441614, rounded to the whole
Problem 7
<h3>Answer: Choice A) 7</h3>
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Work Shown:
p(x) = x^4+x^3-kx-x+6
If (x-2) is a factor of p(x), then x = 2 is a root of p(x). This is a special case of the remainder theorem.
This means p(2) = 0
Replace every x with 2 and solve for k
p(x) = x^4+x^3-kx^2-x+6
p(2) = 2^4+2^3-k(2)^2-2+6
p(2) = 16+8-4k-2+6
p(2) = 28-4k
0 = 28-4k .... replace p(2) with 0
4k = 28
k = 28/4
k = 7
The polynomial
p(x) = x^4+x^3-7x^2-x+6
has the factor (x-2)
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Problem 8
<h3>Answer: D) 40</h3>
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Work Shown:
Check out the diagram below to see the synthetic division table. We're after the remainder which is highlighted in yellow.
An alternative is to use direct substitution
p(x) = 2x^4+4x^3-x^2-5
p(-3) = 2(-3)^4+4(-3)^3-(-3)^2-5 ... replace every x with -3
p(-3) = 2(81)+4(-27)-9-5
p(-3) = 162-108-9-5
p(-3) = 40
This helps confirm we got the right remainder and the right answer.
Answer:
first one: B and C
Second one: x=12, y=10 so the answer is B.
Step-by-step explanation:
First one: Irrational numbers are any numbers that go on forever in the decimal without ever repeating. Any square roots of numbers that aren't perfectly square, such as 4 and 9, are irrational. And anything with pi, or , is always irrational.
Second one: 144 and 100 are perfect squares, meaning it can be created by multiplying the same number by itself, in this case 12 and 10. Subtract those and you get 2.
76 -20 = 56 so then you do 56/8 which is 7
So 7 is the answer Hope this helps
Answer:
24 times
Step-by-step explanation:
75% = 0.75, so then you just do 0.75 * 32 = 24