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This explains the relevance of the scale factor! Let's think about how a scale factor affects the area of a figure before trying to solve. 

Since the original square has dimensions 7cm by 7cm, the scale factor would have to affect both the length and the height. Therefore, the length and the height would be tripled; thus, the area would be affected by the square of scale factor since the scale factor is being applied to both dimensions. 

We already know the area of the original figure; it is $49\text{cm}^2$. If the scale factor affects the area by its square, then the area will be enlarged by $3^2$ or 9.

$49\text{cm}^2*9=441\text{cm}^2$

This is the area of the new square.

1. Let's just pretend for the moment that $c^3+4c>5c^2$ is an equation, so the equation would be $c^3+4c=5c^2$. Let's solve this as if it were a regular equation. 

Therefore, we have defined many possible ranges where the solutions of this inequality can lie. We will have to test all of them. The ranges are as follows:

$c<0\\ 0 < c < 1\\ 0 < c < 4\\ c>4$

Now, let's test values in these ranges. 

For the range $c<0$, let's test a point in this range, say -1, and see if it satisfies the original equation.

Now, let's try the range \(0 . I will choose 1/2.

Now, let's try the terciary range of \(1 . My test point, in this case, will be 2. Always pick a point that is easiest to plug in. Overcomplicating matters is only a burden to yourself.

And finally, $c>4$ is the last one. Let's do the next integer, c=5. 

Consolidating all this information, we can conclude that \(0  or  $c>4$. When you convert to inequality notation, you get  $(0,1)\cup (4,+\infty)$

Yes Melody. On my personal calculator you can, because it has the "Sigma" notation built into it. That is exactly how I got that answer.

Yes I meant cm^2. I have one more question for you. Same perimeter of 28cm and scale factor of 3 but now its the new area of the new figure.

That is the simplified version of my explanation above. It may be a typo on your end, but just be sure that 49m^2 is 49cm^2 

∑[100*1.1^n, n, 0, 11] =$2,138.43

Are you saying you can do it like this on a calculator guest?

What calculator are you referring to?

It appears as if this question has been edited since the replies of other answerers. As of now, the expression to simplify is $\frac{2-\sqrt{3}}{2+\sqrt{3}}$

So the answer would be 49cm^2? So I would I be right if I said "28  divided by 4 is 7, multply that by 7 gives me 49m^2?"

The original figure has a perimeter of 28 centimeters. In this particular situation, the information regarding the scale factor is extraneous information; simply disregard it; the question asks for the area of the original figure--not the new figure.

A square, by definition, is an equilateral quadrilateral, so every side of this four-sided polygon is of equal length. Let's set one of the side lengths of the square as "s."

Since the polygon has four sides of equal length, every side has a length of "s." "4s" represents the total area of a generic square. We know the total perimeter of this current square: 28 centimeters. We can use this information to figure out the length of one side.

$4s=28\\ s=7\text{cm}$

The area of a square is the length of its base multiplied by the length of the height. 

$A_{\fbox{}}=7\text{cm}*7\text{cm}=49\text{cm}^2$

Of course, the area is a square unit, so the answer should be in that format. 

Well, if the perimeter is 28, then 28 / 4 = 7 units, is each side of the square. Right? So, if we scale it up by a factor of 3, or 7 x 3 =21 units, the side of the new square. Therefore 21 x 4 = 84 units, the perimeter of the new square.

Go online to this page and see for yourself. Remember, the higher you go up on the chart to the right, the greater the energy: https://en.wikipedia.org/wiki/Electromagnetic_spectrum

100 + 110 + 121 + 133.1 +146.41 + 161.051 + 177.1561 + 194.87171 + 214.358881 + 235.7947691 + 259.37424601 + 285.311670611 = 285.311670611

these are the terms of a GP

r= 1.1  

this is the best way to present it using sigma notation but it does not give you the answer.

$\displaystyle \sum_{n=0}^{11} 100*101^n$

If you want the answer it is easier to do it as the sum of a GP  (that is if you have learned GPs yet)

a=100

n=12     (because n=1 is always the first one)

r=1.1

$S_{n}=\frac{a(r^n-1)}{r-1}\\ S_{12}=\frac{100(1.1^{12}-1)}{1.1-1}\\ S_{12}=\frac{100(1.1^{12}-1)}{0.1}\\ S_{12}=1000(1.1^{12}-1)\\ $

1000(1.1^12-1) = 2138.428376721

If I take your addition and put it into the web2 calc I get exactly the same answer.

2138.428376721 = 2.138428376721e3 = 2138.428

Sure, you can:

Solve for x:

(3 x + 4)/4 = x - 3  cross multiply

3x + 4 = 4x - 12    move x to the LHS

3x - 4x = - 12 - 4

- x = - 16              Multiply both sides by -1

x = 16

2)  25! =1.5511210043330985984e+25 = 2^22 * 3^10 * 5^6 * 7^3 * 11^2 * 13 * 17 * 19 * 23 / 2^18 * 3^8 * 5^4 * 7^2 * 11 =26,771,144,400= 2^4 * 3^2 * 5^2 * 7 * 11 * 13 * 17 * 19 * 23. This number of 26,771,144,400 will still divide all numbers from 1 to 25. But if 2 of them were wrong, then we can divide it by the 2 larget primes under 25, that is: 19 x 23. So, 26,771,144,400 / [19 x 23] =61,261,200.

This last number of 61,261,200 will still divide every number from 1 to 25 EXCEPT 19 and 23.

Thanks! I don't know if you can, but can you solve it?

(2-3^(1/2))/(2+3^(1/2)) or 2-3^1/2

                                         2+3^1/2

3^1/2 cancels and you are left with 2/2 which equals one.

^ is the same thing as an exponent.

and to clarify 3^1/2, that is the same as saying the square root of 3.

In the rational function $f(x)=\frac{2x}{x^2-5x-14}$, we can determine the vertical asymptotes by setting the denominator equal to 0 and solving for x. 

The horizontal asymptote requires some observation. The horizontal asymptote lies on y=0 since the degree of the numerator is less than the degree of the denominator. Therefore, c=0. We know the unknown variables, so we can now calculate their collective sum.

$a+b+c\\ 7-2+0\\ 5$

one

2/2=1

Let's call the number that one is thinking of "x."

If I take "x" and I multiply "x" by 3, then I have "3x."

If I take "3x" and I add "4," then I have "3x+4."

If I have "3x+4" and I divide by 4, then I have $\frac{3x+4}{4}$.

If the original number is "x," then three less than "x" is x-3.

We know that $\frac{3x+4}{4}$ and $x-3$ are equivalent because of the keyword "is." 

Therefore, the final algabraic equation would be $\frac{3x+4}{4}=x-3$

Solve for a:

1/a - 1/b = 1/c

Bring 1/a - 1/b together using the common denominator a b:

(b - a)/(a b) = 1/c

Cross multiply:

c (b - a) = a b

Expand out terms of the left hand side:

b c - a c = a b

Subtract a b + b c from both sides:

a (-b - c) = -b c

Divide both sides by -b - c:

a = (bc) / (b + c)

EP: The reason for the notation{n, 0, 11} is because in financial investments, the first payment is taken to be made at the END of the period, in this case the END of the first month. Example: First pmt. made on Jan.31 of $100. Now, you will wait for the whole of Feb. to get interest on it. So, the END of Feb. you will have: $100 x 1.1 =$110. Then you add another $100 deposit =$210 at the END of Feb. This has exactly the same outcome as the young man calculated in his question: $100, $110, $121....etc.

Whatever values of 'x' that make the DENOMINATOR = 0 are not allowed.

it is OK if the NUMERATOR = 0

so  any 'x' that makes   x^2-16 = 0 are not allowed

x^2-16=0

x^2 = 16

x= +-4          NOT allowed,  answer is 'c'

OK...I think the question is worded incorrectly..... it  STARTS with 100  then for TWELVE MORE months 10% is added......but I think it MEANT 11 MORE months (for a total of 12 months)