Answer:
14 2/3
Step-by-step explanation:
.....................
Answer:
Complementary
Step-by-step explanation:
To be complementary, your two angles need to add up to 90 degrees
a right triangle is already 90 degrees so if you cut it through the middle they'd form complementary angles
To solve this problem, you must follow the proccedure below:
1. T<span>he block was cube-shaped with side lengths of 9 inches and to calculate its volume (V1), you must apply the following formula:
V1=s</span>³
<span>
s is the side of the cube (s=9)
2. Therefore, you have:
V1=s</span>³
V1=(9 inches)³
V1=729 inches³
<span>
3. The lengths of the sides of the hole is 3 inches. Therefore, you must calculate its volume (V2) by applying the formula for calculate the volume of a rectangular prism:
V2=LxWxH
L is the length (L=3 inches).
W is the width (W=3 inches).
H is the heigth (H=9 inches).
4. Therefore, you have:
V2=(3 inches)(3 inches)(9 inches)
V2=81 inches
</span><span>
5. The amount of wood that was left after the hole was cut out, is:
</span>
Vt=V1-V2
Vt=648 inches³
Answer:
![\frac{2(x^{2} + 5x + 3)}{(x+3)(x+5)}](https://tex.z-dn.net/?f=%5Cfrac%7B2%28x%5E%7B2%7D%20%2B%205x%20%2B%203%29%7D%7B%28x%2B3%29%28x%2B5%29%7D)
Step-by-step explanation:
We need to sum the following two expressions:
![\frac{x}{x+3} + \frac{x+2}{x+5}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7Bx%2B3%7D%20%2B%20%5Cfrac%7Bx%2B2%7D%7Bx%2B5%7D)
![\frac{x(x+5) + (x+2)(x+3)}{(x+3)(x+5)}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%28x%2B5%29%20%2B%20%28x%2B2%29%28x%2B3%29%7D%7B%28x%2B3%29%28x%2B5%29%7D)
expanding the polynomial in the numerator:
![\frac{2x^{2} + 10x + 6}{(x+3)(x+5)}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%5E%7B2%7D%20%2B%2010x%20%2B%206%7D%7B%28x%2B3%29%28x%2B5%29%7D)
![\frac{2(x^{2} + 5x + 3)}{(x+3)(x+5)}](https://tex.z-dn.net/?f=%5Cfrac%7B2%28x%5E%7B2%7D%20%2B%205x%20%2B%203%29%7D%7B%28x%2B3%29%28x%2B5%29%7D)
This is the most simplified form we can get:
![\frac{2(x^{2} + 5x + 3)}{(x+3)(x+5)}](https://tex.z-dn.net/?f=%5Cfrac%7B2%28x%5E%7B2%7D%20%2B%205x%20%2B%203%29%7D%7B%28x%2B3%29%28x%2B5%29%7D)