Which of the following sets shows all the numbers from the set {1, 2, 3, 4} that are part of the solution to the inequality 7x + 6 > 20?

{1, 2, 3}
{2, 3, 4}
{3, 4}
{4}

question 5 (essay worth 6 points)

(07.04)

heather is planning a dessert display. she needs 4 ounces of strawberries for each dessert.

part a: heather is not sure how many desserts she will make. write an expression with a variable that represents the amount of strawberries heather needs for the desserts. identify what the variable represents.

part b: if heather has 24 ounces of strawberries, how many desserts can she make? create an equation and show all work to solve it.

question 6 (essay worth 6 points)

(07.02)

part a: virginia earned $14 walking her neighbors' dogs on saturday. she earned some extra money on sunday doing the same thing. write an expression with a variable that shows the total amount of money virginia earned saturday and sunday.

part b: virginia was able to walk 2 less than twice as many dogs as her friend alicia. write an algebraic expression to represent the number of dogs virginia walked compared with alicia.

Step-by-step explanation:

Part (a)

Consider the provided inequality: 7x + 6 > 20

Now, find the sets which satisfy the inequality.

Substitute x = 1 in the provided inequality.

7(1) + 6 > 20

13 > 20

Which is false.

Substitute x = 2 in the provided inequality.

7(2) + 6 > 20

14 + 6 > 20

20 > 20

Which is false as 20 is not greater than 20.

Substitute x = 3 in the provided inequality.

7(3) + 6 > 20

21 + 6 > 20

27 > 20

Which is true.

Substitute x = 4 in the provided inequality.

7(4) + 6 > 20

28 + 6 > 20

34 > 20

Which is true.

Hence, the correct option is C) {3, 4}.

Question 5 Part (A)

Let x is the number of desserts she wants to make.

Let y is the number of strawberries she needed.

She needs 4 ounces of strawberries for every dessert:

Therefore, the equation can be:

y = 4x

Hence, the required equation is y = 4x.

Part B

Heather has 24 ounces of strawberries, so substitute y = 24 in above equation and solve for x, so that we can find the number of desserts she can make.

24 = 4x

Divide both sides by 4.

24/4 = 4x/4

6 = x 

Hence, she can make 6 desserts.

Question 6 Part (A)

Consider the provided information.

Virginia earned $14 walking her neighbors' dogs on Saturday. She earned some extra money on Sunday doing the same thing.

Let the extra money she earned is x. Thus, the total amount of money Virginia earned Saturday and Sunday is:

$14 + x = Total money

Thus, the required expression is 14 + x.

Part (B)

Consider the provided information.

Virginia was able to walk 2 less than twice as many dogs as her friend Alicia.

Let Alicia walk is represented by x.

Now, convert the provided information into mathematical expression as shown below:

Virginia = 2x - 2

Therefore, the required algebraic expression to represent the number of dogs Virginia walked compared with Alicia is 2x - 2.

Step-by-step explanation:

Part (a)

Consider the provided inequality: 7x + 6 > 20

Now, find the sets which satisfy the inequality.

Substitute x = 1 in the provided inequality.

7(1) + 6 > 20

13 > 20

Which is false.

Substitute x = 2 in the provided inequality.

7(2) + 6 > 20

14 + 6 > 20

20 > 20

Which is false as 20 is not greater than 20.

Substitute x = 3 in the provided inequality.

7(3) + 6 > 20

21 + 6 > 20

27 > 20

Which is true.

Substitute x = 4 in the provided inequality.

7(4) + 6 > 20

28 + 6 > 20

34 > 20

Which is true.

Hence, the correct option is C) {3, 4}.

Question 5 Part (A)

Let x is the number of desserts she wants to make.

Let y is the number of strawberries she needed.

She needs 4 ounces of strawberries for every dessert:

Therefore, the equation can be:

y = 4x

Hence, the required equation is y = 4x.

Part B

Heather has 24 ounces of strawberries, so substitute y = 24 in above equation and solve for x, so that we can find the number of desserts she can make.

24 = 4x

Divide both sides by 4.

24/4 = 4x/4

6 = x 

Hence, she can make 6 desserts.

Question 6 Part (A)

Consider the provided information.

Virginia earned $14 walking her neighbors' dogs on Saturday. She earned some extra money on Sunday doing the same thing.

Let the extra money she earned is x. Thus, the total amount of money Virginia earned Saturday and Sunday is:

$14 + x = Total money

Thus, the required expression is 14 + x.

Part (B)

Consider the provided information.

Virginia was able to walk 2 less than twice as many dogs as her friend Alicia.

Let Alicia walk is represented by x.

Now, convert the provided information into mathematical expression as shown below:

Virginia = 2x - 2

Therefore, the required algebraic expression to represent the number of dogs Virginia walked compared with Alicia is 2x - 2.

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value