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2 years ago

The area of a square is 4 square meters. How long is each side? Please show every step.

2 answers:

3 0

Since you're trying to find the side lenghts of a square, all we need to do is square root the area. So, the square root of 4 (the area) is 2.

So, all of the sides of the square are 2 meters long.

Rom4ik [11]2 years ago

3 0

Since the area of the square is given by side length squared....

let s=side length
s²=4
s=±√4 or±2

but since length can never be negative, we ignore there extraneous answer-2 and conclude the side length s=2

You might be interested in

How do you do inequalities

fgiga [73]

So some quick tips for inequalities:
**What you do to one side you HAVE TO do it to the other 2**
**If you ever divide a negative number past the inequality signs, the signs FLIP!!**
(e.g. 2>-5x>25)
-2/5 <x < -5

I hope that this has helped!

8 0

2 years ago

Which of the following choices is the simple formula for the nth term of the following arithmetic sequence?

VladimirAG [237]

First, we start off with the nth term formula for an arithmetic sequence, which is
$a_{n} =a_{1}+(n-1)d$

plug in the sequence numbers where they belong

$a_{n}=5+(n-1)*(-4)
$
$a_{n}=5+(-4n+4)$
$a_{n}=5-4n+4$
$a_{n}=-4n+9$

And this is the final answer
$-4n+9$

4 0

3 years ago

Niki makes the same payment every two months to pay off his $61,600 loan. The loan has an interest rate of 9.84%, compounded eve

Alenkasestr [34]

The question is an annuity question with the present value of the annuity given.
The present value of an annuity is given by PV = P(1 - (1 + r/t)^-nt) / (r/t) where PV = $61,600; r = interest rate = 9.84% = 0.0984; t = number of payments in a year = 6; n = number of years = 11 years and P is the periodic payment.
61600 = P(1 - (1 + 0.0984/6)^-(11 x 6)) / (0.0984 / 6)
61600 = P(1 - (1 + 0.0164)^-66) / 0.0164
61600 x 0.0164 = P(1 - (1.0164)^-66)
1010.24 = P(1 - 0.341769) = 0.658231P
P = 1010.24 / 0.658231 = 1534.78
Thus, Niki pays $1,534.78 every two months for eleven years.
The total payment made by Niki = 11 x 6 x 1,534.78 = $101,295.48
Therefore, interest paid by Niki = $101,295.48 - $61,600 = $39,695.48

8 0

3 years ago

Read 2 more answers

Find a compact form for generating functions of the sequence 1, 8,27,... , k^3

pantera1 [17]

This sequence has generating function

$F(x)=\displaystyle\sum_{k\ge0}k^3x^k$

(if we include $k=0$ for a moment)

Recall that for $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{k\ge0}x^k$

Take the derivative to get

$\displaystyle\frac1{(1-x)^2}=\sum_{k\ge0}kx^{k-1}=\frac1x\sum_{k\ge0}kx^k$

$\implies\dfrac x{(1-x)^2}=\displaystyle\sum_{k\ge0}kx^k$

Take the derivative again:

$\displaystyle\frac{(1-x)^2+2x(1-x)}{(1-x)^4}=\sum_{k\ge0}k^2x^{k-1}=\frac1x\sum_{k\ge0}k^2x^k$

$\implies\displaystyle\frac{x+x^2}{(1-x)^3}=\sum_{k\ge0}k^2x^k$

Take the derivative one more time:

$\displaystyle\frac{(1+2x)(1-x)^3+3(x+x^2)(1-x)^2}{(1-x)^6}=\sum_{k\ge0}k^3x^{k-1}=\frac1x\sum_{k\ge0}k^3x^k$

$\implies\displaystyle\frac{x+4x^3+x^3}{(1-x)^4}=\sum_{k\ge0}k^3x^k$

so we have

$\boxed{F(x)=\dfrac{x+4x^3+x^3}{(1-x)^4}}$

5 0

3 years ago

What is 1 2/3 multiplied by 4 1/2

horrorfan [7]

Change the mixed numbers into improper fractions:
5/3 X 9/2

Reduce - the 3 and 9 can be simplified
5/1 X 3/2

multiple numerators and denominators
15/2

Not sure how you need the answer - i would change it into a mixed number
7 1/2

3 0

3 years ago