1)Jane Gutierrez earns $8 an hour selling ice cream. If she earns $48 (d) working 6 hours (h), what is the independent variable? What is the dependent variable? Explain your answers.
2)Abigail Nyu went to the mall with $60; she wants to purchase several American Eagle gift cards that are $15 each.
a. Write an inequality that represents how many gift cards Abigail can purchase.
3)Using the following inequality: 2x < 28
a. Identify all of the values that are in the solution set.
b. Graph the solution to this inequality.
4)Using the function rule 4x – 10 = y
a. Create a function table with input values of 0,2, 4, 6, and 8
[ Could you please help me I'm struggling & need help could you also explain it so I can remember !?]
1) An independent variable is the potential stimulus or cause, usually directly manipulated by the experimenter, so it could also be called a manipulative variable.
A dependent variable is the response or measure of results.
2) not an inequality.
60/15 = 4
3) anything < 14 would fit.
4) put those values for x and solve for y.
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1) In this question, the independent variable is the number of hours worked (h) and the dependent variable is the amount of money earned (d). The independent variable is the one that can be changed or manipulated, in this case, the number of hours worked. The dependent variable is the one that depends on the independent variable and varies as a result of changes in the independent variable, in this case, the amount of money earned.
2) To write an inequality representing how many gift cards Abigail can purchase, we can use the following formula:
Let x represent the number of gift cards Abigail can purchase.
The cost of each gift card is $15, so the total cost of x gift cards would be 15x. Abigail has $60, so we can set up the inequality as:
15x ≤ 60
This inequality states that the total cost of the gift cards (15x) must be less than or equal to $60.
3) a. To find the values that are in the solution set of the inequality 2x < 28, we need to solve the inequality:
2x < 28
Divide both sides of the inequality by 2 to isolate x:
x < 14
So, the solution set consists of all real numbers less than 14.
b. To graph the solution to this inequality on a number line, we represent all the values less than 14:
----- 14 ------
4) To create a function table using the function rule 4x - 10 = y and input values of 0, 2, 4, 6, and 8, we can substitute each input value into the equation and calculate the corresponding output value (y):
For x = 0:
4(0) - 10 = -10
The output value (y) is -10.
For x = 2:
4(2) - 10 = 8 - 10 = -2
The output value (y) is -2.
For x = 4:
4(4) - 10 = 16 - 10 = 6
The output value (y) is 6.
For x = 6:
4(6) - 10 = 24 - 10 = 14
The output value (y) is 14.
For x = 8:
4(8) - 10 = 32 - 10 = 22
The output value (y) is 22.
So, the function table would be:
| x | y |
|---|---|
| 0 | -10 |
| 2 | -2 |
| 4 | 6 |
| 6 | 14 |
| 8 | 22 |
I hope this helps! Let me know if you have any further questions or need more clarification.