Answer:
q=35
Step-by-step explanation:
x2 - 12x + q = 0
Let the two roots be r and r+2.
Factor the quadratic expression:
(x - r)[x - (r + 2)] = 0
Expand, simplify, group like terms, and get
x2 - 2(r + 1)x + r(r + 2) = 0
Compare to
x2 - 12x + q = 0
and set equal the coefficients of like terms:
Coefficient of x:
-2(r + 1) = -12 ⇒ r + 1 = 6 ⇒ r = 5
(Then the other root is r + 2 = 5 + 2 = 7)
Constant term:
r(r + 2) = q ⇒ 5(5 + 2) = q
q = 35
Test the solution:
(x - 5)(x - 7) = x2 - 12x + 35
With two roots differing by 2, you get an equation of the form
x2 - 12x + q = 0
with q = 35.
1 Quart = 4 Cups
So, 6 Quarts = 24 Cups
She will need 20x the original amount of each ingredient
what are the regular amounts for the recipe?
Answer: 5 + 25n
Explanation: Let's simplify this problem using the distributive property.
In this problem, the 5 "distributes" through the parentheses which means that it multiplies by each of the terms inside.
So we have 5(1) + 5(5n) which simplifies to 5 + 25n.
Answer:
d = 13.8 feet
Step-by-step explanation:
Because we are talking about cubic feet of water, we need the formula for the VOLUME of a cylinder. That formula is

We will use 3.141592654 for pi; if the tank HALF filled with water is at 20 feet, then the height of the tank is 40 feet, so h = 40; and the volume it can hold in total is 6000 cubic feet. Filling in then gives us:

Simplify on the right to get

Divide both sides by 125.6637061 to get that

Taking the square root of both sides gives you
r = 6.90988299
But the diameter is twice the radius, so multiply that r value by 2 to get that the diameter to the nearest tenth of a foot is 13.8