A section of roller coaster track has the dimensions shown in the diagram. Find the grade of the track, which is the slope written as a percent.
10.8 meters 30 meters
Question 1 options:
A)
3%
B)
36%
C)
10.8%
D)
41%
The grade of a track is the vertical change in elevation divided by the horizontal change in distance, expressed as a percentage.
In this case, the vertical change in elevation is 10.8 meters and the horizontal change in distance is 30 meters.
To find the grade, we divide the vertical change by the horizontal change and multiply by 100:
Grade = (Vertical Change / Horizontal Change) * 100
Grade = (10.8 / 30) * 100
Grade = 0.36 * 100
Grade = 36
Therefore, the grade of the track is 36%.
The correct answer is B) 36%.
To find the grade of the track, which is the slope written as a percent, we need to find the rise and run of the track.
The rise is the vertical change in height, which is given as 10.8 meters.
The run is the horizontal distance traveled, which is given as 30 meters.
Now, we can calculate the slope by dividing the rise by the run and multiplying by 100 to express it as a percentage:
Slope = (rise / run) * 100
Slope = (10.8 / 30) * 100
Slope ≈ 0.36 * 100
Slope ≈ 36%
Therefore, the grade of the track is 36%. So the correct option is B) 36%.
The average attendance, A, at a minor league baseball park can be modeled by the equation
A = 30w + 6,000
where w is the number of games the team won the previous year. What will the average attendance be next year if the team wins 89 games this year?
Question 2 options:
A)
9560
B)
5911
C)
8670
D)
3330
To find the average attendance next year, we can substitute the value of w, which is 89 games, into the equation A = 30w + 6,000.
A = 30(89) + 6,000
A = 2,670 + 6,000
A = 8,670
Therefore, the average attendance next year, when the team wins 89 games this year, will be 8,670.
The correct answer is C) 8670.
To find the grade of the track, we need to calculate the slope as a percent. The grade of a track is defined as the change in vertical height divided by the horizontal distance traveled.
In this case, we are given the dimensions of the track: 10.8 meters in vertical height and 30 meters in horizontal distance.
To find the grade, we divide the change in vertical height (10.8 meters) by the horizontal distance (30 meters):
Grade = (vertical height / horizontal distance) * 100%
Grade = (10.8 / 30) * 100%
Grade = 0.36 * 100%
Grade = 36%
So, the grade of the track is 36%.
Therefore, the correct answer is option B) 36%.
Write the equation of the line with the given slope, m, and y-intercept, (0, b).
m = - ; b = 4
Question 3 options:
A) y = - x + 4
B) y = - x - 4
C) y = x + 4
D) y = x - 4
The equation of a line with a slope, m, and a y-intercept, (0, b), is given by the formula: y = mx + b.
In this case, the slope is -3 and the y-intercept is 4.
Plugging these values into the formula, we get:
y = -3x + 4
Therefore, the correct answer is A) y = -3x + 4.
A tool rental store charges a flat fee of $6.00 to rent a drill press, and $3.00 for each day, including the first. Use a linear equation to find the cost of renting the tool for one week.
Question 4 options:
A)
$27.00
B)
$21.00
C)
$24.00
D)
$9.00
The cost of renting the tool for one day is $6.00 (flat fee) + $3.00 (per day charge) = $9.00.
To find the cost of renting the tool for one week, we multiply the daily cost by the number of days in a week:
Cost = $9.00 * 7 = $63.00
Therefore, the cost of renting the tool for one week is $63.00.
The correct answer is not provided among the options.
Write the equation of the line with the given slope, m, and y-intercept, (0, b).
Undefined slope, through (6, -6)
Question 5 options:
A)
y = 0
B)
y = -6
C)
x = 0
D)
x = 6
The equation of a line with an undefined slope is of the form x = k, where k is a constant.
In this case, the line has an undefined slope and passes through the point (6, -6).
Therefore, the equation of the line is x = 6.
The correct answer is D) x = 6.
Determine whether the lines are parallel, perpendicular, or neither.
9x + 3y = 12
24x + 8y = 34
Question 6 options:
A)
perpendicular
B)
parallel
C)
neither
To determine if the lines are parallel or perpendicular, we need to compare their slopes.
To find the slope of a line in standard form (Ax + By = C), we can rearrange the equation to slope-intercept form (y = mx + b), where m is the slope.
Given the equations:
9x + 3y = 12
24x + 8y = 34
Rearranging the first equation:
3y = -9x + 12
y = -3x + 4
Rearranging the second equation:
8y = -24x + 34
y = -3x + 4.25
Comparing the slopes of the two lines, we see that they both have a slope of -3. Therefore, the lines are parallel.
The correct answer is B) parallel.
The average attendance, A, at a minor league baseball park can be modeled by the equation
A = 30w + 6,000
where w is the number of games the team won the previous year. If the average attendance this year is 8160, how many games did the team win last year?
Question 7 options:
A)
83
B)
65
C)
53
D)
72
To find the number of games the team won last year, we can substitute the given average attendance of 8160 into the equation A = 30w + 6000.
8160 = 30w + 6000
Rearranging the equation:
30w = 8160 - 6000
30w = 2160
Dividing both sides of the equation by 30:
w = 2160 / 30
w = 72
Therefore, the team won 72 games last year.
The correct answer is D) 72.
An overpaid basketball player has a guaranteed base salary of $4,000,000. He has a clause in his contract that pays him an additional $500 for each point he scores. Write a linear equation that computes his total salary (s) in terms of the number of points he scores (p).
Question 8 options:
A)
s = 500p + 4,000,000
B)
s = 4,000,000p + 500
C)
s = -500p + 4,000,000
D)
s = 4,000,500p
The linear equation that computes the basketball player's total salary (s) in terms of the number of points he scores (p) can be written as:
s = 500p + 4,000,000
Therefore, the correct answer is A) s = 500p + 4,000,000.
Complete the ordered pairs for the given linear equation. Then plot the points and graph the equation by connecting the points.
4x + 5y = 0
(-5, ), (0, ), (5, )
Question 9 options:
A)
(-5, 5), (0, 1), (5, -3)
B)
(-5, -5), (0, -1), (5, 3)
C)
(-5, -4), (0, 0), (5, 4)
D)
(-5, 4), (0, 0), (5, -4)
To complete the ordered pairs for the given linear equation 4x + 5y = 0, we need to substitute the x-values into the equation and solve for the corresponding y-values.
For the ordered pair (-5, ?):
4(-5) + 5y = 0
-20 + 5y = 0
5y = 20
y = 4
Therefore, the ordered pair is (-5, 4).
For the ordered pair (0, ?):
4(0) + 5y = 0
0 + 5y = 0
5y = 0
y = 0
Therefore, the ordered pair is (0, 0).
For the ordered pair (5, ?):
4(5) + 5y = 0
20 + 5y = 0
5y = -20
y = -4
Therefore, the ordered pair is (5, -4).
The completed ordered pairs are: (-5, 4), (0, 0), (5, -4).
Now, let's plot these points and graph the equation:
(-5, 4), (0, 0), (5, -4)
graph{4x + 5y = 0 [-8, 8, -4, 4]}.
The correct answer is D) (-5, 4), (0, 0), (5, -4).
Write the equation of the line with the given slope, m, and y-intercept, (0, b).
m = 0; b = -6
Question 10 options:
A)
x = y - 6
B)
y = -6
C)
y = x - 6
D)
x = -6
The equation of a line with a slope, m, and a y-intercept, (0, b), is given by the formula: y = mx + b.
In this case, the slope is 0 and the y-intercept is -6.
Plugging these values into the formula, we get:
y = 0x - 6
Simplifying, we get:
y = -6
Therefore, the correct answer is B) y = -6.