90x^2+15x-30 (hope this helps)
Answer:
- C) (x − 3)2 = 25
- C) Factor out 4 from 4x2 + 40x.
Step-by-step explanation:
1. Adding the square of half the x-coefficient to both sides of the equation will "complete the square." That square is 9, so the result on the right is 16+9 = 25. Only selection C matches.
___
2. To complete the square, you want to be able to put the quadratic into the form a(x -h)^2 = -k. For the purpose, it is most convenient to first factor "a" from the given quadratic. Then you can determine "-h" to be half the x-coefficient inside the parentheses.
Here, that looks like ...
4(x² +10x) = 80 . . . . . . . . . . step 1: factor out 4
4(x² +10x +25) = 180 . . . . . add 25 inside parentheses and the same number (4·25) on the right side of the equation
4(x +5)² = 180 . . . . . . . . . . . written as a square
So we know if there are 5 groups/dozens of Monarch butterflies, there are 2 groups/dozens of Queen butterflies. In other words, there are 5 Monarch butterflies for every 2 Queen butterflies.
Then we can turn that into an equation.

From the last equation we wrote we can see that the total number of butterflies in the farm is

.
When we compare the Queen butterflies to total butterflies, we get

The ratio of Queen butterflies to total butterflies is 2:7.
Answer:
15 degrees
Step-by-step explanation:
2.5x6= 15
Answer:
Test statistic:
z = (0.67 - 0.63) / 0.033 = 1.21
p - Value = P(z > 1.21) = 0.106
My conclusion: Fail to reject null hypothesis
No, there is no evidence of a difference