Question 3
2 answers:
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9514 1404 393
Answer:
(b) -36
Step-by-step explanation:
Synthetic division is often performed using a table of the kind shown in the attachment. The coefficients of f(x) are placed across the top, and the x-value to be evaluated is placed at the left. The rule for finding table entries is shown. (The first (left-most) number at the bottom is the leading coefficient of the polynomial.)
This table shows the remainder, which is f(-2), is -36.
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The equation itself can be rewritten in "Horner form" to facilitate evaluation.
f(x) = (((-x +2)x -1)x +4)x +8
In this form, substituting for x and doing the evaluation is easier for mental arithmetic. You will notice that the contents of parentheses at each level match the bottom line of the synthetic division table.
f(-2) = (((-(-2) +2)(-2) -1)(-2) +4)(-2) +8
= (((4)(-2) -1)(-2) +4)(-2) +8
= ((-9)(-2) +4)(-2) +8
= (22)(-2) +8
= -36
f(-2) = -36 . . . . remainder from synthetic substitution
Problem 17, part A
i = simple interest = 900 dolars
p = principle = 1500 dollars
r = interest rate = 0.03 (decimal form of 3%)
t = time in years = unknown (leave it as t for now)
Plug in those values mentioned above and solve for t.
Simple interest formula
i = p*r*t
900 = 1500*0.03*t
900 = 45*t
900/45 = 45*t/45
20 = t
t = 20
Answer: 20 years
=============================================
Problem 17, part B
p = 1500
r = 0.03
t = 5 years
A = p+p*r*t
A = 1500+1500*0.03*5
A = 1500+225
A = 1725
Answer: 1725 dollars
=============================================
Problem 17, part C
Factor out the GCF p, then divide both sides by 1+rt
A = p+p*r*t
A = p*1+p*r*t
A = p*(1+rt)
A/(1+rt) = p*(1+rt)/(1+rt)
A/(1+rt) = p
p = A/(1+rt)
Answer: p = A/(1+rt)
The right side is the fraction of A all over the quantity (1+rt) which may be more readable if written like so
If you're going to write it in the way p = A/(1+rt) then don't forget to use parenthesis.
i = simple interest = 900 dolars
p = principle = 1500 dollars
r = interest rate = 0.03 (decimal form of 3%)
t = time in years = unknown (leave it as t for now)
Plug in those values mentioned above and solve for t.
Simple interest formula
i = p*r*t
900 = 1500*0.03*t
900 = 45*t
900/45 = 45*t/45
20 = t
t = 20
Answer: 20 years
=============================================
Problem 17, part B
p = 1500
r = 0.03
t = 5 years
A = p+p*r*t
A = 1500+1500*0.03*5
A = 1500+225
A = 1725
Answer: 1725 dollars
=============================================
Problem 17, part C
Factor out the GCF p, then divide both sides by 1+rt
A = p+p*r*t
A = p*1+p*r*t
A = p*(1+rt)
A/(1+rt) = p*(1+rt)/(1+rt)
A/(1+rt) = p
p = A/(1+rt)
Answer: p = A/(1+rt)
The right side is the fraction of A all over the quantity (1+rt) which may be more readable if written like so
If you're going to write it in the way p = A/(1+rt) then don't forget to use parenthesis.