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f(x)  =  x h(x)  =  13x + 1

By the transitive property of equality,

f(x)  =  13x + 1

thanks!

g(x)  =  4 * f(x)

We multiply all the y-values by  4

Here is an example to maybe help you see why this is:

Let's let      \(f(x)=\sqrt{x}\)      and so      \(g(x)=4\sqrt{x}\)

Here is a table of points on the graph of  f(x)  and a graph to go with it:

And here is a table of points on the graph of  g(x)  and a graph to go with it:

Notice that all the y-coordinates of the graph of g(x) are 4 times that of f(x)

We can call this "a vertical strech by a factor of 4"

Here are the two graphs together:

Solve for x:
sqrt(x^2) = 6

Raise both sides to the power of two:
x^2 = 36

Take the square root of both sides:

x = 6      or      x = -6

(125 ft   x  6 ft ) x 2    /  100 ft²/hr  = 1500 ft²  / 100 ft²/hr = 15 hr

ABCDD = 5! /2! = 60

g(x) =  4 f(x)

Number = x

Double the number    2x

add 200           2x + 200

divide by 4       (2x+200)/4

Subtract 1/2 x            (2x+200)/4   - 1/2 x

                              = 1/2x + 50    - 1/2 x    = 50 

[125 * 6 ] * 2  /100  =

125 * 12  /100  =

1500 / 100 =

15 hrs

The graph of cos is shifted up (by d)   , shifted RIGHT (to make c as small as possible ----- c will be NEGATIVE) and amplified (by a)  and period is increased to 3pi (from normal 2pi)

Amplification   'a'    Normal cosine is from -1 to 1  ( amplitude = 1)   this graph is from -1 to 3  (amplitude = 2)    so  a = 2

Period is changed by b    = 2/3

shifted LEFT by 3pi/2 (to make c as small as possible, but still positive) but multiplied by 2/3 (above) makes it just pi   pi = c

And finally ....shifted UP  from midline = 0 to midline = 1       1 = d

Here is a graph:

https://www.desmos.com/calculator/rpslirnhyi

( RED text is edited/corrected text....THANX to CPhil !)

How many ways can you place the 2 identical books into the 5 spaces?

10           (  5 C 2)

In EACH of those 10 ways, how many ways can yo place the other three books?

6           ( 3 P 3)

10 * 6 = 60 ways

tbh, idk if they’re going to switch over to photobucket, and I think the images will stay how they are now.

g(x) = f (x -2)        this will shift f(x) 2 units to the right

i agree wonderman need to mind his own business and he joined the web2.o calc forum just to report people and i have seen all his comments so i know

Center  =  ( 6, -3)

Endpoints of the major axis  are 10 units from the center

Endpoints of the minor axis  are 6 units  from the center

The final answer is just the next to the last answer box given

Let the given expression  = x

So....we have that

x  =  3  +   1 / x

x - 3  =  1  / x              multiply through by  x

x^2  - 3x   =  1             complete the square on x

x^2 - 3x + 9/ 4  =  1 + 9/4

(x - 3/2)^2  =  13/4       take the positive root

x - 3/2  = √13 / 2

x =  [ 3  + √13 ]

      __________

              2

g(2x)  =   [ (2x + 3)/ 4]^(1/3)

2g(x)  = 2 [ (x + 3) / 4] ^(1/3)

So.....we have that

[ (2x + 3)/4]^(1/3)  =  2[ (x + 3)/4]^(1/3)         cube both sides

(2x + 3)/4     =  8 (x + 3)/4

2x + 3   =  8(x + 3)

2x + 3  =  8x + 24

-6x = 21

x  = -21/6

x = -7/2

a)  C (5,3)   = 10 subsets

b)  

Total of subsets with no elements  =  1

Total of subsets with one element  = 5

Total of subsets with two elements  =C (5,2)  = 10

Total of subsets with three elements = C(5,3)  = 10

So....we have 1 + 5 + 10 + 10  =   26 subsets with no more than three elements

4)  When a tower is added at Hilda Hills we have that  

A)  (x + 8)^2  + (y + 7)^2  = 49

B) x^2 + y^2  + 16x  + 14y  + 64  = 0

Here's the new graph with the tower at Hilda Hills  :

The towns not covered fall outside the four circles  !!!