Add one-fourth to 3 times c
1 answer:
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Answer:
Vertex is (-4, -18)
Step-by-step explanation:
f(x) =
Let (h, k) be the vertex
An easy way to find h is to use the formula h = -b/2a
In your case where f(x) = a = 2 and b = 8
So, h = -8/2(1) = -8/2 = -4
Substitue -4 in for x to find k
k = () + 8(-4) - 2
= (16) - 32 - 2
= 16 - 32 - 2
= -18
Vertex is (-4, -18)
Note: Another way to find the vertex is to complete the square, but this can really be difficult in some cases
Answer:
<em>The club needs to raise $477 to go on an the field trip.</em>
Step-by-step explanation:
Each student in the club has to raise $53 by selling chocolate bars.
There are 9 students in the club.
Now for finding the total money raised by all 9 students, we just need to multiply $53 by 9.
So, the total money raised
Thus, the club needs to raise $477 to go on an the field trip.
I'm not sure what is meant by "partitioning the <em>x</em>-axis" - partition is a term more often used with computing Riemann sums. So either partitioning has a special meaning for you, or you have to approximate the area with a Riemann sum.
I'm going to assume you just want the exact area of the given region. Notice that the two curves <em>y</em> = 4<em>e</em> ˣ and <em>y</em> = -<em>x</em> + 4 intersect when <em>x</em> = 0 at the point (0, 4). Both curves then meet the vertical line <em>x</em> = 4. The exponential function is increasing while the linear one is decreasing, so 4<em>e</em> ˣ ≥ -<em>x</em> + 4.
The region is then the set of points,
<em>R</em> = {(<em>x</em>, <em>y</em>) | 0 ≤ <em>x</em> ≤ 4 and -<em>x</em> + 4 ≤ <em>y</em> ≤ 4<em>e</em> ˣ}
so the area is given by the integral,