x + 15 = 24
subtract 15 from both sides
x = 24 - 15 = 9
Given the expression:
-x^2+18x-99
to solve by completing squares we proceed as follows:
-x^2+18x-99=0
this can be written as:
-x^2+18x=99
x^2-18x=-99.......i
but
c=(-b/2)²
Hence:
c=(-(-18)/2)²=81
adding 81 in both sides of i we get:
x^2-18x+81=-99+81
factorizing the quadratic we obtain:
(x-9)(x-9)=-18
thus
(x-9)²+18=0
the above takes the vertex form of :
y=(x-k)²+h
where (k,x) is the vertex:
the vertex of our expression is:
(9,18)
hence the maximum point is at (9,18)
NOTE: The vertex gives the maximum point because, from the expression we see that the coefficient of the term that has the highest degree is a negative, and since our polynomial is a quadratic expression then our graph will face down, and this will make the vertex the maximum point.
Your answer is that last one 8 3/4
Answer:
a
Step-by-step explanation:
First cake requires x cups of flour.
Second cake: x + 1/2
Third cake: 2x
2 pound bag has 8 1/2 cups and it's exactly what Carly needs, so we can write it down as:
8 1/2 = x + x + 1/2 + 2x
8 1/2 = 2x + 1/2 + 2x
8 1/2 = 4x + 1/2 / - 1/2 (both sides)
8 = 4x / ÷ 4 (both sides)
<u>x = 2</u>
Doublecheck:
2 + 2 + 1/2 + 2 * 2 =
= 2 + 2 + 1/2 + 4 =
= 4 + 1/2 + 4 =
= 8 + 1/2 =
= 8 1/2
It's the same, so it must be correct ;)
Answer: Carly needs 2 cups of flour for each cake.
