Because the coefficient of x^2 is -1, we know that a will be -1. Knowing that the coefficient of x is -4, we can calculate that p=2. Thus, we have -1(x+2)^2+q is our equation. This is equal to -x^2-4x-4+q. As the constant term must be 2, we can then see that q is 6.
As such, we have -1(x+2)^2+6=0 as our factorization.
To solve this equation, we can use the quadratic formula. Plugging in values, we have:
which is equal to: (when the fraction is simplified)
3x - y = 0 . . . (1)
5x + 2y = 22 . . . (2)
From (1), y = 3x . . . (3)
Putting (3) into (2) gives:
5x + 2(3x) = 22
5x + 6x = 22
11x = 22
x = 2
From (3), y = 3(11) = 33
x = 11, y = 33.
Answer:
The answer is 85
Step-by-step explanation:
The equation used to find the sum of an arithmetic series is: (n/2) * (a1 + an).
n in this case is 10 (the number of numbers in the series)
an is 22 (plug in 10 to the expression 3n-8)
and a1 is -5 (plug in 1 to the expression 3n-8)
so when you plug everything in to the final equation, you get
(10/2) * (-5 + 22)
5 * 17
85
Answer:
x = 0
Step-by-step explanation:
There's no horizontal shift.
Answer:
3 cups of water
Step-by-step explanation:
Henry is making a corn grits recipe that calls for 1/4 cup of corn grits for every 1/2 cup of water. How much water will he need if he uses 1 1/2 cups of corn grits?
Expand 1/2 to 2/4, if there is 1 1/2 cups of corn grits, that means that 1/4 cups of corn grits was used 6 times, 1/2x6=3. He will need 3 cups of water
