Answer:
4 units
Step-by-step explanation:
The volume of a square pyramid is (a²)*h/3
256=a²*12/3
256=a²*4
256/4=a²
64=a²
a=8
Now we know that the square is 8 by 8.
The volume of a square prism is a²h
256=64h
256/64=h
h=4
Also, a square pyramid is 1/3 the volume of a square prism.
12÷3=4
31.

32.

33.

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Answer:
B. y= 2x–15
Step-by-step explanation:
The equation that represents the line that passes through the points (8, 1) and (10,5) is y= 2x–15
"x" is found on the left hand side of the bracket and "y" is found on the right hand side of the bracket :)
(8, 1) and (10, 5)
x in the first bracket is 8 and x in the second bracket is 10.
y in the first bracket is 1 and y in the second bracket is 5.
When this equation is applied to find the value for y we get:
y= 2x-15
y= 2(8)-15
y= 16-15
y= 1
y= 2x-15
y= 2(10)-15
y= 20-15
y= 5
We got back the values of y and this means that the equation was correctly chosen and the answer is correct :)
Let the acute angle be 2x.
Its complement is 90 - 2x.
It is given that this complementary angle is less than each of the bisected angle.
Therefore, 90 - 2x < x
90 < 3x
or, x > 30.
2x > 60
Therefore, the statement is true for all angles that are greater than 60 degrees.
Answer:
6 gallons per minute
Step-by-step explanation:
Let the function that models the quantities of water, Q (in gallons) in a pool over time, t (in minutes), is
Q = a + bt ........... (1)
Now, Q(t = 0) is given to be 50 gallons.
So, a = 50 and b denotes the rate at which the quantity of water in the pool is decreasing and it is given by the slope of equation (1).
Now, two points on the graph are (0,50) and (1,44).
So, the slope = b = = - 6 gallons per minute.
Therefore, the equation of this situation is given by Q = 50 - 6t, where the slope is equal to - 6 gallons per minute. (Answer)