Please help me with these problems! 43, 44, and 45!
Giving brainiest!!

see explanation

Step-by-step explanation:

(43)

To find f(- 12) substitute x = - 12 into f(x)

f(- 12) = (- 12) + 8 = - 4 + 8 = 4, thus

3f(- 12) + 4 = 3(4) + 4 = 12 + 4 = 16

(44)

Given

f(x) = 2x² + 3x - 4 , then

f(x + 1) = 2(x + 1)² + 3(x + 1) - 4 ← expand factors

           = 2(x² + 2x + 1) + 3x + 3 - 4

           = 2x² + 4x + 2 + 3x - 1

          = 2x² + 7x + 1

-----------------------------------------

f(- x) = 2(- x)² + 3(- x) - 4 = 2x² - 3x - 4

(45)

The equation of a line in slope intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

4x + 6y + 5 = 0 ( subtract 4x + 5 from both sides )

6y = - 4x - 5 ( divide all terms by 6 )

y = - x - ← in slope- intercept form

with slope m = -

Parallel lines have equal slopes, thus

y = - x + c ← is the partial equation

To find c substitute (5, 2) into the partial equation

2 = - + c ⇒ c = 2 +

y = - x + ( multiply through by 3 )

3y = - 2x + 16 ( subtract - 2x + 16 from both sides )

2x + 3y - 16 = 0 ← equation of parallel line

----------------------------------------------------------------

Given a line with slope m then the equation of a line perpendicular to it is

= - = - = , thus

y = x + c ← is the partial equation

To find c substitute (5, 2) into the partial equation

2 = + c ⇒ c = 2 -

y = x - ( multiply through by 2 )

2y = 3x - 11 ( subtract 2y from both sides )

3x - 2y - 11 = 0 ← equation of perpendicular line

the answer is (4,3)

since the rule for r0, 90º is (-y,x) and it was already applied to form the image, all you have to do is reverse the answer using this formula.