Math Help, Can anyone help me!?

Question

1.Which of the following best describes the solution to the equation below? 

6x + 20 = -30 + 6x 

2.Solve the following system of equations. 

8x + 4y = -48 
3x + y = -12 

3.What is the length of the longest side of a triangle that has the vertices (2, 6), (-4, 6), and (-4, 4)? 

4.A small college opened in 1999. In the linear model below, x represents the number of years after 1999, and y represents the student population. Interpret the slope. 

y = 576 + 173x 

5.Which value of x makes the following equation true? 

3(x - 3) - 14 = 2(x - 7) + 11 

6.Which shows the expression below in simplified form? 

(7.2 × 10^-2) - (3 × 10^-5)

Answer 1

1) The equation 6x + 20 = - 30 + 6x

In the above equation the variable terms are equal, so there is no solution.

Answer 2

Substitution method

2) The system of equations are 8x + 4y = - 48 -----> (1)

3x + y = - 12 ---> (2)

Solve the second equation for y since the coefficient of y is 1.

y = - 12 - 3x

Find the value of x by substituting - 12 - 3x for y in the First equation.

8x + 4(- 12 - 3x) = - 48

8x - 48 - 12x = - 48

- 4x  = - 48 + 48

-4x = 0

x = 0

Substitute 0 for x  in either equation to find the value of y.

Second equation 3x + y = - 12

3(0) + y = - 12

y = -12

Solution x = 0, y = - 12.

Answer 3

3) Let the vertices of the triangle are

Find the distance between every two vertices of triangle and it would be lengths of sides.

Calculate the distance using following formula.

CA side length is greater then remaining sides.

Longest side vertices are (2, 6) and (-4 , 4).

Answer 4

4) The equation y = 576 + 173x

Rewrite as y = 173x + 576

Compare it to slope intercept form of linear equation y = mx + b

Where m is slope and b is y - intercept.

in this case m = 173

Every year of the college being open is associated with an additional 173 students.

Answer 5

5) The equation 3( x - 3) - 14 = 2(x - 7) + 11

Apply distributive property a (b + c ) = ab + ac.

3x  - 9 - 14 = 2x - 14 + 11

3x - 23 = 2x - 3

Separate the variable terms and constants.

3x - 2x = - 3 + 23

x = 20

The value of x = 20 makes the equation  true.

Answer 6

6) The expression is

Apply the negative exponent property

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