Answer:
The side length is multiplied by 6.
Step-by-step explanation:
The area of a square is A = s². Suppose the side is 8 inches. This means the area is A = 8² = 64.
If you were to multiply by 36, then it becomes 64*36 = 2,304. Since squaring gave the area, it's side length would be found using the reverse operation a square root. Take the square root of 2,304.
√2304 = 48
The side length changed from 8 to 48 which is a scale factor of 6. This means 8 * 6 = 48.
Answer: Kim can mow the greens alone in 6 hours.
Step-by-step explanation:
Let K be the rate Kim mows the greens, and S the rate for Shayla. The rates K and S will be in greens/hour.
We know they can mow 1 green in 4 hours. We can state this as a sum of their rates times the 4 hours equals one green:
(4 hours)*(K + S) = 1 green
We are told that K = 2S [Kim is twice as fast as Shayla]
Subsititute:
(4 hours)*(K + S) = 1 green
(4 hours)*(2S + S) = 1 green
4*(2S + S) = 1 green
12S = 1 green
Shalya's rate is 1 green/12 hours
Kim is twice as fast: K = 2S
Kim's rate is 1 green/6 hours.
First, we are going to find the vertex of our quadratic. Remember that to find the vertex

of a quadratic equation of the form

, we use the vertex formula

, and then, we evaluate our equation at

to find

.
We now from our quadratic that

and

, so lets use our formula:




Now we can evaluate our quadratic at 8 to find

:




So the vertex of our function is (8,-72)
Next, we are going to use the vertex to rewrite our quadratic equation:



The x-coordinate of the minimum will be the x-coordinate of the vertex; in other words: 8.
We can conclude that:
The rewritten equation is

The x-coordinate of the minimum is 8
1 quart = 32 ounces
She will need 13 quarts <span>of coffee.</span>
Answer:
x² + 10x - 24
Step-by-step explanation:
3x² - 12 + (x - 4)(2 - x) - (x² - 4x + 4)
= 3x² - 12 + (2x - x² - 8 + 4x) - x² + 4x - 4
= 3x² - 12 + 2x - x² - 8 + 4x - x² + 4x - 4
= x² + 10x - 24