Question
Simply the Expression:
5a + 3b - 3a + 4b + 7c
(1 point)
Responses
8a + 4b + 7c
8a + 4b + 7c
2a + 7b + 7c
2a + 7b + 7c
22abc
22abc
8a + 7b + 7c
5a + 3b - 3a + 4b + 7c
(1 point)
Responses
8a + 4b + 7c
8a + 4b + 7c
2a + 7b + 7c
2a + 7b + 7c
22abc
22abc
8a + 7b + 7c
Answers
Answered by
GPT-4o mini
To simplify the expression \( 5a + 3b - 3a + 4b + 7c \), you combine the like terms:
1. Combine the \( a \) terms:
\( 5a - 3a = 2a \)
2. Combine the \( b \) terms:
\( 3b + 4b = 7b \)
3. The \( c \) term remains the same:
\( 7c \)
Putting it all together, the simplified expression is:
\[ 2a + 7b + 7c \]
So the correct response is:
**2a + 7b + 7c**
1. Combine the \( a \) terms:
\( 5a - 3a = 2a \)
2. Combine the \( b \) terms:
\( 3b + 4b = 7b \)
3. The \( c \) term remains the same:
\( 7c \)
Putting it all together, the simplified expression is:
\[ 2a + 7b + 7c \]
So the correct response is:
**2a + 7b + 7c**
Answer
Simplify the Expression:
4.5x - 2 + 3.7x + 6.5
(1 point)
Responses
7.12x + 4.5
7.12x + 4.5
0.8x + 8.5
0.8x + 8.5
8.2x + 6.5
8.2x + 6.5
8.2x + 4.5
4.5x - 2 + 3.7x + 6.5
(1 point)
Responses
7.12x + 4.5
7.12x + 4.5
0.8x + 8.5
0.8x + 8.5
8.2x + 6.5
8.2x + 6.5
8.2x + 4.5
Answered by
GPT-4o mini
To simplify the expression \( 4.5x - 2 + 3.7x + 6.5 \), follow these steps:
1. Combine the \( x \) terms:
\[
4.5x + 3.7x = 8.2x
\]
2. Combine the constant terms:
\[
-2 + 6.5 = 4.5
\]
Putting it all together, the simplified expression is:
\[
8.2x + 4.5
\]
So the correct response is:
**8.2x + 4.5**
1. Combine the \( x \) terms:
\[
4.5x + 3.7x = 8.2x
\]
2. Combine the constant terms:
\[
-2 + 6.5 = 4.5
\]
Putting it all together, the simplified expression is:
\[
8.2x + 4.5
\]
So the correct response is:
**8.2x + 4.5**
Answer
You and your three friends are going to the State Fair. It costs $3 for each ride and $5 per person to get into the fair. Which algebraic expression represents the TOTAL amount of money it will cost for four friends to get into the fair and ride "x" amount of rides? (1 point)
Responses
4(x + 5)
4(x + 5)
4x + 20
4x + 20
4(3x + 5)
4(3x + 5)
5x + 3
Responses
4(x + 5)
4(x + 5)
4x + 20
4x + 20
4(3x + 5)
4(3x + 5)
5x + 3
Answered by
GPT-4o mini
To find the total cost for you and your three friends (4 people total) to get into the fair and ride "x" amount of rides, we'll break down the costs.
1. **Entry Cost per Person**: It costs $5 per person, and since there are 4 friends, the total entry cost is:
\[
4 \times 5 = 20
\]
2. **Cost for Rides**: It costs $3 for each ride. If there are \( x \) rides, the total cost for rides is:
\[
3x
\]
So, the total cost for entry and rides can be expressed as:
\[
\text{Total Cost} = \text{Entry Cost} + \text{Cost for Rides} = 20 + 3x
\]
This can also be factored to show the entry cost per person:
\[
4 \times (3x + 5)
\]
Thus, the correct algebraic expression representing the total amount of money it will cost is:
**4(3x + 5)**
1. **Entry Cost per Person**: It costs $5 per person, and since there are 4 friends, the total entry cost is:
\[
4 \times 5 = 20
\]
2. **Cost for Rides**: It costs $3 for each ride. If there are \( x \) rides, the total cost for rides is:
\[
3x
\]
So, the total cost for entry and rides can be expressed as:
\[
\text{Total Cost} = \text{Entry Cost} + \text{Cost for Rides} = 20 + 3x
\]
This can also be factored to show the entry cost per person:
\[
4 \times (3x + 5)
\]
Thus, the correct algebraic expression representing the total amount of money it will cost is:
**4(3x + 5)**
Answer
Bailey has two part-time jobs. He earns $13 an hour, c, as a cashier and $18 an hour, t, as a technology support specialist. This is modeled by 13c + 18t. He worked for 10 hours as a cashier and 12 hours as a technology support specialist this week. Evaluate the expression 13c+ 18t for c= 10 and t= 12 to find out how much Bailey will earn at his two jobs this week. (1 point)
Responses
$22
$22
$346
$346
$31
$31
$148
Responses
$22
$22
$346
$346
$31
$31
$148
Answered by
GPT-4o mini
To find out how much Bailey will earn at his two jobs this week, we can evaluate the expression \( 13c + 18t \) using the values \( c = 10 \) (hours as a cashier) and \( t = 12 \) (hours as a technology support specialist).
Substituting the values into the expression:
\[
13c + 18t = 13(10) + 18(12)
\]
Now, calculate each part:
1. Calculate \( 13(10) \):
\[
13(10) = 130
\]
2. Calculate \( 18(12) \):
\[
18(12) = 216
\]
Now add the two amounts together:
\[
130 + 216 = 346
\]
Thus, Bailey will earn **$346** this week.
Therefore, the correct response is:
**$346**
Substituting the values into the expression:
\[
13c + 18t = 13(10) + 18(12)
\]
Now, calculate each part:
1. Calculate \( 13(10) \):
\[
13(10) = 130
\]
2. Calculate \( 18(12) \):
\[
18(12) = 216
\]
Now add the two amounts together:
\[
130 + 216 = 346
\]
Thus, Bailey will earn **$346** this week.
Therefore, the correct response is:
**$346**
Answer
Expand using the Distributive Property:
8(4p + 3)
(1 point)
Responses
32p + 24
32p + 24
24p + 16
24p + 16
56p
56p
12p + 11
8(4p + 3)
(1 point)
Responses
32p + 24
32p + 24
24p + 16
24p + 16
56p
56p
12p + 11
Answered by
GPT-4o mini
To expand the expression \( 8(4p + 3) \) using the Distributive Property, you multiply each term inside the parentheses by 8.
Here are the steps:
1. Multiply \( 8 \) by \( 4p \):
\[
8 \times 4p = 32p
\]
2. Multiply \( 8 \) by \( 3 \):
\[
8 \times 3 = 24
\]
Now, combine these results to form the expanded expression:
\[
32p + 24
\]
So, the correct response is:
**32p + 24**
Here are the steps:
1. Multiply \( 8 \) by \( 4p \):
\[
8 \times 4p = 32p
\]
2. Multiply \( 8 \) by \( 3 \):
\[
8 \times 3 = 24
\]
Now, combine these results to form the expanded expression:
\[
32p + 24
\]
So, the correct response is:
**32p + 24**
Answer
Expand using the Distributive Property:
-6(5h - 3)
(1 point)
Responses
-30h + 18
-30h + 18
30h +18
30h +18
30h - 18
30h - 18
-30h - 18
-6(5h - 3)
(1 point)
Responses
-30h + 18
-30h + 18
30h +18
30h +18
30h - 18
30h - 18
-30h - 18
Answered by
GPT-4o mini
To expand the expression \(-6(5h - 3)\) using the Distributive Property, you will multiply each term inside the parentheses by \(-6\).
Here are the steps:
1. Multiply \(-6\) by \(5h\):
\[
-6 \times 5h = -30h
\]
2. Multiply \(-6\) by \(-3\):
\[
-6 \times -3 = 18
\]
Now, combine these results to form the expanded expression:
\[
-30h + 18
\]
So the correct response is:
**-30h + 18**
Here are the steps:
1. Multiply \(-6\) by \(5h\):
\[
-6 \times 5h = -30h
\]
2. Multiply \(-6\) by \(-3\):
\[
-6 \times -3 = 18
\]
Now, combine these results to form the expanded expression:
\[
-30h + 18
\]
So the correct response is:
**-30h + 18**