Equations & Inequalities
Solve: 2x+5=15
x = 5
What is the slope of the line that passes through (1, 2) and (3, 6)?
2
What is the scale factor if a figure doubles in size?
Scale factor = 2
What is the range of this data: 5, 10, 8, 7, 12?
Range = 12−5=7
A taxi charges $3 plus $2 per mile. Write an equation for total cost, C, in terms of miles, m.
C=2m+3
Solve: 3(x−4)=18
x=10
Is this a function?
{(1, 2), (2, 3), (1, 5)}
Not a function, because the x-value 1 repeats with different y-values
A triangle is rotated 90° clockwise. What transformation occurred?
Rotation around the origin
What does a positive correlation on a scatterplot mean?
As one variable increases, the other also increases
A graph shows a line going through the origin and (4, 8). Is this a direct variation? Why?
Yes, because it goes through the origin and is proportional (constant rate of change)
Solve: x−7<4
x<11
Find the slope and y-intercept of y=−3x+4
Slope: -3, y-intercept: 4
Identify the transformation: Pre-image (2, 3) → Image (-2, 3)
Reflection over the y-axis
Find the mean absolute deviation of: 4, 6, 8
1.33
A shirt costs $15. It’s on sale for 20% off. What’s the sale price?
20% of $15 = $3 → Sale price = $12
Which of the following equations has no solution?
A. x+2=x+2
B. 2x+3=2x−1
C. 4x=4x
B.2x+3=2x−1— No solution because the variables cancel and the statements are not equal
A table shows a constant rate of change of -2. What does that tell us about the slope?
The slope is negative; the graph goes downhill left to right
Which transformation does NOT preserve orientation: reflection, translation, rotation, or dilation?
Reflection, because it flips the figure, changing orientation
What type of sampling method is being used if every 5th person is selected?
Systematic sampling
A savings account earns 2% interest annually. If you deposit $500, how much interest in one year?
2% of $500 = $10
Miranda solved this equation: 5(x−2)=3x+4. What was her mistake if she got x=3?
She probably didn’t distribute the 5 correctly or didn’t combine like terms correctly. Correct answer is x=7
A line has a slope of 1/2 and passes through (0, 5). Write its equation in slope-intercept form.
y=1/2x+5
Triangle ABC is dilated by a scale factor of 3 centered at the origin. If A is at (1, 2), where is A′?
A′ = (3, 6) — multiply each coordinate by 3
A bag has 4 red, 3 blue, and 5 green marbles. What is the probability of drawing a blue marble?
1/4
A student scored 70, 80, 90, and needs at least an 85 average. What’s the lowest score they can make on the 4th test?
100