Jeanne babysits for $6 per hour. She also works as a reading tutor for $10 per hour. She is only allowed to work 20 hours per week. This week, her goal is to make at least $75. A. Use a system of inequalities to model the scenario above. Let x represent babysitting hours and y represent tutoring hours.
B. Use the model created in part A to create a graph representing Jeanne’s probable income earned and possible number of hours worked this week.
C. Analyze the set of coordinate values that represent solutions for the model created in part A. Choose one of the coordinates within the solution and algebraically prove that the coordinate represents a true solution for the model.

Answers

Answer 1

Answer: For the answer to the question above, I would start with a simple equation 6x+10y is more than or equal to 75
A.
If we let x represent babysitting hours and y represent tutoring hours:
x+ y ≤ 20
6x + 10y ≥ 75

B. The inequality: x+ y ≤ 20 can be graphed by graphing the line x + y = 20 and shading the area below the line.
The inequality 6x + 10y ≥ 75 can be graphed by graphing the line 6x + 10y = 75 and shading the area above the line.

C. The area where the two shaded regions from the two inequalities overlap are the possible number of hours for tutoring and for babysitting. Algebraically:
x ≤ 20 - y
6(20 - y) +10y ≥ 75
y ≤ 11.25
x ≤ 8.75

Answer 2

Answer:

x+y≤20

6x+10y ≥ 75

Step-by-step explanation:

Let the number of hours of babysitting be x and that for tutoring be y

As per the given conditions

The total no of hours of work must be less than or equal to 20

Hence

x+y≤20

Also Her target is to earn atleast $75

Hence the second inequation will be

6x+10y≥75

Hence our system of inequatlites representing above conditions are

x+y≤20

6x+10y≥75

Now in order to graph them , we first graph the lines x+y=20 and 6x+10y=75 and shade the region which satisfies the respective inequality by taking a coordinate (0,0) .

Please refer to the graph attached with this.

The shaded region gives us the set of coordinates probably the solution to above inequations.

Let us pick one coordinate (10,5) from the shaded region and check for the solution.

put (10,5) in two inequations and see if they are true for them.

10+5≤20

15≤20 True

6(10)+10(5) ≥75

60+50≥75

110≥75 true

Hence checked , both stands true for (10,5)

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MODELING REAL LIFE Bowling alley A charges $3.75 to rent shoes and $4 per game. Bowling alley B charges $2.50 torent shoes and $4.50 per game.
a. For what numbers of games is the total cost, including a pair of rental shoes, less at bowling alley A? at bowling alley B?
Bowling alley A:
Bowling alley B:
or more games
or
games
b. Bowling alley A increases the cost per game by $0.50. How does this affect your answer in part (a)? Explain.o

Answers

Using linear functions, it is found that:

a) The cheaper costs are given as follows:

Bowling alley A: 3 or more games.

Bowling alley B: 1 or 2 games.

b) Due to the same cost per game and higher cost for the pair of shoes, bowling alley A will never be cheaper than bowling alley B.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For this problem, we have that:

The cost to rent shoes is the intercept.

The cost per game is the slope.

Hence the cost functions are given as follows:

A(x) = 3.75 + 4x.

B(x) = 2.5 + 4.5x.

The costs are equal when:

A(x) = B(x)

3.75 + 4x = 2.5 + 4.5x

0.5x = 1.25

x = 1.25/0.5

x = 2.5.

Hence the cheaper costs are given as follows:

Bowling alley A: 3 or more games.

Bowling alley B: 1 or 2 games.

Alley B has the lower initial cost due to the lower cost for the pair of shoes.

For item b, if we increase the cost per game by $0.50 for alley A, we have that:

A(x) = 4.5x + 3.75.

Hence:

Due to the same cost per game and higher cost for the pair of shoes, bowling alley A will never be cheaper than bowling alley B.

More can be learned about linear functions at brainly.com/question/24808124

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The sum of two odd numbers is 198. Both of the numbers are multiples of 3. One of the numbers is 5 times the other. Which equation could you use to find the two numbers?

Answers

Answer:

The equation used to find the two numbers is:

x+5x=198

and numbers are:

33 and 165

Step-by-step explanation:

The sum of two odd numbers is 198.

One of the numbers is 5 times the other.

Let one number be x

other number=5x

⇒ x+5x=198

⇒ 6x=198

Dividing both sides by 6,we get

x=33

Other number=5x=5×33=165

The equation used to find the two numbers is:

x+5x=198

and numbers are:

33 and 165

You could use m= the lesser number and n as the greater number. Since one is 5 times the other you will start with m+5m=198. Then you will combine like terms so it will become 6m=198. Then you will solve it as a regular equation. m=33 and n=165.

Melinda's lights went out. She has 3 pairs of red socks in her drawer 2 pairs of black socks and 5 pairs of white socks . What Is the minimum number of pairs she must remove from the drawer to ensure that she has a pair of each color? a. 3
b. 5
c. 7
d. 9
e. 10

Answers

Melinda must removeatleast 5 pairs of socks to ensure that she has a pair of each color.

Option B is the correct answer.

We have,

To ensure that Melinda has a pair of eachcolor, she needs to remove at least one sock from each color until she has one sock remaining from each color.

Since she has 3 pairs of red socks, 2 pairs of black socks, and 5 pairs of white socks, the minimumnumber of pairs she must remove is the maximum of these numbers.

The maximum among 3, 2, and 5 is 5.

Therefore,

Melinda must removeatleast 5 pairs of socks to ensure that she has a pair of each color.

Learn more about expressions here:

brainly.com/question/3118662

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The answer would be D because she cant be assured that she gets one of each pair if she grabs less.

What number could be a common denominator for these two fractions?
3/10 and 1/5

Answers

Answer:

5 could be the common denominator

Step-by-step explanation:

10
The common denominator is 10

Sin43×cos47+cos47×sin43

Answers

sin(α + β) = sin(α)cos(β) + cos(α)sin(β)

sin43×cos47+cos47×sin43 = sin(43 + 47)

= sin(90) = 1

PLEASE ANSWER QUICKLY... Liam and Michelle split the cost of supplies to build some trebuchets. The expression for the cost that each must pay to make t (trebuchets) is (2.5t+2)+(1.8t+3) as the numerator and 2 as the denominator. What is the cost for each person if t=2

Answers

I got you.

Just plug 2 in for t into your expression.
You should get 6.8

5.6+7=12.6 meaning the answer in 12.6

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