# Equations

1) Solve the following algebraically. All answers should be written in rational form.

a) 3x + 7 = 9

Answer:

Show your work here:

b)-3(x+5) +3=12

Answer:

Show your work here:

c) 2/3x+1/6x=2

Answer:

Show your work here:

d)-2x-4<10

Answer:

Show your work here:

2) a)3x+4y=8 Solve for y

Answer:

Show your work here:

b) When graphed this equation would be a line. By examining your answer to part a, what is the slope and y-intercept of this line?

Slope = ______

Y-intercept = _____

c) Using your answer from part a, find the corresponding value of y when x =8.

Answer:

Show your work here:

3) Suppose that the width of a rectangle is 2 inches shorter than the length and that the perimeter of the rectangle is 80.

a) Set up an equation for the perimeter involving only L, the length of the rectangle.

Answer:

b) Solve this equation algebraically to find the length of the rectangle. Find the width as well.

Answer: Length ______, Width ______

Show your work here:

4) A tennis club offers two payment options:

Option1: $32 monthly fee plus $3/hour for court rental

Option 2: No monthly fee but $6.50/hour for court rental.

Let x = hours per month of court rental time.

a) Write a mathematical model representing the total monthly cost, C, in terms of x for the following:

Option 1: C=_________________

Option 2: C=_________________

b) How many hours would you have to rent the court so that the monthly cost of option 1, is less than option 2. Set up an inequality and show your work algebraically using the information in part a. Round to 3 decimal places if necessary.

Answer:

Show your work here:

5) Plot the following points on the given rectangular coordinate system by clicking on the given dots and dragging them.

point to plot: (-4, -1)

(-2,1)

(2,5)

If you were to connect these points with a line, where would the y-intercept be located? Give answer in (x, y) form.

(___, ___)

6).Solve the following by factoring:

a)5t^2-10t=0

Answer:

Show your work here:

b)x^2-3x-10=0

Answer:

Show your work here:

7.If f(x)=3x^2+5x-2 , find:

a) f(-2)

Answer:

Show your work here:

b) f(4)

Answer:

Show your work here:

8.Solve 3x^2+19x-14=0 using the quadratic formula.

Answer:

Show your work here:

9.a) Calculate the value of the discriminant of x^2+2x+1=0 .

Answer:

Show your work here:

b) By examining the sign of the discriminant in part a, how many x-intercepts would the graph of y=x^2+2x+1 have? Why?

Answer:

10.

7) The path of a falling object is given by the function s=-16t^2+v0t=s0 where represents the initial velocity in ft/sec and represents the initial height in feet. Also, s represents the height in feet of the object at any time, t, which is measured in seconds.

a) If a rock is thrown upward with an initial velocity of 40 feet per second from the top of a 30-foot building, write the height (s) equation using this information.

Typing hint: Type t-squared as t^2

Answer:

b) How high is the rock after 2 seconds?

Answer:

Show your work here:

#### Solution Preview

Here you go!

1) Solve the following algebraically. All answers should be written in rational form.

a) 3x + 7 = 9

Answer: x = 2/3

Show your work here:

Subtract 7:

3x = 2

Divide by 3:

x = 2/3

b)-3(x+5) +3=12

Answer: x = -8

Show your work here:

subtract 3:

-3(x+5) = 9

Divide by -3:

x+5 = -3

Subtract 5:

x = -8

c) 2/3x+1/6x=2

Answer: x = 12/5

Show your work here:

Convert to a common denominator:

4/6 x + 1/6 x = 2

Add:

5/6 x = 2

Multiply by 6:

5x = 12

Divide:

x = 12/5

d)-2x-4<10

Answer: x > -7

Show your work here:

Add 4:

-2x < 14

Divide by -2 and flip the sign:

x > -7

2) a)3x+4y=8 Solve for y

Answer: y = -3/4 x + 2

Show your work here:

Subtract 3x:

4y = -3x + 8

Divide by 4:

y = -3/4 x + 2

b) When graphed this equation would be a line. By examining your answer to part a, what is the slope and y-intercept of this line?

Slope = -3/4

Y-intercept = (0, 2)

c) Using your answer from part a, find the corresponding value of y when x =8.

Answer: -4

Show your work here:

-3/4 * 8 + 2

= -6 + 2

= -4

3) Suppose that the width of a rectangle is 2 ...

#### Solution Summary

This includes examples of solving a variety of type of equations, including fractions, graphing, quadratics, and word problems.