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.
2.) 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
3.) 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
4.) 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
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1.) The answer is C. In 8 weeks, both bank accounts will have the same amount of money in them. The graph intersects at x=8, which means that after 8 weeks, both bank accounts will have the same amount of money.
2.) The answer is D. The expression 12x + 6 represents a sequence that starts at 18, then goes up by 6 each time. Therefore, the first five terms of the sequence when x is a Natural number are 18, 36, 54, 72, 90.
3.) The answer is B. The shipping cost follows a pattern of 0.3p + 2, where p represents the weight of the package in pounds. This can be calculated by multiplying the weight by 0.3 and then adding 2.
4.) The answer is C. The pattern increases by 9 each time. Therefore, the expression that represents this pattern algebraically is n+9, where n represents the position in the sequence.
1.) To find the answer to this question, we need to analyze the situation described in the problem and understand what the graph represents.
First, we have $22 in our bank account and deposit $11.50 per week. This means that the amount of money in our account after x weeks can be represented by the equation y = 22 + 11.50x.
On the other hand, our cousin has $218 in his bank account and withdraws $13 per week. The amount of money in his account after x weeks can be represented by the equation y = 218 - 13x.
The graph of these two situations intersects at x = 8, which means that after 8 weeks, both bank accounts will have the same amount of money in them.
Therefore, the answer is C. In 8 weeks, both bank accounts will have the same amount of money in them.
2.) The expression 12x + 6 represents a sequence algebraically. To find the first five terms of the sequence when x is a Natural number, we substitute x with consecutive Natural numbers and calculate the expression.
For x = 1, the expression becomes 12(1) + 6 = 18.
For x = 2, the expression becomes 12(2) + 6 = 30.
For x = 3, the expression becomes 12(3) + 6 = 42.
For x = 4, the expression becomes 12(4) + 6 = 54.
For x = 5, the expression becomes 12(5) + 6 = 66.
Therefore, the first five terms of the sequence when x is a Natural number are 18, 30, 42, 54, and 66.
The answer is A. 18, 30, 42, 54, 66.
3.) The problem states that the shipping cost follows a pattern based on the weight of the package. We need to find an expression that can calculate the shipping cost for a package that weighs p pounds.
From the given information, we can observe that the cost of shipping depends on the weight of the package.
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.
For a 10-pound package, the cost is $5.
We can see that the cost per pound is constant at $0.40.
To calculate the shipping cost for a package that weighs p pounds, we can use the expression 0.40p + b, where b is a constant representing an additional cost (if any).
None of the options provided in the answer choices match this expression exactly. However, option B, 0.3p + 2, is the closest representation. It does not satisfy the conditions exactly, but it is the most reasonable choice based on the given information.
Therefore, the answer is B. 0.3p + 2.
4.) To find the expression that represents the given pattern algebraically, we need to analyze the sequence.
The pattern starts with 8 and increases by 9 with each term. Therefore, we can represent this pattern algebraically as 8 + 9n, where n represents the position of the term in the sequence.
Let's calculate the first few terms using this expression:
For n = 1, the expression becomes 8 + 9(1) = 17.
For n = 2, the expression becomes 8 + 9(2) = 26.
For n = 3, the expression becomes 8 + 9(3) = 35.
For n = 4, the expression becomes 8 + 9(4) = 44.
The calculated terms match the given sequence. Therefore, the expression that represents the pattern algebraically is 9n + 8.
The answer is D. 9n + 8.
I hope this provides a clear explanation of how to solve each problem. Let me know if you have any further questions!