Solve the following algebraically. Trial and error is not an appropriate method of solution. You must show all of your work and write answers in rational form.
3 x + 7 = 9
Answer: x = 2/3
Show your work here: 3 x + 7 = 9
-7 - 7
3/3 x = 2/3
X = 2/3
b)
Answer: x= -2
Show your work here: -3(x +5) + 3 = 12
-3x+15 +3 =12
- 3 x + 18 = 12
- 18 - 18
3/3x = -6/3
X = -2
C)
Answer: x = 12/5
Show your work here: 3(2/3 x+ 1/6x)=2.3 2x + ½ x = 6 x =6 x =5 x= 12/5
d)
Answer: x = - 7
Show your work here: -2 x – 4 < 10 + 4 +4 -2/-2 x < 14/-2 x = - 7
2)
a) Solve for y
Answer: y = 2 – 3 x
Show your work here: 3 x + 4 y = 8
-3 x 3 x
4/4 y = 8 -3 x
Y = 2 – 3 x
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
Y-intercept = 2
c) Using your answer from part a, find the corresponding value of y when x =8.
Answer: y = 22
Show your work here: x =8 y = 2 -3x y = 2 – 3 (8) y = 2 -24 y =22
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.
(x3, y¹ 5), (x²1-, 1y²)
b) Find the slope of this line:
Answer: m =y² - y¹
X² - x¹
Show your work here: m= - 1 + ¯5 = ¯6
1 + ¯3 = ¯2 slope = 3
c) Find the equation of this line in slope-intercept form.
Answer: y =3 x + 1
Show or explain your work here: y = m x + b
Y = 3 x + 1
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: Mary salary will be 43,500 in 2004.
Show or explain your work here: m x b = y
1500(7) + 33,000 = y 10,500 +33,000= y= 43,500
4) Suppose that the width of a rectangle is 2 inches shorter than the length and that the perimeter of the rectangle is 80. P= 80 x = width x +2 = length
P = 2 (1) + 2 (w)
a) Set up an equation for the perimeter involving only L, the length of the rectangle. Answer: x + 2 = length
b) Solve this equation algebraically to find the length of the rectangle. Find the width as well.
Answer: Length _x = 2 = 19 + 2= 21, Width _x = 19
a) Show your work here: 2 (x = 2) + 2x = 80 2x + 4 + 2 x = 80 4x + 4 = 80 -4 -4 4x/4 = 76/4 x = 19 width = x= 19 length = x = 2 =19 + 2 = 21
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 of x for the following:
Option 1: C=32 + 3 (x)
Option 2: C=_$6.50 (x)
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:
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.
(___, ___)
So much for the rules. Where is the problem?
Solve the two sided inequality and show the solution on real line
7 < 1-2x ≤ 10
To find the y-intercept, we need to determine the point where the line crosses the y-axis. In this case, the y-intercept can be determined by looking at the point where x=0.
From the graph provided, it appears that the line crosses the y-axis at the point (0, -2). Therefore, the y-intercept is located at (0, -2).
To solve the equation 3x + 7 = 9 algebraically, we want to isolate the variable x on one side of the equation.
Here's a step-by-step solution:
1. Start with the equation: 3x + 7 = 9.
2. Subtract 7 from both sides to isolate the term containing x:
3x = 9 - 7.
Simplifying, we get: 3x = 2.
3. Divide both sides of the equation by 3 to solve for x:
x = 2/3.
So, the solution to the equation 3x + 7 = 9 is x = 2/3.
Here's the work:
3x + 7 = 9
Subtract 7 from both sides:
3x = 9 - 7
Simplify:
3x = 2
Divide both sides by 3:
x = 2/3