Step-by-step explanation:
Pythagoras (for right-angled triangles) :
c² = a² + b²
c being the Hypotenuse, the side opposite of the right angle. and that would be here the diagonal.
c = diagonal = 10 ft
therefore, the width of the rectangle is 10/2 = 5 ft
10² = 5² + b²
100 = 25 + b²
b² = 75
b = length = sqrt(75) = 8.660254038... ft
Answer: 9/81
Step-by-step explanation:
I did 3 to the second power then 3 to the fourth power. Then put them on top of each other. If the over is supposed to mean division then the answer would be 9.
Answer:
y = 3
+ 4
Step-by-step explanation:
Create 2 equations using values from the table to find a and b.
Using (0, 10), then
10 = acos0° + b ( cos0° = 1 ), thus
a + b = 10 → (1)
Using (90, 4), then
4 = acos90° + b ( cos90° = 0 ), thus
b = 4
Substitute b = 4 into (1)
a + 4 = 10 ( subtract 4 from both sides )
a = 6
Thus
y = 6cosx° + 4
When x = 45°, then
y = 6cos45° + 4 = 6 × 
+ 4 = 3 + 4
<h3>
Answer: 7 cm</h3>
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Explanation:
x = side length of the original square (measured in cm).
One side increases by 8 cm to go from x to x+8. At the same time, an adjacent side decreases from x to x-2 (aka it decreases by 2 cm).
The x by x square turns into a x+8 by x-2 rectangle.
L = x+8 = length
W = x-2 = width
P = perimeter of rectangle
P = 2(L+W)
P = 2(x+8+x-2)
P = 2(2x+6)
P = 4x+12
The perimeter of this rectangle is 4x+12, which is set equal to the stated perimeter 40 cm. We'll use this to solve for x.
P = 40
4x+12 = 40
4x = 40-12
4x = 28
x = 28/4
x = 7
The square originally had side lengths of 7 cm.
Increasing this by 8 cm gets us x+8 = 7+8 = 15 cm. So L = 15.
Also, W = x-2 = 7-2 = 5 cm is the width.
Then note how P = 2(L+W) = 2(15+5) = 40 to help confirm the answer.
