All the interior angles of a triangle always add up to 180 degrees.
3x + (2x + 20) + (4x - 20) = 180
3x + 2x + 20 + 4x - 20 = 180
3x + 2x + 4x + 20 - 20 = 180
10x = 180
x = 180/10
Therefore, x = 18
Answer:
69
Step-by-step explanation:
5(
–
q+6)=
–
20
5q–30=
–
20
Add -5 to both sides
Subtract -5 from both sides
Multiply both sides by -5
Divide both sides by -5
Apply the distributive property
5q=
Add 30 to both sides
q=
Divide both sides by 5 would be 69
9514 1404 393
Answer:
B. Figure B
Step-by-step explanation:
The figure is difficult to read. We assume the height of the pyramid is 9, and the radius of the cylinder is 1.
The pyramid volume is ...
V = 1/3Bh
V = 1/3(4²)(9) = 48 . . . cubic units
__
The cylinder volume is ...
V = πr²h
V = π(1²)(48) = 48π . . . cubic units
The cylinder has π times as much volume as the pyramid. Figure B is larger.
_____
<em>Additional comment</em>
If the diameter (not the radius) of the cylinder is 1 unit, then its volume is 12π cubic units and the pyramid has more volume.
Answer:
a. 
and 41.6
b. 52.1
Step-by-step explanation:
a.
Considering the left side triangle the blue dotted side is the side "opposite" to the angle given and the side 24 is the side that is "adjacent" to the angle given. The trigonometric ratio tan relates opposite to adjacent. Also, let the blue dotted side be y.
<u>Note:</u> the exact value of tan 60 is 
Thus, we can write 
Approximate value (rounded to nearest tenth): 
b.
Considering the triangle to the right, the side "opposite" to the angle given (53 degrees) is 41.6 (just found in part (a)) and the side "hypotenuse" (side opposite to 90 degree angle) is x. The trigonometric ratio sine relates opposite and hypotenuse.
Thus we can write and solve:
Answer:
The y-intercept is 33ft.
Step-by-step explanation:
The ball is 33 feet away from the wall.
It will take the ball 11 seconds to touch the wall.
The slope is -3 feet. The ball is rolling towards the wall at 3 ft per second.
I hope this helps!
~Princess <3
