The Variable
Solve: −2|m − 2| = −6
m = 5, m = −1
Which of these is NOT a function — a table where x-values repeat with different y-values, or one where y-values repeat?
x-values repeating with different y-values
A spring stretches 0.1 cm for every 2 kg added. How much does it stretch per kilogram?
0.05 cm
Jackie buys 3 hot dogs and 1 pretzel for $12.25. Sylvia buys 2 hot dogs and 4 pretzels for $16.50. Write the system of equations.
3h + p = 12.25
2h + 4p = 16.50
A museum had 25,000 visitors in 1980 and loses 2.5% per year. Write the decay function.
v(t) = 25,000(0.975)ᵗ
Solve the inequality: 4x − 7 ≥ 3x + 2
x ≥ 9
If f(x) = −16t² + 192t + 2560, what is f(8)?
3,072
What is the slope of a line passing through (1, 2) and (3, 8)?
3
A system of equations has the same slope and same y-intercept. How many solutions does it have and what does that mean graphically?
Infinitely many solutions, the lines are the same/coincide.
The equation A = 1,750(1.04)ᵗ models an account. What does this tell you?
the account grows 4% per year, started with 1,750 dollars.
Grace and her brother need $400. They earn $25 per lawn mowed (m) and $10 per hour babysitting (b). Write the equation.
25m + 10b = 400
If f(x) = 3x − 7, what is f(5)?
f(5) = 3(5) − 7 = 8
Convert to slope-intercept form: 2x − y = 6
y = 2x − 6
Solve by substitution: y = 2x and x + y = 9
x = 3, y = 6
Factor: (x² − 4)(x + 3) = 0. What are ALL values of x?
x = −3, −2, 2
Simplify: (3x⁴ + 9x³ − 7x + 15) + (−6x⁴ − 8x² + 5x − 3)
−3x⁴ + 9x³ − 8x² − 2x + 12
Is the relation {(1,3), (2,5), (2,7), (4,9)} a function? Why or why not?
No, the input 2 maps to two different outputs
A phone plan charges a flat fee of $30 per month plus $0.10 per text. Write and interpret the linear function.
C(t) = 0.10t + 30; slope = cost per text, y-intercept = base fee
Solve by elimination: x + y = 7 and x − y = 1
x = 4, y = 3
The length of a garden is 6 feet more than its width, and the area is 40 sq ft. What is the length?
10 feet
John has ridden 12 miles and wants to ride 100 miles total. He has 40 days left. How many miles per day does he need to average?
2.2 miles/day
If f(x) = x² − 4 and g(x) = 2x + 1, for what value of x does f(x) = g(x)?
x = −1 and x = 5
Two lines are graphed: y = 2x + 1 and y = 2x − 4. Will these lines ever intersect?
No, same slope, different y-intercepts means they are parallel; no solution
Karen wants to spend at least $100 on food (f) and at least $50 on favors (p), with a total no more than $250. Write the system of inequalities.
f ≥ 100, p ≥ 50, f + p ≤ 250
Solve: 3(x − 5)² + 6 = 54. What is the value of x?
x = 9