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Thx, CentsLord   !!!!

First  one....the cost per hr  = 150/5   = $30

So  the points  (1,30)   (2,60) and (3, 90)   are on the graph

63 /  (.42)   = 150

For John-Boy:

Every time the hour increases, the amount John-Boy owes will increase by $150 / 5 = $30. So, it will be 30, 60, 90, namely the points (1, 30), (2, 60) and (3, 90). By your description this one would be the Third Graph :D

a. Where y is the monthly cost and x is the number of minutes the phone is used, the linear equation is y=5.05+0.6x.
b. Plugging in 18 in the place of x, we can solve for y: y=5.05+0.6(18)=15.85. The answer is $15.85.

3)

Circles with centers of (2,2) and (17,10) are both tangent to the x-axis. What is the distance between the closest points of the two circles?

The distance  between the  centers is

sqrt  [ (17-2)^2   + (10-2)^2]  = sqrt  [15^2  + 8^2]   =sqrt 289   = 17

The radius  of  the first circle is 2  and the radius  of   the second circle  is 10

So.....the  distance between the two closest points =  17 - 2 - 10    =  5

5)   x^2  + 10x + 21

The  x coordinate  of the vertex  =  -10/[ 2 * 1 ] =  -5

The  y coordinate of the vertex is the min  =

(-5)^2 + 10(-5) + 21  =

-4

Thank you 

6)

(2∇3)  = 3^2 - 2   =  7

(7)∇2   =  2^7 - 2   =  126

Good Job CPhill!

L = 2W + 5

Perimeter =  2 (L + W)

So

160  =  2  [ 2W + 5 + W]       divide  both sides by 2  and simplify

80  =  3W  + 5      subtract 5 from both sides

75  = 3W     divide both sides by 3

25  = W

L  = 2W + 5   =  2(25) + 5  =    55

Thank you very much CPhill!

Hey by the way next time please do one question per question!!! 

Thanks :D
 

36 eggs = $1.08

$1.08/36 = 0.03

\( x = 3 + \sqrt{5}$ and $x = 3 - \sqrt{5}.\)

By Vieta  the  sum of the roots  = -b/-2  = 6   ⇒   -b  = -12   ⇒ 12

And the product of the roots  [ i.e., 4]  =  c / -2   ⇒   c = -8 

By symmetry, the  x  coordinate of  the  vertex  =  3 

So......the y coordinate of the  vertex =  -2(3)^2  + 12(3) - 8  = 10

So.....the  vertex =  (3, 10)  

Here I will give you a place to start find the decrease in percent from 38450-2035

I hope you solve it!

Forget the above!! I misread the question. The smallest positive n =432

30 ways

The smallest positive integer n = 3. Next to that will be n = 192.

Please fix LaTeX.

x  = 3  - t    ⇒ t  = 3 - x

When t  = - 3

x = 6   and  y  = 4  =   (6, 4)  =  initial point

When t  =  1

x = 2   and  y  =  4  =    (2, 4)  = terminal point

So

y  = (t + 1)^2

y  = (3 - x + 1)^2

y = (4 - x)^2  =  (x - 4)^2   +  0

The  vertex is (4, 0)

The  motion  is  right to left       { (2,4)  is  to the left of (6,4)  }

See the graph here  : https://www.desmos.com/calculator/hxfat2kymd

The  sides  =  40

FD   = 20...so.....FE  = 10

Note  that triangle BGC  is similar to triangle FGE

The  base  of triangle  FGE  =  (1/4)   of  base of triangle FGE

So...the  height  of  triangle FGE  = must  be (1/4)  the  height of  triangle BGC

So  height of BGC   = 4 times height of FGE

So....

height of FGE  + 4 *height of FGE  = side length  =   40

5 *height FGE   = 40

height of FGE  =40/5  =  8

So  the area of triangle FGE  =(1/2) FE * 8    =  (1/2) (10)(8)  =   40

No problem!

Happy to help :D