At the beginning of the summer, Jenna had saved $247. To earn money over the summer, she is working part time at the local community center. She will earn $35 per day of work. If x represents the number of days she works, which of the following equations represents how much money she will have, including her savings?
A.
y = 35x + 247
B.
y = 247 - 35x
C.
y = 247x + 35
D.
y = x + 247
The correct equation is A.
y = 35x + 247
To determine the equation that describes the relationship between the amount of money collected (y) and the number of days (x), we need to identify the pattern or relationship between these two variables.
From the given table, we can see that the amount of money collected increases by $65 every 2 days. This means that for every 2 days, the amount collected increases by $65.
To express this relationship in the form of an equation, we can use the slope-intercept form: y = mx + b, where m is the slope (change in y) and b is the y-intercept (initial amount collected).
From the given information, we can determine that the slope is 65/2 and the y-intercept is 250.
Therefore, the equation that describes the relationship is:
A. y = 65/2x + 250
The equation which represents the number of customers in the store is y = 5x + 12.
To determine the equation of the line represented by the given table, we need to find the slope (m) and y-intercept (b) of the line.
From the given table, we can calculate the slope using two points:
Slope, m = (change in y) / (change in x)
Using the points (-4, -7) and (3, 21):
m = (21 - (-7)) / (3 - (-4)) = (21 + 7) / (3 + 4) = 28 / 7 = 4
Now, we have the slope (m = 4).
Next, we can use one of the points and the slope to find the y-intercept (b).
Using the point (-4, -7):
y = mx + b
-7 = 4(-4) + b
-7 = -16 + b
b = -7 + 16
b = 9
Therefore, the equation of the line represented by the given table is:
y = 4x + 9
So, the correct answer is A.
y = 4x + 9
Sally's school donated an initial amount for a fundraising event to be organised. Sally was in charge of collecting more money for the event over the course of 10 days. The table below shows the total amount collected at the end of a given number of days.
Number of Days, x Amount Collected, y ($)
2 315
4 380
6 445
8 510
Which equation describes the relationship between the amount of money collected and the number of days the fundraiser has been in progress?
A. y = 65/2x - 250
B. y = 2/65x + 250
C. y = 2/65x - 250
D. y = 65/2x + 250
A water tank is being filled with water. Before water is pumped in, the water level in the tank is 12 inches high. After 20 minutes, the water level is 51 inches high.
If t represents the time in minutes and h represents the water level, which of the following equations can be used to model this situation?
A. h = 39 + 12t
B. h = 1.95t - 12
C. h = 1.95t + 12
D. h = 12t + 1.95
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Jaren is the manager of a department store. The morning of a big holiday sale, when Jaren opened the door, 12 customers were waiting outside to come into the store.
Each hour the store is open, another 13 customers enter the store, and 8 customers leave the store. Use this information to complete the table below.
Hours Open Number of Customers
In the Store
0 12
1 17
2 22
3
4
The x-values represent the number of hours the store is open. The y-values represent the number of customers in the store.
The equation which represents the number of customers in the store is y =
x +
.
What is the equation of the line represented by the following table?
x y
-4 -7
-1 5
3 21
5 29
A.
y = -4x + 9
B.
y = 4x + 9
C.
y = 9x + 4
D.
y = 9x − 4
Jackson is playing a video game that has 3 castles to conquer within each level. Jackson has completed 6 levels so far.
If x represents the number of remaining levels to complete, which of the following equations can be used to find the total number of castles Jackson will have conquered once he completes the final level?
A.
y = 3x + 6
B.
y = 3x + 18
C.
y = 6x + 3
D.
y = 18x + 3
If Jackson has completed 6 levels so far, and each level has 3 castles to conquer, then the total number of castles Jackson will have conquered once he completes the final level can be calculated as 3 times the number of remaining levels (x) plus the number of castles he has already conquered (6).
Therefore, the equation that represents this relationship is:
A. y = 3x + 6