Elliot is building a sandbox in the shape of a triangle. A model of the sandbox is shown. Which expression represents the perimeter of Elliot's sandbox?

Question

(1 point)
Responses

x+10
x plus 10

x+11
x plus 11

3x−2
3 x minus 2

3x+10

Answer 1

To determine which expression represents the perimeter of Elliot's triangular sandbox, we need the lengths of all three sides.

If we assume the sides of the triangle are given by expressions involving \( x \), we would typically see something like:

1. Side 1: \( a \)
2. Side 2: \( b \)
3. Side 3: \( c \)

The formula for the perimeter \( P \) of a triangle is:

\[ P = a + b + c \]

If the options provided are the potential results of \( P \), we can analyze the expressions:

• \( x + 10 \)
• \( x + 11 \)
• \( 3x - 2 \)
• \( 3x + 10 \)

If we assume that each side contributes a linear term involving \( x \), we would likely be looking for an expression that sums to the total length of all three sides.

Without specific side lengths given, one strategy could be to guess that the option \( 3x + 10 \) suggests that there are three sides of the triangle involving the variable \( x \) and a constant, which might hint that it's derived from three linear components.

Consequently, the expression that reasonably represents the perimeter based on standard practices of assigning side lengths in this format would be:

3x + 10

It's best to reconfirm this by checking if \( 3x + 10 \) can be decomposed into three plausible linear side lengths that could vary with \( x \). If you've got more explicit measurements, we could ensure that \( 3x + 10 \) correctly reflects the sum of those sides. But based on the information at hand, the best choice is 3x + 10.

Answer 2

Question
Sierra and Charlie are paid $12 per hour. However, this week Charlie received a $40 bonus. Given that S and C represent the number of hours worked by Sierra (S) and Charlie (C), which expression can be used to represent their combined earnings for this week?(1 point)
Responses

12+40+SC
12 plus 40 plus cap s cap c

12SC+40
12 cap s cap c plus 40

12+40+S+C
12 plus 40 plus cap s plus cap c

12S+12C+40

Answer 3

To determine the correct expression for the combined earnings of Sierra and Charlie in a week where they are paid $12 per hour and Charlie receives a $40 bonus, we can break down their earnings as follows:

1. Sierra's earnings: She is paid $12 per hour, so if she works \( S \) hours, her earnings would be: \[ 12S \]

2. Charlie's earnings: He also gets $12 per hour for \( C \) hours, plus a $40 bonus. Therefore, his earnings would be: \[ 12C + 40 \]

To find the combined earnings of both Sierra and Charlie, we need to add their individual earnings together:

\[ \text{Combined earnings} = \text{Sierra's earnings} + \text{Charlie’s earnings} = 12S + (12C + 40) \]

This simplifies to:

\[ 12S + 12C + 40 \]

From the options provided, the expression that correctly represents their combined earnings for the week is:

12S + 12C + 40

Answer 4

Which number sentence shows how the distributive property can be used to represent the area of the entire rectangle (both rectangles together)?

(1 point)
Responses

5⋅3⋅7
5 times 3 times 7

(5⋅3)+(5⋅7)
open paren 5 times 3 close paren plus open paren 5 times 7 close paren

5(3+7)
5 times open paren 3 plus 7 close paren

(5+3)⋅(5+7)

Answer 5

To represent the area of an entire rectangle using the distributive property, we typically look at a rectangle that can be divided into smaller rectangular sections or can be thought of as the product of its length and width when expressed through addition.

Assuming you have a rectangle divided into two smaller rectangles, where one dimension of the rectangle is constant (5) and the other dimension is the sum of two parts (3 and 7), we can express the area of the total rectangle using the distributive property.

The correct expression to use the distributive property to find the area of the whole rectangle would be:

5(3 + 7)

This shows that you are taking a dimension (5) and multiplying it by the total of the other dimension (3 + 7), thereby finding the area of the entire rectangle.

So, the answer is:

5(3 + 7)