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Thank you so much! also, how did you get b and c? thanks!

What percent of 24 is 80?

x%  of  24   =   80

                                       Replace  %  with  /100   and   replace  "of"  with  *

x/100  *  24   =   80

                                       Divide both sides of the equation by  24

x/100   =   80/24

                                       Multiply both sides of the equation by 100

x   =   80/24 * 100

                                       Calculate  80/24 * 100

x   ≈   333.33

So.....

333.33%  of  24  is  80.

(a) See the graph below.

(b) g(x) = 1/3*f(2x + 2).

(c) We stretch the graph horiztonally by a factor of 2, then stretch the graph vertically by a factor of 3, then shift down 2 units.

N=25*12; R=0.06/12;PV=25000; PMT=PV*R*((1 + R)^N) / ((1 + R)^(N) - 1);print"LOAN PMT =$",PMT

LOAN PMT =$ 161.08 - monthly.

sumfor(n, 1, 12, (2*n - 1)) = 144

Two cylinders are similar. The volume of the larger cylinder is 343 ft³ and the volume of the smaller cylinder is 125 ​​ft³. The height of the smaller cylinder is 10 ft.

What is the height of the larger cylinder? 

Hello Guest!

\(\color{blue}343ft^3:125ft^3=h_{l}^3:10^3ft^3\\ h_{l}^3= \frac{343ft^3\cdot 10^3ft^3}{125ft^3}\\ h_l= \sqrt[3]{\frac{343ft^3\cdot 10^3ft^3}{125ft^3}}\\ h_l=\frac{7ft\cdot10ft}{5ft}\)

\(h_l=14ft\)

The height of the larger cylinder is 14ft.

  !

a + b = 14,    a^3 + b^3 = 812, solve for a, b
Use substitution to get:
a=14 - b
(14 - b)^3 + b^3 =812
Solve for b:
(14 - b)^3 + b^3 = 812

Expand out terms of the left hand side:
42 b^2 - 588 b + 2744 = 812

Divide both sides by 42:
b^2 - 14 b + 196/3 = 58/3

Subtract 196/3 from both sides:
b^2 - 14 b = -46

Add 49 to both sides:
b^2 - 14 b + 49 = 3

Write the left hand side as a square:
(b - 7)^2 = 3

Take the square root of both sides:
b - 7 = sqrt(3) or b - 7 = -sqrt(3)

Add 7 to both sides:
b = 7 + sqrt(3) or b - 7 = -sqrt(3)

Add 7 to both sides:

b = 7 + sqrt(3) or b = 7 - sqrt(3)
Sub this value of b into: a + b = 14 and should get:

a = 7 - sqrt(3)  and  b = 7 + sqrt(3)
a = 7 + sqrt(3)  and b = 7 - sqrt(3)

Like this 1

             10

9.41 = 15.3 * 1/2^(t/5730)

9.41 / 15.3 = 1/2^(t / 5730)

Log(0.6150326797) =(t / 5730) * Log(1/2)

 -0.4860798748  = (t / 5730) *  -0.69314718056

- 2,785.237682604 = -0.69314718056t

t = 4018.25 years + or - 28.3 years.

Yay that is correct! Thanks so much :DD

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Look under the LaTex heading at the first option.... type in your numbers between the brackets

example of result ......   

\(\frac{3}{4}\)

most people just use the forward slash on the keyboard      3/4

Look for all of the y lines that cross the graph 6 times

  y = -1   -2   -3     all cross the graph 6 times  

                                 continue to answer your Q ......

I wiil do this without a calculator:

$4456 \cdot 4455 = 4455^2+4455 = 4450\cdot4460 + 25 + 4455.$

$4450\cdot4460  = 100\cdot(445\cdot446)  = 10\cdot((445^2)+445) = 100*((100*(44\cdot45) + 25) + 445)$

Yay, $44 \cdot 45$ is easy! Everyone knows it's $1980!$ So, $1980\cdot100=198000,$ and plus $25$ yields $198025.$ Next, we add $445$ getting $198470.$ Then times $100$ yields $19847000!$ Now, we can add this to $25$ and $4455,$ easy addition gets $19851480!$ That's your answer, WITHOUT A CALC!

I think it is right back to where it started    x, y

example   3,4         then    3,-4       then    -4,-3     then    3,4  

Yes! That is what I put at first, too, before I made a calculation error and fixed it to 3 

There is a right triangle ABC. Square XBYZ is inscribed in it, where Z is touching AC and XB is on AB. If [XBYZ] = 36, then what are the side lengths of the triangle?

Since the type of right triangle is not specified we may use an isosceles right triangle.

The sides of that triangle are 12, 12, and  4√18

First ....no x values that cause the denominator of g(x) = 0 would be allowed

    -2 +- sqrt(6)/3   not allowed

then any value of g(x) that causes denominator to f(x) = 0 is not allowed

   this woud be when g(x) = -4

      3x^2-10x-25 / (3x^2+12x+10) = - 4

       3x^2-10x-25 = -12x^2-48x-40

   15x^2 +38x+15 = 0 

       results in -19/15 +-2 sqrt(34)/15     not allowed

Summed = -2 + -2 + -19/15 + -19/15 = .................

Are you sure the numbers in your question are correct? Check them carefully. However, these numbers satisfy the congruence: 12,500*n mod 9,999,999 ==171, where n =136,800