11. If x + 2y = 8, and x - y = 5, what is the value of x?
(A) 1
(B) 2
(C) 3
(D) 6
(E) 18
12. If the volume of a cube is 512 cubic inches, what is the edge length of the cube, in inches?
(A) 6
(B) 8
(C) 12
(D) 32
(E) 64
Answer (2)
To solve these problems, we need to approach each one step by step.
Problem 11: Given the system of equations:
x + 2 y = 8
x − y = 5
We want to find the value of x . Let's use the method of substitution or elimination to solve the system of equations.
Step 1: Solve one of the equations for x. Using equation (2): x = y + 5
Step 2: Substitute this expression into the other equation. Now, substitute x = y + 5 into equation (1): ( y + 5 ) + 2 y = 8
Step 3: Simplify and solve for y. y + 5 + 2 y = 8 3 y + 5 = 8 3 y = 3 y = 1
Step 4: Substitute back to find x. Substitute y = 1 back into x = y + 5 : x = 1 + 5 x = 6
The value of x is 6.
The correct choice is (D) 6.
Problem 12: The volume of a cube is given as 512 cubic inches. We need to find the edge length of the cube.
Step 1: Use the formula for the volume of a cube. The volume V of a cube with edge length s is given by the formula: V = s 3
Step 2: Substitute and solve for s. Since the volume is 512 cubic inches, we have: s 3 = 512
To find s , we need to find the cube root of 512: s = 3 512
Calculating the cube root: 3 512 = 8
So, the edge length of the cube is 8 inches.
The correct choice is (B) 8.
For Problem 11, the value of x is 6 (D). For Problem 12, the edge length of the cube is 8 inches (B).
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