John had $20. He earned $5, spent $10, earned $5 again, and then spent $3. After this series of earings and expenses, how much m
2 answers:
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Answer:
D
Step-by-step explanation:
If the polynomial p(x) is divided by a polynomial of the form x+k (which accounts for all of the possible answer choices in this question), the result can be written as
p(x)/x+k = q(x) + r/x+k
where q(x) is a polynomial and r is the remainder. Since x+k is a degree-1 polynomial (meaning it only includes and no higher exponents), the remainder is a real number.
Therefore, p(x) can be rewritten as p(x) = (x+k)q(x) + r, where r is a real number.
The question states that p(3) = −2, so it must be true that
−2 = p(3) = (3+k)q(3) + r
Now we can plug in all the possible answers. If the answer is A, B, or C, r will be 0, while if the answer is D, r will be −2.
A. −2=p(3)=(3+(−5))q(3)+0
−2=(3−5)q(3)
−2=(−2)q(3)
This could be true, but only if q(3)=1
B. −2=p(3)=(3+(−2))q(3)+0
−2=(3−2)q(3)
−2=(−1)q(3)
This could be true, but only if q(3)=2
C. −2=p(3)=(3+2)q(3)+0
−2=(5)q(3)
This could be true, but only if q(3) = −2/5
D. −2=p(3)=(3+(−3))q(3)+(−2)
−2=(3−3)q(3)+(−2)
−2=(0)q(3)+(−2)
This will always be true no matter what q(3) is.
Of the answer choices, the only one that must be true about p(x) is D, that the remainder when p(x) is divided by x−3 is -2.
The final answer is D.
Answer:
275 ft³
Step-by-step explanation:
Given the ratio of radii of 2 similar figures = a : b , then
ratio of volumes = a³ : b³
Here the ratio of radii = 5 : 2 , so
ratio of volumes = 5³ : 2³ = 125 : 8
Calculate the volume (V) of A using proportion
=
=
( cross- multiply )
V = 275 ft³
That is the volume of figure A = 275 ft³