Today's challenge
In the xy-plane, line p has a slope of −53 and an x-intercept of (−6, 0). What is the y-coordinate of the y-intercept of line p?
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Today's challenge
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Challenge 001
In the xy-plane, line p has a slope of −53 and an x-intercept of (−6, 0). What is the y-coordinate of the y-intercept of line p?
Challenge 002
The functions f and g are defined as f(x) = 14x − 9 and g(x) = 34x + 21. If h(x) = f(x) + g(x), what is the x-coordinate of the x-intercept of y = h(x)?
Challenge 003
During a month, Morgan ran r miles at 5 miles per hour and biked b miles at 10 miles per hour. She traveled 200 miles total and biked for twice as many hours as she ran. How many miles did Morgan bike?
Challenge 004
12x + 284 − s13 = r(x − 8)
In the equation, s and r are constants, and s > 0. If the equation has infinitely many solutions, what is the value of s?Challenge 005
What system of linear equations is represented by the lines shown?
Challenge 006
2(8x) + 4(7y) = 12
−2(8x) + 4(7y) = 12
The solution to the system is (x, y). What is the value of 8x + 7y?−2(8x) + 4(7y) = 12
Challenge 007
| x | y |
|---|---|
| k | 13 |
| k + 7 | −15 |
Challenge 008
3x = 36y − 45
One equation in a system is shown. The system has no solution. Which equation could be the second equation?Challenge 016
Which function gives the museum's total charge for a group of n people?
Challenge 017
Which equation represents the graphed linear relationship?
Challenge 018
Which function gives the carpet cleaner's rental cost for d days?
Challenge 019
How many solutions will the resulting system of three equations have?
Challenge 020
Use the table to find the value of a.
Challenge 021
The solution to the system is (x, y). What is the value of 30x?
Challenge 022
What is the smaller of the two positive integers?
Challenge 023
Find the product of g(15a) and g(7a).
Challenge 024
What is the y-intercept of the graph of y = f(x)?
Challenge 032
Which of the following expressions is a factor of 3x2 + 20x − 63?
I. x − 9
II. 3x − 7
II. 3x − 7
Challenge 033
For every positive value of x,
√(x5)∛(x4) = xab
What is the value of ab?Challenge 034
The function f is defined by f(x) = −ax + b, where a and b are constants. The graph of y = f(x) − 12 has a y-intercept at (0, −75/7). The product of a and b is 320/7. What is the value of a?
Challenge 035
f(x) = (x − 44)(x − 46)
For what value of x does f(x) reach its minimum?Challenge 036
r2 + qr = 2r − 55
In the equation, q is an integer constant. The equation has no real solutions. What is the largest possible value of q?Challenge 037
1x2 + 10x + 25 = 4
If x is a solution, which choice is a possible value of x + 5?Challenge 048
| Texting behavior | Talks on cell phone daily | Does not talk on cell phone daily | Total |
|---|---|---|---|
| Light | 110 | 146 | 256 |
| Medium | 139 | 164 | 303 |
| Heavy | 166 | 74 | 240 |
| Total | 415 | 384 | 799 |
In a study of cell phone use, 799 randomly selected US teens were asked how often they talked on a cell phone and about their texting behavior. The data are summarized in the table above. Based on the data from the study, an estimate of the percent of US teens who are heavy texters is 30% and the associated margin of error is 3%. Which of the following is a correct statement based on the given margin of error?
Challenge 049
Jennifer bought a box of Crunchy Grain cereal. The nutrition facts on the box state that a serving size of the cereal is 34 cup and provides 210 calories, 50 of which are calories from fat. In addition, each serving of the cereal provides 180 milligrams of potassium, which is 5% of the daily allowance for adults. If p percent of an adult's daily allowance of potassium is provided by x servings of Crunchy Grain cereal per day, which of the following expresses p in terms of x?
Challenge 050
The expression 0.35x represents the result of decreasing a positive quantity x by what percent?
Challenge 051
The box plots summarize the masses, in kilograms, of two groups of gazelles. Based on the box plots, which of the following statements must be true?
Challenge 052
A school district is forming a committee to discuss plans for the construction of a new high school. Of those invited to join the committee, 15% are parents of students, 45% are teachers from the current high school, 25% are school and district administrators, and the remaining 6 individuals are students. How many more teachers were invited to join the committee than school and district administrators?
Challenge 053
The histogram summarizes data set A, which represents the number of points per player earned by 50 players of a game. A new player earns 18 points playing the game, and this number of points is added to data set A to create data set B with 51 values. Which of the following must be true?
I. The median number of points per player for data set B is less than the median number of points per player for data set A.
II. The mean number of points per player for data set B is less than the mean number of points per player for data set A.
II. The mean number of points per player for data set B is less than the mean number of points per player for data set A.
Challenge 054
A sample of 40 fourth-grade students was selected at random from a certain school. The 40 students completed a survey about the morning announcements, and 32 thought the announcements were helpful. Which of the following is the largest population to which the results of the survey can be applied?
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