikii [3]3 years ago
5 0

y=5-3x\\5x-4y=-3\\\\5x-4(5-3x)=-3\\5x-20+12x=-3\\17x-20=-3\\17x=-3+20\\17x=17\\x=17/17\\x=1\\\\y=5-3x\\y=5-3(1)\\y=5-3\\y=2\\\\5x-4y=-3\\5(1)-4(2)=-3\\5-8=-3\\-3=-3

So:

x=1

y=2

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What is the area of a parallelogram whose vertices are A(−12, 2) , B(6, 2) , C(−2, −3) , and D(−20, −3) ? Enter your answer in t
nikdorinn [45]

Let

A(-12,2)\\B(6,2)\\C(-2,-3) \\D(-20.-3)\\E(-12.-3)

using a graphing tool

see the attached figure to better understand the problem

we know that

Parallelogram is a quadrilateral with opposite sides parallel and equal in length

so

AB=CD \\AD=BC

The area of a parallelogram is equal to

A=B*h

where

B is the base

h is the height

the base B is equal to the distance AB

the height h is equal to the distance AE

Step 1

<u>Find the distance AB</u>

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

A(-12,2)\\B(6,2)

substitute the values

d=\sqrt{(2-2)^{2}+(6+12)^{2}}

d=\sqrt{(0)^{2}+(18)^{2}}

dAB=18\ units

Step 2

<u>Find the distance AE</u>

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

A(-12,2)\\E(-12.-3)

substitute the values

d=\sqrt{(-3-2)^{2}+(-12+12)^{2}}

d=\sqrt{(-5)^{2}+(0)^{2}}

dAE=5\ units

Step 3

<u>Find the area of the parallelogram</u>

The area of a parallelogram is equal to

A=B*h

A=AB*AE

substitute the values

A=18*5=90\ units^{2}

therefore

<u>the answer is</u>

the area of the parallelogram is 90\ units^{2}

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I think is...

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Answer:

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Explain why the vertical line test is used to determine if a graph represents a function.
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