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2 years ago

58 - 8x = 30x - 75 Need help

Mathematics

1 answer:

Sever21 [200]2 years ago

5 0

Steps to solve:

58 - 8x = 30x - 75

~Subtract 58 to both sides

-8x = 30x - 133

~Subtract 30x to both sides

-38x = -133

~Divide -38 to both sides

x = 3.5

Best of Luck!

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Fine length of BC on the following photo.

MrMuchimi

Answer:

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Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

In the right triangle ACD

Find the length side AC

Applying the Pythagorean Theorem

$AC^2=AD^2+DC^2$

substitute the given values

$AC^2=16^2+8^2$

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step 2

In the right triangle ACD

Find the cosine of angle CAD

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substitute the given values

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step 3

In the right triangle ABC

Find the cosine of angle BAC

$cos(\angle BAC)=\frac{AC}{AB}$

substitute the given values

$cos(\angle BAC)=\frac{8\sqrt{5}}{16+x}$ ----> equation B

step 4

Find the value of x

In this problem

$\angle CAD=\angle BAC$ ----> is the same angle

equate equation A and equation B

$\frac{8\sqrt{5}}{16+x}=\frac{2}{\sqrt{5}}$

solve for x

Multiply in cross

$(8\sqrt{5})(\sqrt{5})=(16+x)(2)\\\\40=32+2x\\\\2x=40-32\\\\2x=8\\\\x=4\ units$

$DB=4\ units$

step 5

Find the length of BC

In the right triangle BCD

Applying the Pythagorean Theorem

$BC^2=DC^2+DB^2$

substitute the given values

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$BC^2=80$

$BC=\sqrt{80}\ units$

simplify

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