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Answer:</h2>
The expression which represents the perimeter P of the rectangle as a function of L is:
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Step-by-step explanation:</h2>
The length and width of a rectangle are denoted by L and W respectively.
Also the diagonal of a rectangle is: 10 inches.
We know that the diagonal of a rectangle in terms of L and W are given by:
( Since, the diagonal of a rectangle act as a hypotenuse of the right angled triangle and we use the Pythagorean Theorem )
Hence, we have:
But we know that width can't be negative. It has to be greater than 0.
Hence, we have:
Now, we know that the Perimeter of a rectangle is given by:
Here we have:
Answer:
174.6 ft
Step-by-step explanation:
It can be helpful to draw a diagram of the triangle we're concerned with. (See attached.)
We know the angle at the end of the shadow inside the triangle is 52°-22° = 30°. We assume the tree is growing straight up out of the hillside, so its angle with the hill inside the triangle is 90°+22° = 112°. Then the remaining angle between the shadow and the tree at the top of the tree is ...
180° -30° -112° = 38°
Now, we have the angle opposite the tree, and the angle opposite the known side length of the triangle (215 feet along the hill, AC in the diagram). This is enough information to usefully use the Law of Sines.
c/sin(C) = a/sin(A)
c = a(sin(C)/sin(A)) = (215 ft)(sin(30°)/sin(38°)) ≈ 174.6 ft
The height of the tree is about 174.6 feet.
Answer:
50
Step-by-step explanation:
Because of supplementary angles that line has to equal to 180
180-75 = 105
so 105 = (2x + 5)
you can subtract 5 from each side and get
100 = (2x)
then divide each side by 2 and you get
x = 50
you can check it by doing (2 x 50 + 5)
2 x 50 = 100 + 5 = 105 + 75 = 180
The area of any rectangle is:
A=xy, and a square is just a special rectangle where the two dimensions are equal. x=y=s, where s is the side length so the area of a square is:
A=s^2 we want to solve for s so
s^2=A
s=√A, and we are told that the area is 113 in^2
s=√113 in
s≈10.63 in (to nearest hundredth of an inch)
Answer:
c. 15
Step-by-step explanation: 15 is divisible by 3
