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3 years ago

Solve the following system of equations by substitution and select the correct answer below:

Mathematics

2 answers:

Bingel [31]3 years ago

6 0

Answer:

Step-by-step explanation:

2x-8y=32

Alexxx [7]3 years ago

5 0

Okay so for substitution, chose one of of the equations to solve for x. Let's solve for the second one. So you have 2x-8y=32.
Start by adding 8y to both sides:
2x=8y+32.
Then you have to get x by itself so you divide both sides by 2 which will give you:
x=4y+16.

Now you have:
6x-4y=36
x=4y+16 (this was 2x-8y=32)

Now, plug in the second equation to the first one. You would do so by plugging in the second equation to where you see x. You would have:
6(4y+16)-4y=36

Now, multiply the 6 with the 4y and 16. you would then have:
24y+96-4y=36.

Now, combine your like terms to get:
20y+96=36
Then subtract 96 to both sides:
20y=-60
Then divide both sides so that you have y all by itself:
y=-30!

You now have the answer for y, so now plug what you got for y into the other equation: x+4y=16:
x+4(-30)=60
Solve for x:
x-120=60
add 120 to both sides:
x=180!
so Your answer is Y=-30 and X=180

I hope this helped:)

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An observer at the top of a 532 foot cliff measures the angle of depression from the top of the cliff to a point on the ground t

Over [174]

Answer:

Distance from the base of the cliff to the point on the ground = 7608 feet

Step-by-step explanation:

Given: Height of the cliff is 532 feet, angle of depression from the top of the cliff to a point on the ground is equal to 4 degrees.

To find: distance from the base of the cliff to the point on the ground

Solution:

In ΔABC,

$\angle ACB=4^{\circ}$ (Alternate interior angles)

For any angle $\theta$ , $\tan \theta =$ side opposite to angle/side adjacent to angle

$\tan C=\frac{AB}{BC}$

Put $AB=532\,,\,\angle C=4^{\circ}$

$\tan 4^{\circ}=\frac{532}{BC}\\\\BC=\frac{532}{\tan 4^{\circ}}\\\\=7607.95\\\\\approx 7608\,\,feet$

Distance from the base of the cliff to the point on the ground = 7608 feet

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3 years ago

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cestrela7 [59]

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