1.) You have $22 in your bank account, and you deposit $11.50 per week. Your cousin has $218 in his bank account and is withdrawing $13 per week. The graph of this problem situation intersects at x=8. What does this mean?
A.
In 8 weeks, you will have triple the amount of money in your account.
B.
In 8 weeks, your cousin will run out of money.
C.
In 8 weeks, both bank accounts will have the same amount of money in them.
D.
In 8 weeks, you will break-even.
The expression 12x + 6 can be used to describe a sequence algebraically. Which of the following could be the first five terms of the sequence when x is a Natural number?
A.
18, 30, 42, 54, 66
B.
6, 12, 18, 24, 30
C.
6, 18, 24, 36, 42
D.
18, 36, 54, 72, 90
Isabella shipped a 5-pound package for $4. She shipped a 3-pound package for $3.60 and a 1-pound package for $3.20. A 10-pound package cost $5 to ship. The shipping cost follows a pattern based on the weight of the package.
Which expression can be used to calculate the shipping cost for a package that weighs p pounds?
A.
3p+2
B.
0.3p+2
C.
2p +3
D.
0.2p +3
Look at the pattern that follows. Which expression represents this pattern algebraically?
8, 17, 26, 35, 44, …
A.
9n-1
B.
n-9
C.
n+9
D.
9n+1
THANKS! :)
Ohh sorry, they go in order, 1.), 2.), 3.). and 4.). All separate questions! :)
stop cheating
1 C. the amounts are equal where their graphs intersect.
2 A. since natural numbers start with x=1
3 D.
4 A Assuming we start with n=1
To answer the questions:
1.) To find the answer to this question, let's first analyze the situation. You start with $22 in your bank account and deposit $11.50 per week. Your cousin starts with $218 in his bank account and withdraws $13 per week. After x weeks, your bank account balance can be represented by the equation 22 + 11.50x, and your cousin's bank account balance can be represented by the equation 218 - 13x.
To determine when the graph of these two equations intersect, we set them equal to each other:
22 + 11.50x = 218 - 13x
Simplifying the equation, we get:
24.50x = 196
Dividing both sides by 24.50, we find:
x = 8
This means that the graph of the situation intersects at x=8, which represents 8 weeks.
Now, let's analyze the answer choices:
A. In 8 weeks, you will have triple the amount of money in your account.
This is not true because the equation for your bank account balance is 22 + 11.50x. Substituting x=8, we find that the balance after 8 weeks is 22 + 11.50(8) = 110. This is not triple the initial amount of $22.
B. In 8 weeks, your cousin will run out of money.
This is not true because the equation for your cousin's bank account balance is 218 - 13x. Substituting x=8, we find that the balance after 8 weeks is 218 - 13(8) = 112. This is not zero or negative.
C. In 8 weeks, both bank accounts will have the same amount of money in them.
This is the correct answer because at x=8, the bank account balances for both you and your cousin are equal. Your bank account balance is 22 + 11.50(8) = 110, and your cousin's bank account balance is 218 - 13(8) = 112.
D. In 8 weeks, you will break even.
This is not true because breaking even means having a balance of zero, but at x=8, both bank account balances are positive.
Therefore, the correct answer is C. In 8 weeks, both bank accounts will have the same amount of money in them.
2.) To find the first five terms of the sequence described by the algebraic expression 12x + 6, substitute Natural numbers for x:
For x = 1, the term is 12(1) + 6 = 18.
For x = 2, the term is 12(2) + 6 = 30.
For x = 3, the term is 12(3) + 6 = 42.
For x = 4, the term is 12(4) + 6 = 54.
For x = 5, the term is 12(5) + 6 = 66.
Therefore, the correct answer is A. 18, 30, 42, 54, 66.
3.) To determine the expression that represents the shipping cost for a package weighing p pounds based on the given information, we can analyze the pattern:
For a 5-pound package, the cost is $4.
For a 3-pound package, the cost is $3.60.
For a 1-pound package, the cost is $3.20.
We can observe that as the weight of the package increases by 2 pounds, the cost increases by 0.40.
Therefore, we can use the expression 0.40p + 2 to calculate the shipping cost for a package weighing p pounds.
The correct answer is B. 0.3p+2.
4.) To find the algebraic expression that represents the given pattern 8, 17, 26, 35, 44, ..., we can observe that each term is 9 more than the previous term.
Therefore, the expression that represents this pattern algebraically is:
9n + 8
The correct answer is D. 9n+1.