1. The formula V=lwh is used to find the volume of rectangular prisms. Which equation solves for w?
a. w=V-l-h
b. w=Vlh
c. w=lh/V
D. w=V/lh
2. Mr. Marsupial invested $8,000, part at 6% interest and the reamainder at 8% interest. At the end of the first year he received &600 i interest. How much money did he invest at 6%?
3. Which equation is equivalent to y-1=-3/4(x-1)?
A. 4x+3y=7
B. 3x+4y=7
C. 3x+4y=1
D. 4x+3y=1
(D) $2000 (B)
1. To solve for "w" in the equation V = lwh, you need to isolate "w" on one side of the equation. Let's see which option accomplishes that:
a. w = V - l - h (This option subtracts l and h from V, which is not correct)
b. w = Vlh (This option multiplies V, l, and h, which is not correct)
c. w = lh/V (This option divides lh by V, which is not correct)
D. w = V/lh (This option divides V by lh, which is the correct way to solve for "w")
Therefore, the correct answer is option D: w = V/lh.
2. Let's solve this problem step-by-step:
Let x be the amount of money Mr. Marsupial invested at 6% interest.
Since the total investment was $8,000, the amount invested at 8% interest is (8000 - x).
The interest earned from the 6% investment can be calculated using the formula: Interest = Principal * Rate * Time.
So, the interest earned from the 6% investment is 0.06x.
Similarly, the interest earned from the 8% investment is 0.08(8000 - x).
According to the problem, the total interest earned at the end of the first year is $600.
Now, we can set up the equation:
0.06x + 0.08(8000 - x) = 600
To solve this equation, you would need to simplify and solve for x.
3. Let's solve this equation step-by-step:
Given equation: y - 1 = -3/4(x - 1)
To make it easier to work with, we can distribute -3/4 to (x - 1):
y - 1 = (-3/4)x + 3/4
Now, let's rearrange this equation to match the options given:
Option A: 4x + 3y = 7 (This equation is not equivalent to the given equation)
Option B: 3x + 4y = 7 (This equation is not equivalent to the given equation)
Option C: 3x + 4y = 1 (This equation is not equivalent to the given equation)
Option D: 4x + 3y = 1 (This equation is equivalent to the given equation)
Therefore, the correct answer is option D: 4x + 3y = 1.