MTH133
Unit 1 Individual Project
Name:
1)Solve the following algebraically. All answers should be written in rational form.
a)3x+7= 9
Answer:
b)
Answer:
c)
Answer: 12/5
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)
Answer: x > -7
Show your work here:
Add 4:
-2x < 14
Divide by -2 and flip the sign:
x > -7
2)a)Solve for y
Answer: -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)The following graph shows Mary’s salary from the year 2004 to the year 2007. She was hired in the year 2004; therefore x=0 represents the year 2004.
a)List the coordinates of any two points on the graph in (x,y) form.
(0, 28000), (1, 29500)
b)Find the slope of this line:
Answer: 1500
Show your work here:
= (29500-28000)/(1-0)
= 1500/1
= 1500
c)Find the equation of this line in slope-intercept form.
Answer: y = 1500x + 28000
Show or explain your work here:
y-y1 = m(x-x1)
y-28000 = 1500(x-0)
y-28000 = 1500x
y = 1500x + 28000
d)If Mary’s salary trend continued, what would her salary be in the year 2014? Show how you obtained your answer using part c).
Answer: $43,000
Show or explain your work here:
Plug in x = 10 (since that is year 2014):
y = 1500*10 + 28000
y = 15000 + 28000
y = 43000
4)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:
W = L - 2
P = 2L + 2W = 80
2L + 2(L-2) = 80
b)Solve this equation algebraically to find the length of the rectangle. Find the width as well.
Answer: Length 21, Width 19
Show your work here:
Distribute:
2L + 2L - 4 = 80
Combine:
4L - 4 = 80
Add 4:
4L = 84
Divide by 4:
L = 21
W = L - 2 = 21 - 2 = 19
5)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 ofx for the following:
Option 1: C= 3x+32
Option 2: C= 6.5x
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: x > 9.143 hours
Show your work here:
3x + 32 < 6.5x
Subtract 3x:
32 < 3.5x
Divide by 3.5:
9.143 < x
x > 9.143
6)Plot the following points on the given rectangular coordinate system by clicking on the given dots and dragging them.
If you were to connect these points with a line, where would the y-intercept be located? Give answer in (x,y) form.
(0, 3)