Answer:
q=1
Step-by-step explanation:
5+4q=6+3q
subtract 3q on both sides
5+q=6
subtract 5 on both sides
q=1
BRANLIEST PLZ!!!!
Micah was asked to add the following expressions:

First, he combined like terms in the numerator and kept the common denominator
First step is correct. He added the like terms in the numerator, because the denominators are same.

So he got , 
In the next step, he cannot cancel out x^2 from the top and bottom . Because x-4 and 3x+2 are added with x^2
If we have x^2 is multiplied with other terms at the top and bottom , then we can cancel out x^2.
So Micah added the expression incorrectly. Final answer is not correct.
Rationalizing the denominator involves exploiting the well-known difference of squares formula,

We have

so that

Rewrite 16 and 32 as powers of 2, then simplify:






So we have <em>A</em> = 8, <em>B</em> = 2, <em>C</em> = 4, and <em>D</em> = 7, and thus <em>A</em> + <em>B</em> + <em>C</em> + <em>D</em> = 21.
Answer:
Length = 11
Width = 6
Step-by-step explanation:
We know that the length is x and the width is x - 5 since it is 5 less than the length.
The equation to find the perimeter of a rectangle is 2w + 2l
We will plug in the values and solve
2(x-5) + 2(x) = 34
2x - 10 + 2x = 34
4x - 10 = 34
4x = 44
x = 11
Since the length is simply x, we know that it is 11. We subtract 5 to find the width.
11 - 5 = 6.
The width is 6.
Answer:
500 lbs of mixed nuts
Step-by-step explanation:
15.4% of mixed nuts = 77 lbs of pecans
Divide the weight of pecans by the percent of mixed nuts to find how many pounds of pecans equal 1% of the mixed nuts:
77 / 15.4 = 5, so 5 lbs equals 1% of mixed nuts
Now multiply that number by 100 to get 100% of mixed nuts:
5 x 100 = 500
Therefore, there are 500 lbs of mixed nuts in a batch altogether.
To check, 15.4% = 15.4/100 = 0.514
Therefore, 15.4% of 500 = 0.514 x 500 = 77
Thereby proving that 15.4% of 500 is 77.