MTH133
Unit 1 Individual Project –
Name:
1) Solve the following algebraically. Trial and error is not an appropriate method of solution. You must show all of your work:
a) 2x + 5 = 9
Answer:
Show your work here:
b)
Answer:
Show your work here:
c)
Answer:
Show your work here:
d)
-4
Answer:
Show your work here:
2) a) 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 =12.
Answer:
Show your work here:
3) The following graph shows Bob’s salary from the year 2002 to the year 2005. He was hired in the year 2002; therefore x = 0 represents the year 2002.
a) List the coordinates of any two points on the graph in (x, y) form.
(___, ___),(___, ___)
b) Find the slope of this line:
Answer:
Show your work here:
c) Find the equation of this line in slope-intercept form.
Answer:
Show or explain your work here:
d) Using the result in part c, determine Bob’s salary in 2008.
Answer:
Show or explain your work here:
4) Suppose that the length of a rectangle is 3 inches longer than the width and that the perimeter of the rectangle is 78.
a) Set up an equation involving only W, the width 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:
5) A tennis club offers two payment options:
Option1: $35 monthly fee plus $4/hour for court rental
Option 2: No monthly fee but $6.50/hourfor 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.
Answer:
Show your work here:
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.
(___, ___)
Practice Problems from Live Lecture
Problem
Solve the following:
5x + 2 = 3
- 2 - 2
5x = 1
÷5 ÷5
x = 1/5 (this is the answer)
Problem
Distribute (multiply) the -3 to get
-3x – 12 + 5 = 4
Get like terms together
-3x – 7 = 4
+ 7 +7
-3x = 11
÷(-3) ÷(-3)
x = -11/3 (this is the answer)
Problem
Find the Least Common Multiple (Lowest number denominators will go into) It’s 6, multiply both sides by 6 to clear the fractions.
4x + 5x = 18
9x = 18
÷9 ÷9
x = 2 (this is the answer)
Problem
-2 -2
÷(-3) ÷(-3)
x > -3 (this is the answer) (REMEMBER TO SWAP THE DIRECTION OF THE SIGN IF YOU DIVIDE OR MULTIPLY EACH SIDE BY A NEGATIVE NUMBER )
Problem
Solve 3x + 5y = 10 for y
3x + 5y = 10
-3x -3x
5y = -3x + 10
÷5 ÷5 ÷5
y = (-3/5 )x + 2 (this is the answer)
Problem continued
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 = ___-3/5___ (this is the answer) because in y= mx + b form -3/5 is “m” or the slope
Y-intercept = __2___ (this is the answer) because in y= mx + b form 2 is “b” or the y intercept, this could also be noted as (0,2)
Problem continued
Using your answer from the first part, find the corresponding value of y when x =10.
Simply substitute 10 for x in your equation
y = (-3/5 )10 + 2
y = (-30/5) + 2
y = -6 + 2
y = -4 (this is the answer)
Problem
The following graph shows Bob’s business income from the year 2000 to the year 2003. He was hired in the year 2000; therefore, t=0 represents the year 2000.
List the coordinates of two points on the graph in (x, y) form.
(0, 5000), (1, 11000)
Find the slope of this line:
Slope is difference in y’s over difference in x’s (y2 – y1)/(x2 – x1)=11000-5000/1 – 0 = 6000/1 = 6000 (this is the answer)
Find the equation of this line in slope-intercept form.
y=6000x+5000 (this is the answer) (the 6000 is the slope, the 5000 is the y intercept because it is where x was equal to zero (the point (0, 5000)
If Bob’s business income trend continued, what would his business make in the year 2006?
Simply substitute 6 (because 6 would stand for the year 2006 in this equation) for x
y=6000(6)+5000
y=36000 + 5000
y=41000 (this is the answer)
Problem
Suppose that the width of a rectangle is 4 inches shorter than the length and that the perimeter of the rectangle is 32.
Set up an equation for the perimeter involving only L, the length of the rectangle.
L+L+L-4+L-4=32 or 4L-8=32 (I used “L” to represent Length) so I would have
4L-8=32 (this is the answer)
Solve this equation algebraically to find the length of the rectangle. Find the width as
well.
Solve
4L-8=32
+8 +8
4L = 40
÷4 ÷4
L = 10 inches so Width would be 10 – 4 or 6 inches
(this is the answer)
Problem
A tennis club offers two payment options:
Option1: $50 monthly fee plus $4/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.
Write a mathematical model representing the total monthly cost, C, in terms of x for both options
Option 1: C=_____50+4x______(this is the answer)
Option 2: C=______6.50x______(this is the answer)
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 the first part.
50+4x < 6.5x
-4x - 4x
50 < 2.5x
÷2.5 ÷2.5
20 < x which is more correctly written as
x> 20 (this is the answer) (thus more than 20 hours per month)
Problem
Plot the following points on the given rectangular coordinate system by clicking on the given dots and dragging them.
If you have a hard time getting these in the correct place, try using the arrow keys and holding the “ctrl” button down at the same time.
If you were to connect these points with a line, where would the y-intercept be located? Give answer in (x, y) form.
Drawing a straight line you can see it would hit at (0,-3)