Linear Equations and Inequalities
Solve for x:
x=2(x-1)+6
x = -4
What do all quadratic functions create when you graph them?
a parabola
Solve this system of equations:
3x+3y=6 and
2x-3y=4
(2,0)
Ms. Sumner is having her lawn mower tuned up. The Sears repairman charges $50 service call plus $35 per hour. Write an equation to represent the money Ms. Sumner will pay depending on the "x" hours the repairman works.
y = 35x + 50
Multiply:
(9r + 3)(2r - 1)
18r^2-3r-3
Write the equation of a line in standard form, given m= 2 and b= -1.
2x - y= 1
The maximum point, or minimum point on a parabola is called the...
the vertex
Solve this system of equations:
x=5y and
2x+3y=-13
(-5,-1)
For $5.00 you could buy 1 coke and 3 pieces of pizza. For $8.00 you could buy 3 cokes and 2 pieces of pizza . Write the systems of equations to represent the situation.
5 = 1c + 3p
8 = 3c + 2p
Find the x and y intercepts of the following line: 8x+2y=-16
(-2,0) and (0, -8)
Solve for x:
3 - x > 2x - 6
3 > x
Solve:
4x^2+23x-6
-6 and .25 or
1/4
Giselle works as a carpenter and as a blacksmith. She earns $20 per hour as a carpenter and $25 per hour as a blacksmith. Last week, Giselle worked both jobs for a total of 30 hours, and earned a total of $690. How long did Giselle work as a carpenter last week, and how long did she work as a blacksmith?
12 hours as a carpenter and 18 hours as a blacksmith
A student works at a job which plays $5.00 per hour. This week the student also received a bonus of $75. If the total pay for the week was $200, how many hours did the student work?
25 hours
The average health premiums have been increasing at a rate of 8.5%. If the average family's premiums are $54,000 this year write an exponential function to determine the premium after x years.
y=54000(1.085)^x
Solve for x:
3-(x+8) < -4x-26
x < -7
Find the roots:
10x^2+100x+250
-5
Solve this system of equations:
-4x-15=5y and
5y=11-4x
no solution
Four drinks and 2 pizza slices costs $11.00 and 6 drinks and 5 pizza slices cost $19.50. How much does one slice of pizza cost?
$1.50
Simplify:
5x + 3y + 9 + 8x - 4y + 12x
25x - y + 9
Solve for x:
6 < -(-8-2x)
-1 < x
Solve the following:
(x-7)(x-1) = 0
x = 7 and x = 1
Solve this system of equations:
y = 2x - 3 and
-4x + 2y = -6
infinite solutions
You are buying brats and hot dogs for a barbecue. Brats cost $2.00 per pound and hot dogs cost $3.00 per pound. You have $36 to spend. Create a linear equation to represent the different number of combinations of brats and hot dogs you can have, then write it in slope-intercept form.
y=-2/3x+12
How do you check to see if a relation is a function?
vertical line test or
x does not repeat