Solve the system of equations. y = x + 6 y = x^2 + 8x + 16

(-5,1)

(-2,4)

Step-by-step explanation:

y = x + 6

y = x^2 + 8x + 16

Since both equations are equal to y, we can set them equal to each other

x + 6  = x^2 + 8x + 16

Subtract x from each side

x -x + 6

= x^2 + 8x-x + 16

6 = x^2 +7x +16

Subtract 6 from each side

6-6 = x^2 +7x +16-6

0 = x^2 +7x +10

Factor

What 2 numbers multiply together to give us 10 and add together to give us 7?

5*2 = 10

5+2 =7

0 = (x+5) (x+2)

Using the zero product property

x+5 = 0  x+2 = 0

x = -5   x=-2

Now we need to find the y's that go with the x's

x=-5

y= x+6

y =-5+6

y=-1

(-5,1)

x=-2

y = -2+6

y=4

(-2,4)

answer: cos [   arcsin (3/5) - arccos (1/2) ] =

step-by-step explanation: × = 3/5 = 0.6--> x = 36.87 and x = 180 - 36.87 = 143.13 deg

cos y = 1/2 --> y = +- 60 deg a. cos (x - y) = cos (143.13 - 60) = cos 83,13  

=

0.12

b. cos (36.87 - 60) = cos (-23.23) = 0.92