Factor the expression completely. 63x – 9
1 answer:
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<span>The correct answer is $1452.50 per year.
Explanation:<span>
We use the formula
</span></span>![P(1+\frac{r}{n})^{nt}+PMT(\frac{[(1+\frac{r}{n})^{nt}-1]}{\frac{r}{n}})\times (1+\frac{r}{n})](https://tex.z-dn.net/?f=P%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D%2BPMT%28%5Cfrac%7B%5B%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D-1%5D%7D%7B%5Cfrac%7Br%7D%7Bn%7D%7D%29%5Ctimes%20%281%2B%5Cfrac%7Br%7D%7Bn%7D%29)
,<span><span>
where P is the amount of principal invested, r is the interest rate as a decimal number, n is the number of times per year the interest is compounded, PMT is the monthly deposit added, and t is the number of years.
Since the amount of principal is not stated, we will assume that Bob is depositing the same amount every following year as he does the first year, so we will let PMT=P.
Our interest rate, r, is 4.2%; 4.2%=4.2/100=0.042.
The number of times the interest is compounded annually, n, is 1.
The amount of time, t, is 7.
We know he wants $50,000. This gives us the equation
50000=P(1+0.042/1)</span></span>⁽¹ˣ⁷⁾<span><span>+P{[(1+0.042/1)</span></span>⁽¹ˣ⁷⁾<span><span>]/(0.042/1)}*(1+0.042/1).
Simplifying this a bit, we have
50000=P(1.042)</span></span>⁷<span><span>+P((1.042</span></span>⁷<span><span>)/0.042)*(1.042).
We can factor out P, giving us
50000=P[1.042</span></span>⁷<span><span>+((1.042</span></span>⁷<span><span>)/0.042)*1.042].
This then gives us
50000=P(34.4234).
Divide both sides:
50000/34.4234 = (P(34.4234))/34.4234,
which gives us P=1452.50.</span></span>
Explanation:<span>
We use the formula
</span></span>
where P is the amount of principal invested, r is the interest rate as a decimal number, n is the number of times per year the interest is compounded, PMT is the monthly deposit added, and t is the number of years.
Since the amount of principal is not stated, we will assume that Bob is depositing the same amount every following year as he does the first year, so we will let PMT=P.
Our interest rate, r, is 4.2%; 4.2%=4.2/100=0.042.
The number of times the interest is compounded annually, n, is 1.
The amount of time, t, is 7.
We know he wants $50,000. This gives us the equation
50000=P(1+0.042/1)</span></span>⁽¹ˣ⁷⁾<span><span>+P{[(1+0.042/1)</span></span>⁽¹ˣ⁷⁾<span><span>]/(0.042/1)}*(1+0.042/1).
Simplifying this a bit, we have
50000=P(1.042)</span></span>⁷<span><span>+P((1.042</span></span>⁷<span><span>)/0.042)*(1.042).
We can factor out P, giving us
50000=P[1.042</span></span>⁷<span><span>+((1.042</span></span>⁷<span><span>)/0.042)*1.042].
This then gives us
50000=P(34.4234).
Divide both sides:
50000/34.4234 = (P(34.4234))/34.4234,
which gives us P=1452.50.</span></span>
Answer:
(a) Rule: Multiply the input (x) by 2 and add 5 to the result of the product
(b)
Step-by-step explanation:
Given
The attached table
Solving (a): The rule of the table in words
First, we calculate the slope (m)
Using:
So, we have:
The equation is calculated using:
Using:
We have:
Make y the subject
Hence, the rule is:
Multiply the input (x) by 2 and add 5 to the result of the product
(b): The rule, in algebra
As solved in (a), the rule is: