An SAT tutoring service charges a $500 fee for two sessions, plus $50 for each additional session. Emily doesn't want to spend more than $700 on tutoring. What is the maximum number of additional sessions (beyond the first two) that Emily can book for her tutoring sessions?(1 point)
Responses
Let x be the number of additional sessions beyond the first two.
The cost of the additional sessions is 50*x.
The total cost for the tutoring sessions is 500 + 50*x.
Since Emily doesn't want to spend more than 700, we can write the inequality: 500 + 50*x ≤ 700.
Subtracting 500 from both sides, we get: 50*x ≤ 200.
Dividing both sides by 50, we get: x ≤ 4.
Therefore, the maximum number of additional sessions Emily can book is 4. Answer: \boxed{4}.
Ashley and Liam both have playlists on their music apps.
The number of playlists on Ashley’s app can be represented by X.
The number of playlists on Liam’s app is 4 times the number of playlists on Ashley’s app.
The total number of playlists on both their apps is at least 45.
What is the solution set for x, representing the number of playlists on Ashley’s app?
Let x be the number of playlists on Ashley's app.
The number of playlists on Liam's app is 4 times the number of playlists on Ashley's app, so it is 4x.
The total number of playlists between the two apps is x + 4x = 5x.
We are given that the total number of playlists is at least 45, so we can write the inequality: 5x ≥ 45.
Dividing both sides by 5, we get: x ≥ 9.
Therefore, the solution set for x, representing the number of playlists on Ashley's app, is x ≥ 9.
Olivia visited a stationery shop to buy journals.
She had $36 allocated for the purchase.
Olivia bought 4 journals.
Following the purchase, Olivia had less than $12 remaining.
What is the solution set for x, representing the cost of each journal?
(1 point)
Let x be the cost of each journal.
The total cost of the 4 journals is 4x.
Olivia had $36 allocated for the purchase and had less than $12 remaining, so we can write the inequality: 4x + 12 > 36.
Subtracting 12 from both sides, we get: 4x > 24.
Dividing both sides by 4, we get: x > 6.
Therefore, the solution set for x, representing the cost of each journal, is x > 6.
solve the inequalitys
2.1x+5.6≥8.75
0.9x+2.8≤5.95
5.6x−18.9≤0.7
3.4x−1.2≥4.75
To solve the inequalities, we will isolate the variable x in each case.
1) 2.1x + 5.6 ≥ 8.75
Subtracting 5.6 from both sides:
2.1x ≥ 3.15
Dividing both sides by 2.1:
x ≥ 1.5
2) 0.9x + 2.8 ≤ 5.95
Subtracting 2.8 from both sides:
0.9x ≤ 3.15
Dividing both sides by 0.9:
x ≤ 3.5
3) 5.6x - 18.9 ≤ 0.7
Adding 18.9 to both sides:
5.6x ≤ 19.6
Dividing both sides by 5.6:
x ≤ 3.5
4) 3.4x - 1.2 ≥ 4.75
Adding 1.2 to both sides:
3.4x ≥ 5.95
Dividing both sides by 3.4:
x ≥ 1.75
Therefore, the solutions for the inequalities are:
1) x ≥ 1.5
2) x ≤ 3.5
3) x ≤ 3.5
4) x ≥ 1.75
Which one of these is NOT a characteristic of a proportional graph?(1 point)
Responses
The line passes through the origin (0,0).
The line passes through the origin (0,0).
The y values are always larger than the x values.
The y values are always larger than the x values.
The graph is a straight line.
The graph is a straight line.
The value of y/x is the same for all points on the line.
The answer is: The y values are always larger than the x values.
In a proportional graph, the value of y divided by x is constant for all points on the line. The line may or may not pass through the origin, and it can still be a proportional graph even if the y values are not always larger than the x values. However, the characteristic that is not true for all proportional graphs is that the y values are always larger than the x values.