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:
Function; Not a function
Step-by-step explanation:
Write the ordered pair in the first set (x, y): (1, 11), (2, 7) , (3, 2)
Write the ordered pair in the second set (x, y): (1, 3), (1, 4), (2, 4) , (3, 2)
The first set in a function because no ordered pair has the same x value.
The second set in not a function because the x value is the same in two of the ordered pairs.
Answer:
B is 22.12 degrees; ∠C is 57.88°; c=29.24
Step-by-step explanation:
So, first, it's important to draw a diagram of the triangle the problem is talking about (see attached picture).
Once the triangle has been drawn, we can visualize it better and determine what to do. So first, we are going to find what the value of angle B is by using law of sines:

which can be solved for angle B:


and substitute the values we already know:

which yields:
B=22.12°
Once we know what the angle of B is, we can now find the value of angle C by using the fact that the sum of the angles of any triangle is equal to 180°. So:
A+B+C=180°
When solving for C we get:
C=180°-A-B
C=180°-22.12°-|00°=57.88°
So once we know what angle C is, we can go ahead and find the length of side c by using the law of sines again:

and solve for c:

so we can now substitute for the values we already know:

which yields:
c=29.24