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# Equations

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

a) 3x + 7 = 9

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

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

d)-2x-4<10

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

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.

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

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.

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

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

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

a) f(-2)

b) f(4)

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

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

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?

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

b) How high is the rock after 2 seconds?

#### Solution Preview

Here you go!

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

a) 3x + 7 = 9

Subtract 7:
3x = 2
Divide by 3:
x = 2/3

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

subtract 3:
-3(x+5) = 9
Divide by -3:
x+5 = -3
Subtract 5:
x = -8

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

Convert to a common denominator:
4/6 x + 1/6 x = 2
5/6 x = 2
Multiply by 6:
5x = 12
Divide:
x = 12/5

d)-2x-4<10

-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

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.