CPhill

We can use the Law of Sines for the first one

Sin A  / 7  =  sin (95) / 9

Sin A  =    7 sin (95)/ 9

Use the sine inverse

arcsin ( 7 sin (95)/ 9 )  =  A  ≈  51°

For the second, we can use the Law of Cosines

x  =  sqrt  [  3^2 + 7^2  - 2(3)(7)cos (54)  ]    ≈  5.8

OK....got it....here's the answers

Angle Addition Postulate

Alternate Exterior

Definition of a Bisector

Substitution Property of Equality

y = x^3

Sequentially

Vertical stretch by a factor of 3  ⇒  y = 3x^3

Horizontal shift 4 units to the right  ⇒  y = 3(x - 4)^3

Vertical shift 3 units down   ⇒  y  = 3(x - 4)^3 - 3

Trapezoid EFGH is not congruent to trapezoid E′F′G′H′ because there is no sequence of rigid motions that maps trapezoid EFGH to trapezoid E′F′G′H′ .

( d  - 4b)^3   

C(3,0) *d^3   -  C(3,1)* d^2 * (4b)  + C(3,2)* d * (4b)^2  - C(3,3)*(4b)^3

1 * d^3    -   3*d^2 * (4b)    +  3 *  d *  16b^2  -   1 * 64b^3

d^3   -   12d^2b  + 48db^2  -  64b^3

Third one

Subtraction Property of Equality

Multiplication Property of Equality

Symmetric Property of Equality

First one

XY  perp  to  AA'

P is midpoint of AA'

the set of point A and point B and all the points between point A and point B

-3x^4 + 27x^2 + 1200  =  0    multiply through by - 1

3x^4  -  27x^2  - 1200  =  0       divide through by 3

x^4  - 9x^2  -  400  =  0        factor as

(x^2 - 25)  ( x^2 + 16)  = 0 

(x - 5) ( x + 5) (x^2  + 16)  =  0

x  -  5   =  0         x + 5   =  0          x^2 +  16  =  0

x  =  5                x  =  -5                 x^2  =  - 16

                                                       x  =  ±√ [-16]

                                                       x   =  ± i√ 16

                                                        x  =  ±4i

The zeroes are    -5, 5, 4i, -4i

2....For this one....I'm using  x for a  and y for b

So we have

y  = 4x + 8

y = -2x +30

Here's the graph :  https://www.desmos.com/calculator/25etgvd1ja

2b     

-2x + 30 > 12  subtract 30 from both sides

-2x  >  -18      divide both sides by  -2 and reverse the inequality sign

x <  9

Here's the graphical solution  : https://www.desmos.com/calculator/wqeiyuxd89

2c.....break even point.....set the functions equal  and solve for x

4x  + 8  =  -2x  + 30     add 2x to both sides, subtract 8 from both sides

6x  =  22     divide both sides by 6

x  = 22/6  =  11/3

And y  = 4(11/3)  +  8

y = 44/3  + 24/3

y = 68/3

Here's the graph with the break-even point  : https://www.desmos.com/calculator/iwcgpjjzqf

2d......we want to solve this

4x + 8  >  -2x  + 30   

6x >  22

x > 22/6

x > 11/3