Algebra 2 summer packet?

Question

will someone please help and explain how to do this problems with step by step?

im clueless.

1.Solve by linear combinations: 4x+y=-12 ; 3x-y=-16

2.Write (4x-3)^2 as a trinomial

3. Solve: x^2 - 3x = 0

4.Factor: 2x^2 = 3x - 20

5. Solve the equation : 4x^2 + 7x - 2 = 0


step by step please. and thank you to anyone who helps!

Answer 1

1. switch around the first, so y=-12-4x .. plug that into the second .. 3x - (-12-4x)=-16. 7x=-28 .. x=-4. then plug that back in to one of the equations to get y. y=-4
2. (4x+3)(4x+3) .. foil (first outside inside last) 16x^2+12x+12x+9 .. 6x^2+24x+9
3. (x)(x-3)
4. doesn't factor .. check to see if you made a mistake in typing it
5. (4x-1)(x+2)

Answer 2

1.
4x + y = -12
3x - y = -16

Add these together.

7x = -28
x = -4

3(-4) - y = -16
-12 - y = -16
y = 4

2.
(4x - 3)(4x - 3)(4x - 3) =
(16x^2 - 24x + 9)(4x - 3) =
64x^3 - 144x^2 + 108x - 27

3.
x(x-3) = 0
x = 0 or x = 3

4.
2x^2 - 3x + 20 = 0
x = (3 +/- sqrt(9 - 160))/(2 * 2)
This doesn't have real roots.

If it was 2x^2 = 3x + 20, you would get
x = (3 +/- sqrt(9 + 160))/(2 * 2)
x = (3 +/- sqrt(169))/(4)
x = (3 +/- 13)/(4)
x = -10/4 or x = 16/4
x = -2.5 or x = 4

5,
4x^2 + 7x - 2 = 0
x = (-7 +/- sqrt(49 + 32))/(2 * 4)
x = (-7 +/- sqrt(81))/(8)
x = (-7 +/- 9)/(8)
x = -16/8 or x = 2/8
x = -2 or x = 1/4

Answer 3

2. Trinomial means it is an expression with three different terms. So you will multiply it out
FOIL-Multiply first terms, Multiply outside terms, multiply inside terms, multiply last terms,
(4x-3)^2 = (4x-3)(4x-3)=16x^2-12x-12x+9
Now combine like terms
=16x^2-24x+9 This is your trinomial, it has three terms

3. x^2 - 3x = 0
You will factor and solve
x(x - 3) = 0
This means either x=0 or x-3 = 0
So your two solutions are x = 0 and x = -3