Answer:
g(4) = 157
Step-by-step explanation:
g(x) = 8x^2 + 9x - 7
Let x =4
g(4) = 8 * 4^2 +9*4 -7
=8*16 +36 - 7
=128+36-7
=157
Answer:
Part 1)
The possible multiplicities are:
multiplicity 1
multiplicity 3
multiplicity 1
multiplicity 2
Part 2
The factored form is
Step-by-step explanation:
Part 1.
The missing diagram is shown in the attachment.
The zeroes of the seventh degree polynomial are the x-intercepts of the graph.
From the graph, we have x-intercepts at:
, , , and .
The multiplicities tell us how many times a root repeats.
Also, even multiplicities will not cross their x-intercept, while odd multiplicities cross their x-intercepts.
The possible multiplicities are:
multiplicity 1
multiplicity 3
multiplicity 1
multiplicity 2
Note that the total multiplicity must equate the degree.
Part 2)
According to the factor theorem, if 
is a zero of p(x), then 
is a factor.
Using the multiplicities , we can write the factors as:
Therefore the completely factored form of this seventh degree polynomial is
<h3>
Answer: 0.157</h3>
========================================================
Explanation:
Convert the fraction 9/50 to decimal form. You can use either long division or a calculator.
You should find that 9/50 = 0.18 which is the same as 0.180
So the original compound inequality is the same as saying 0.125 < x < 0.180
This tells us that x is between 0.125 and 0.180 where x is not equal to either endpoint. We simply need to pick anything in this interval. It can be anything you want (I recommend to use a number line to help pick a value). One such value is 0.157. There are infinitely many values you can select from.
The number 0.157 is between 0.125 and 0.180, ie 0.125 < 0.157 < 0.180
It's very similar to saying 157 is between 125 and 180, ie 125 < 157 < 180.
Answer:
512
Step-by-step explanation:
Suppose we ask how many subsets of {1,2,3,4,5} add up to a number ≥8. The crucial idea is that we partition the set into two parts; these two parts are called complements of each other. Obviously, the sum of the two parts must add up to 15. Exactly one of those parts is therefore ≥8. There must be at least one such part, because of the pigeonhole principle (specifically, two 7's are sufficient only to add up to 14). And if one part has sum ≥8, the other part—its complement—must have sum ≤15−8=7
.
For instance, if I divide the set into parts {1,2,4}
and {3,5}, the first part adds up to 7, and its complement adds up to 8
.
Once one makes that observation, the rest of the proof is straightforward. There are 25=32
different subsets of this set (including itself and the empty set). For each one, either its sum, or its complement's sum (but not both), must be ≥8. Since exactly half of the subsets have sum ≥8, the number of such subsets is 32/2, or 16.
General form for vertex form is:
y = a(x - h)² + k
Where the vertex is the point (h, k). We know this to be (5, -3), so we can substitute the values for h and k to get:
y = a(x - 5)² - 3
We then also have another point (6, 1) that gives us an x and y. Substitute those in to leave one unknown which we can solve for:
1 = a(6 - 5)² - 3
1 = a(1)² - 3
1 = a(1) - 3
1 = a - 3
4 = a
So the equation of this parabola in vertex form is:
y = 4(x - 5)² - 3
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