Linear Equations
Determine if the slope between (5, -8) & (-10, -8) is negative, positive, zero, or undefined.
Zero Slope
2(5x - 20) - (15 + 8x) = 7
x = 31
Kaylie is selling tickets to the annual talent show. After one week of ticket sales, she sold 85 tickets. The adult tickets sold for $5 each, while the student tickets are $3 each. She collected a total of $305. Write a system of equations that represents this situation, if x = number of adult tickets sold, and y = number of student tickets sold.
x + y = 85
5x + 3y = 305
Simplify the expression: 63 x 63
66
Factor x2 + 5x + 6
(x + 3) (x + 2)
A line passes through the point (-4, 7) and has a slope of -3/5. Write an equation in point-slope form.
y - 7 = -3/5 (x + 4)
If 4x - 20 = 16, what is the value of 10x2 + 5?
815
Find d so that the following system has infinite solutions
4x - 5y = -7
12x + dy = -21
d = -15
Simplify the expression (-2x-7)/(x-3)
-2/x4
Factor x2 - 7x + 12
(x - 3)(x - 4)
Graph the line x = -3.
Vertical line at x = -3.
Determine if the following equations have the same solution.
-3x + 5 = 12 - 4x -4(x - 4)2 + 10 = -26
Yes, they have the same solution, x = 7
How many soltuions does the following system have?
8x - 3y = 6
y = 8/3 x - 8
None
Expand (3x + 10)2
9x2 + 60x + 100
Factor 2x3 - x2 + 8x - 4
(x2 + 4)(2x - 1)
Determine the y-intercept of the line: y - 2 = -3/4 (x + 8)
y-intercept = (0, -4)
Solve the following equation: (3x - 2)/5 = (2x + 4) /2
x = -6
In a system of linear equations, the point (-2, 5) is a solution to the system, as well as the point (6, -1). What conclusion can you draw about this system? Explain.
The system must have infinite solutions, since more than one point satisfies the system.
Simplify (-2m2n3)(4mn4)(m5n2)
-8m8n9
Factor 3x2 - 2x - 8
(3x + 4)(x - 2)
The points (3, k) & (9, 6) lie on a line that passes through the origin. What is the value of k?
k = 2
Knox and Henry are writing letters for the same election campaign. Knox writes at a pace of 5 letters every hour, and Henry writes 7 letters every hour. Each day, they go to the office and write letters for the same amount of hours. Their goal is to write 200 letters to people in town. How much time will it take to reach 20% of their goal?
3 hours and 20 minutes
Solve the following system:
4x + 2y = 12
3x - 3y = 9
(3, 0)
Write a simplified expression which represents the volume of a rectangular prism if the height is x + 2, width is x + 4, and length is x.
x3 + 6x2 + 8x
What are the x-intercepts of y = (x + 2)(x - 3)
(-2, 0) & (3, 0)