Answer:
36 ft by 16 ft
Step-by-step explanation:
To solve this problem, you need to find dimensions of a rectangle such that the perimeter is 104 ft and the area is 576 ft. The perimeter is twice the sum of length and width, so the sum of length and width is 52 ft.
The area is the product of length and width, so if w represents the width, we have ...
w(52 -w) = 576
w² -52w = -576 . . . . . eliminate parentheses, multiply by -1
w² -52w +26² = 26² -576 . . . . . . complete the square
(w -26)² = 676 -576 = 100
w = 26 ±√100 = {16, 36}
If the width is the short dimension, it is 16 feet. Then the length is 36 feet.
The answer is D. Three over two
Answer: 
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Work Shown:
Apply the following trig identity
Now let's rationalize the denominator
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As confirmation, you can use the idea that if x = y, then x-y = 0. We'll have x = tan(165) and y = -2+sqrt(3). When computing x-y, your calculator should get fairly close to 0, if not get 0 itself.
Or you can note how
which helps us see that they are the same thing.
Further confirmation comes from WolframAlpha (see attached image). They decided to write the answer as 
but it's the same as above.
-7 + 3w = 4w - 8
-7 = 4w - 8 - 3w
-7 = w - 8
-7 + 8 = w
1 = w
hope this helped, blessings! :)
Answer:
x=-6, y=0
Step-by-step explanation:
Use the 3x-9y=-18 equation and add 9y to both sides to have 3x on its own on the left side. Then, divide by 3 on both sides. Then you'll have x=-6+3y. Plus this back into the 5x+4y=-30 equation and you'll get 5(-6+3y)+4y=-30. Use the distributive property and you'll get -30+15y+4y=-30. Simplify and get -30+19y=-30, then add 30 to both sides and you'll get 19y=0. Divide by 19 on both sides and you'll get y=0. Now that we know y=0, plug that back into the 5x+4y=-30 equation, and you'll get 5x+4(0)=-30. Simplify and you'll get 5x=-30. Divide by 5 on both sides and you'll get x=-6.
