Answer:
F has 10 marbles and I has 5 marbles.
Step-by-step explanation:
First, I subtracted 10 from 15 since F has 10 more marbles than I. When I subtracted I got 5.
Hope this helps!!!!
Answer:
128√5/3 mm³
Step-by-step explanation:
Since we are not told what to find, we can as well look for the volume of the pyramid
Volume of a square pyramid: V = (1/3)a²h
a is the side length of the square
h is the height of the pyramid
Given
a = 8mm
l² = (a/2)² + h²
l² = (a/2)² + h²
6² = (8/2)² + h²
h² = 6² - 4²
h² = 36 - 16
h² = 20
h = √20
Volume of a square pyramid = (1/3)*8²*√20
Volume of a square pyramid = 1/3 * 64 * 2√5
Volume of a square pyramid = 128√5/3 mm³
Answer:
Fraction of the original board left = 
Step-by-step explanation:
Let the length of the board is = l feet
Marty saws off 
of a wooden board.
Length of the board left = l - 
= 
feet
He saws off 
of the remaining board,
Board left = ![(\frac{4}{5})l-[(\frac{4}{5})l\times (\frac{3}{4})]](https://tex.z-dn.net/?f=%28%5Cfrac%7B4%7D%7B5%7D%29l-%5B%28%5Cfrac%7B4%7D%7B5%7D%29l%5Ctimes%20%28%5Cfrac%7B3%7D%7B4%7D%29%5D)
= 
= 
feet
He finally saws off 
rd of the remaining board.
Board left = ![\frac{1}{5}l-[\frac{1}{5}\times \frac{1}{3}]l](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7Dl-%5B%5Cfrac%7B1%7D%7B5%7D%5Ctimes%20%5Cfrac%7B1%7D%7B3%7D%5Dl)
= 
= 
feet
Fraction of the original board left = 
=
Answer: The ratio is 2.39, which means that the larger acute angle is 2.39 times the smaller acute angle.
Step-by-step explanation:
I suppose that the "legs" of a triangle rectangle are the cathati.
if L is the length of the shorter leg, 2*L is the length of the longest leg.
Now you can remember the relation:
Tan(a) = (opposite cathetus)/(adjacent cathetus)
Then there is one acute angle calculated as:
Tan(θ) = (shorter leg)/(longer leg)
Tan(φ) = (longer leg)/(shorter leg)
And we want to find the ratio between the measure of the larger acute angle and the smaller acute angle.
Then we need to find θ and φ.
Tan(θ) = L/(2*L)
Tan(θ) = 1/2
θ = Atan(1/2) = 26.57°
Tan(φ) = (2*L)/L
Tan(φ) = 2
φ = Atan(2) = 63.43°
Then the ratio between the larger acute angle and the smaller acute angle is:
R = (63.43°)/(26.57°) = 2.39
This means that the larger acute angle is 2.39 times the smaller acute angle.
