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liberstina [14]

3 years ago

13

If the perimeter of a square is 4x - 24, what is the area of the square?

1 answer:

DedPeter [7]3 years ago

7 0

Answer:

A = (x - 6)² sq. units or

A = (x² - 12x + 36) sq. units

Step-by-step explanation:

P = 4s, where s is the side.

4s = 4x - 24

s = x - 6

A = s²

A = (x - 6)² sq. units or

A = (x² - 12x + 36) sq. units

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I need help with questions #7 and #8 plz

katen-ka-za [31]

Answer:

7. A = 40.8 deg; B = 60.6 deg; C = 78.6 deg

8. A = 20.7 deg; B = 127.2 deg; C = 32.1 deg

Step-by-step explanation:

Law of Cosines

$c^2 = a^2 + b^2 - 2ab \cos C$

You know the lengths of the sides, so you know a, b, and c. You can use the law of cosines to find C, the measure of angle C.

Then you can use the law of cosines again for each of the other angles. An easier way to solve for angles A and B is, after solving for C with the law of cosines, solve for either A or B with the law of sines and solve for the last angle by the fact that the sum of the measures of the angles of a triangle is 180 deg.

7.

We use the law of cosines to find C.

$18^2 = 12^2 + 16^2 - 2(12)(16) \cos C$

$324 = 144 + 256 - 384 \cos C$

$-384 \cos C = -76$

$\cos C = 0.2$

$C = \cos^{-1} 0.2$

$C = 78.6^\circ$

Now we use the law of sines to find angle A.

Law of Sines

$\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$

We know c and C. We can solve for a.

$\dfrac{a}{\sin A} = \dfrac{c}{\sin C}$

$\dfrac{12}{\sin A} = \dfrac{18}{\sin 78.6^\circ}$

Cross multiply.

$18 \sin A = 12 \sin 78.6^\circ$

$\sin A = \dfrac{12 \sin 78.6^\circ}{18}$

$\sin A = 0.6535$

$A = \sin^{-1} 0.6535$

$A = 40.8^\circ$

To find B, we use

m<A + m<B + m<C = 180

40.8 + m<B + 78.6 = 180

m<B = 60.6 deg

8.

I'll use the law of cosines 3 times here to solve for all the angles.

Law of Cosines

$a^2 = b^2 + c^2 - 2bc \cos A$

$b^2 = a^2 + c^2 - 2ac \cos B$

$c^2 = a^2 + b^2 - 2ab \cos C$

Find angle A:

$a^2 = b^2 + c^2 - 2bc \cos A$

$8^2 = 18^2 + 12^2 - 2(18)(12) \cos A$

$64 = 468 - 432 \cos A$

$\cos A = 0.9352$

$A = 20.7^\circ$

Find angle B:

$b^2 = a^2 + c^2 - 2ac \cos B$

$18^2 = 8^2 + 12^2 - 2(8)(12) \cos B$

$324 = 208 - 192 \cos A$

$\cos B = -0.6042$

$B = 127.2^\circ$

Find angle C:

$c^2 = a^2 + b^2 - 2ab \cos C$

$12^2 = 8^2 + 18^2 - 2(8)(18) \cos B$

$144 = 388 - 288 \cos A$

$\cos C = 0.8472$

$C = 32.1^\circ$

8 0

2 years ago

What is the first step in solving the equation?<br><br> 14 = -2m

ollegr [7]

Answer:

first you need to divide each side by -2

Step-by-step explanation:

start with dividing by -2, then you are left with -7 = m which is the answer.

7 0

2 years ago

3912 divided by 48!!!!!!!!! Pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeee

iogann1982 [59]

Answer:

81.5

Step-by-step explanation:

7 0

2 years ago

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What is the constant of posprtainality in the equation y=0.41

KATRIN_1 [288]

Answer:

The constant of proportionality in the equation y=0.41 is 0.41

Step-by-step explanation:

5 0

2 years ago

Evaluate x2 + y3. If x =2 and y=1/4. Write your answer in simplest form. I need it now!

mart [117]

If x equals 2 and y equals 1/4 , the equation is 2 • 2 + 1/4 • 3
and that equals 4.75

8 0

3 years ago

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