Equations and Inequalities
Solve for x.
3x + 5 = 10
x = 5/3
The equation of a line is y = 2x - 4. What is the slope of the line? What is the y-intercept?
Slope: 2
y-intercept: -4
What is the probability of a 6-sided die landing on a 4?
1/6
What is the cube root of 125?
5
A researcher records the amount of people who go to a water park each month. Should the researcher use a scatter plot of a line graph to represent the data?
The researcher should use a line graph because the data shows a variable (the number of people at the park) changing over time (month to month).
Solve for y.
-5x - 7 = 3
x = -2
Find the slope of a line that passes through the points (4, 3) and (-5, 0).
The slope is 3/9 (AKA 1/3).
What is the probability of a coin landing on tails 2 times in a row?
1/4, or 25%
√21 is between which two whole numbers?
4 and 5
Which value of g would make the inequality true?
-2g - 5 < -11
A) g = 0
B) g = 3
C) g = 7
D) All of the above.
C (g = 7) would make the inequality true.
The hypotenuse of a right triangle is 39 meters long. One of the legs of the triangle is 36 meters long. How long is the third side?
15 meters
Write the equation of the line that passes through (3, 3) and (0, -6).
y = 9x - 6
You roll a 6-sided die twice. What is the probability that both rolls give you an odd number?
1/4, or 25%
What value of y would make the equation true?
x-3(x2) = xy
Which of these lists of ordered pairs is NOT a function?
A) (3, 3), (4, 4), (5, 5), (0, 0)
B) (-1, 3), (-3, 3), (4, 0), (9, 1)
C) (0, 8), (1, 5), (5, 7), (0, -6)
D) (-2, 4), (0, 4), (9, 4), (13, 4)
C is not a function. There is an input (0) with more than one output (-6 and 8).
Solve for t.
t + 6 = 3t - 9
t = 15/2, or 7.5
The equation y = -3x + 63 models the relationship between the temperature outside, in degrees Fahrenheit (y-axis), and the time of day, in hours (x-axis). Interpret the slope of the line.
The slope, -3, means that the temperature decreases by 3 degrees Fahrenheit per hour.
A bag has 3 marbles in it: one red, one blue, and one yellow. If you pick a marble from the bag 30 times, how many times will you pick a red marble?
10 times
Convert 6,320,000 to scientific notation.
6.32 x 106
Reflect the point (-3, 7) across the x-axis.
(-3, -7)
Solve the equation.
-3(2h - 4) = -6h + 12
Infinitely many solutions.
The equation y = -3x + 63 models the relationship between the temperature outside, in degrees Fahrenheit (y-axis), and the time of day, in hours (x-axis). Interpret the y-intercept of the line.
The y-intercept, 63, means that it was 63 degrees Fahrenheit outside at the start of the day.
A spinner has 7 sections labeled 1 through 7. If you spin the spinner 21 times, how many times will you land on a number greater than 4?
9 times
Which of these numbers are irrational?
√8, 3.293471..., 1.33333..., -6/7, π (pi), √9
√8, 3.293471..., and π are all irrational. The rest are rational numbers.
Figure ABCD was dilated with a scale factor of 3/4. If Point B was at (8, 4), where is B'?
(6, 3)