Answer:
b
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The volume of a pyramid is one third the height times the area of the base.
V = ⅓ h A
The base is a square, so the area is the width times length.
V = ⅓ h wl
Problem is, we don't know the height, only the slant length. But we can use this to find the height.
If we cut a cross section down the middle of the pyramid, we get an isosceles triangle. The base of the triangle is 24, and the legs are 37.
If we cut this triangle in half, we get two right triangles. Each right triangle has a base of 12 and a hypotenuse of 37.
Now we can use Pythagorean theorem to find the height of the triangle, which is also the height of the pyramid.
c² = a² + b²
37² = 12² + h²
h = 35
Now we can find the volume. h = 35, w = 24, and l = 24:
V = ⅓ h wl
V = ⅓ (35) (24) (24)
V = 6720
So the volume is 6720 ft³, or answer A.
Answer:
Step-by-step explanation:
Let represent the length of the rectangle. The width can be represented as .
The perimeter of a rectangle with lengths and is given by .
Thus, we have:
The width is then .
Answer:
x = -1 and y = 18
Step-by-step explanation:
Given the system of equations
y + 8x = 10... 1
2y - 4x = 40 ... 2
From 1; y = 10-8x
Substitute into 2;
2(10-8x) - 4x = 40
20 - 16x - 4x = 40
20 - 20x = 40
-20x = 40 - 20
-20x = 20
x = -1
Recall that y = 10-8x
y = 10 - 8(-1)
y = 10 + 8
y = 18
therefore your answer is x = -1 and y = 18
Answer:
27 pages.
Step-by-step explanation:
Let l be the number of pages in the long paper and s be the number of pages in the short paper.
We have been given that the total number of pages for both papers is 40. We can represent this information in an equation as:
We are also told that the number of pages in the long paper is one more than two times the number of pages in the short paper. We can represent this information in an equation as:
We will use substitution method to solve system of linear equations.
From equation (1) we will get,
Upon substituting this value in equation (2) we will get,
Upon adding 2l to both sides of our equation we will get,
Let us divide both sides of our equation by 3 we will get,
Therefore, there must be 27 pages in the long paper.