Answer:
a)
Completing the square
b)
You can prove that is always positive, stating;
The sum of two squared numbers can't be negative. Hence is always positive.
Also, if we take the discriminant of
Once the discriminant is negative, the quadratic has no real root. So, the function never touches the real axis and the function lies above or below the real axis. If we take x as 0, y = 20, therefore, the function lies above the real axis. It is always positive.
Answer:
The formula showing how many ounces (c) that are in x quarts (q) is given as :
c = q x 32
Step-by-step explanation:
Step 1:
Conversion scale of quart to ounce.
This is illustrated below:
1 quart = 32 ounce
Step 2:
Determination of the number of ounce that are in X quart.
Let q represent X quart
Let c represent the number of ounce in X quart.
1 quart = 32 ounce
Therefore, X quart (q) = q x 32 ounce.
But we said that 'c' should represent the number of ounce in X quart.
Therefore,
c = (q x 32) ounce
The formula showing how many ounces (c) that are in x quarts (q) is :
c = q x 32
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Answer:
Rafael will read 240 pages.
Step-by-step explanation:
Let's start by setting up the unknowns:
x = # of Rafael's pages
x/2 = # of Philippe's pages
(3/4)x = # of Denise's pages
Set these all equal to 540:
(x) + (x / 2) + (3/4(x)) = 540
Let's multiply both sides by 4 to make this easier.
4x + 2x + 3x = 2160
9x = 2160
x = 240
x was the # of Rafael's pages, so Rafael will read 240 pages. This means that Philippe will read 120 pages (one-half of Rafael), and Denise will read 180 pages (three-fourths of Rafael). Adding these all up will get you 540 pages, so it checks out.
Hope this helps!