Mathematics High School

Seth and Karen are college students who take on different jobs for income. Seth needs $750 for expenses and savings each month; Karen needs $700.
Seth has a part-time job where he earns $7.50 per hour. He also mows lawns and earns $15 per lawn that he mows. His monthly earnings can be expressed with the equation 7.50x + 15y = 750, where x is the number of hours Seth works and y is the number of lawns he mows.
Karen has a part-time job babysitting, where she earns $6 per hour. She also walks dogs and earns $4 per dog that she walks. Her monthly earnings can be expressed with the equation 6x + 4y = 700, where x is the number of hours Karen works and y is the number of dogs she walks.
Before you begin, decide with your partner who will work with Seth's information and who will work with Karen's information.
Working with the Equations
Work Separately
Each partner must change the equation that represents his or her chosen college student to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.
Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology.
Comparing Students
Work Together
Each partner now has an equation, function, and graph that represent the combinations of activities resulting in the income needed for each student. Compare these items and answer the following questions:
Which student, Seth or Karen, has the higher slope when the graphs of their earnings are compared? How can you tell?
Whose graph, Seth's or Karen's, has a greater y-intercept? What does that mean for this person?
If both students work 80 hours for the month, is the number of lawns Seth has to mow greater than or less than the number of dogs Karen has to walk? Justify your answer.
Karen begins charging $8 per hour for babysitting, and Seth begins earning $8 per hour. How does this change affect their graphs if everything else remains the same?

Answers

Answer 1

Answer:

Seth:

Equation 7.50x + 15y = 750, where x is the number of hours Seth works and y is the number of lawns he mows.

Karen:

Equation 6x + 4y = 700, where x is the number of hours Karen works and y is the number of dogs she walks.

Part A: Converting it in function for by solving for y first.

Solving 7.50x + 15y = 750, equation we get

7.50x + 15y = 750

15y = -7.50x + 750

y = -1/2x + 50

Solving 6x + 4y = 700 for y, we get

6x + 4y = 700

4y = -6x + 700

y= -3/2x + 175.

On comaring with slope-intercept form y=mx+b, we got slope for Seth equation is -1/2 and slope for Karen is -3/2.

If we take absolute of those -1/2 and -3/2 we get 1/2 and 3/2.

Therefore, Karen has the higher slope. We can see the graph that blue line has greater slope as it's increasing/decreasing with greater rate.

In function form we could write equation as

f(x) = -1/2x + 50 and

f(x) = -3/2x + 175.

Part B : y-intercept of Karen equation is 175 and y-intercept of Seth equation is 50.

Therefore, Karen has greater y-intercept.

This means Karen earns $175 by just walking dogs.

Part C: If both students work 80 hours for the month.

Let us plug x =80 in each of the equations.

y = -1/2x + 50  => y = -1/2(80) + 50 = -40 +50 = $10.

Seth would earn $10 from mowing lawn.

Therefore, the number of lawns Seth has to mow = 10/15 = 0.67 that is approximately 1 lawn.

y = -3/2x + 175  => y = -3/2(80) + 175 = -120 +175 = $55.

Karen would earn $50 from walking dog.

So, the number of dogs Karne has to walk = 55/4 = 13.75 that ia approximately 14 dogs.

Therefore, the number of lawns Seth has to mow is less than the number of dogs Karen has to walk.

Part D: If Karen begins charging $8 per hour for babysitting and Seth begins earning $8 per hour.

The equations would become : 8x + 15y = 750, 8x + 4y = 700.

It would not effect the graph much. Even the y-intercepts would remain same.

There would be a slightly change in slopes.

Step-by-step explanation:

Answer 2

Answer:

If you see this give him brainliest

Step-by-step explanation:

Related Questions

Read the top and answer the question!!

Answers

Answer:

Um... ithink it would be 3 but please tell me and correct me if im wrong

Step-by-step explanation:

HELP only answer to give right answer pleaseeee

Answers

Answer:

B=4

Step-by-step explanation:

The Y intercept is where the line meets with the middle of the graph

B=4!!!
The y-intercept of the line is B4

really confused on this! help is appreciated!!

Answers

I am not sure what the question is asking but that line’s slope is 3/2 and the point (1,4) is on the line so the first line on the table is correct for that graph

please help i’ll give brainliest!!

Answers

Answer:

no correlation

Step-by-step explanation:

the dots are all scattered randomly

Liberty Middle School’s enrollment increased to 660 students. This is an increase of 10% over last year’s enrollment. What was last year’s enrollment?

Answers

Answer:

600

Step-by-step explanation:

Last years enrollment was 100% of the number.

This year, the enrollment went up by 10%, so now, it's 110% of last years number.

Let last year's enrollment be x.

110% of x is 660

1.1x = 660

x = 660/1.1

x = 600

Answer: 600

Answer:

600

Step-by-step explanation:

Bella makes bracelets. She uses 20 beads for each bracelet. How
many beads will she use to make 7 bracelets?

Answers

Answer:

140 beads.

Step-by-step explanation:

Hope this helps. :)

How do I plot this?


​

Answers

you should have a dot on the -2 on the y line

I NEED HELP ASAP IT IS FOR CHRISTMAS!!!!!!THESE ARE ALL MY POINTS!!
If three kids that want to buy something that cost $35.99 how much would each of them have to pay? Any ideas for what i should get my mom and dad?!!!! please help

Answers

Answer:

They should pay $12 each

Answer:

about 12 dollars probably more with tax maybe around 12.03

how many times does 90 go into 490

Answers

Answer:

may be 5 times is answer but I am not sure I have done 5 times I got like this

Given a+2 when a=5 I need help

Answers

Answer:

The answer to this is 7.

a+2

5+2

7

The answer would be 7 so the top person is right :)

What would 3 1/3 be if you had to borrow?

Answers

we will eat chocolate of rupee 1 and divide other amount ofoney equally

What is the surface area of the solid?

Answers

Answer:

B

Step-by-step explanation:

You have a standard deck of cards. What is the probability of drawing a heart or a face card?

Answers

Answer:

3/4

Step-by-step explanation:

Find the centroid of the triangle with these vertices: P (-1,7), Q (9,5), and R (4,3).
The coordinates of the centroid are?​

Answers

Answer:

The coordinates of the centroid are:

[tex]O\:=\:\left(4,\:5\right)\:\:[/tex]

The diagram is also attached below.

Step-by-step explanation:

Given the vertices

P (-1, 7)Q (9, 5)R (4, 3)

We know that the intersection of medians brings the centroid of the triangle.

The centroid of a triangle is given by

[tex]O\:=\:\left(\frac{P_x+Q_x+R_x}{3},\:\frac{P_y+Q_y+R_y}{3}\:\right)[/tex]

In this example,

[tex]P_x=-1,\:P_y=7[/tex]

[tex]Qx=9,\:Q_y=5[/tex]

[tex]Rx=4,\:R_y=3[/tex]

substituting in the formula

[tex]O\:=\:\left(\frac{-1+9+4}{3},\:\frac{7+5+3}{3}\:\right)\:\:[/tex]

[tex]O\:=\:\left(\frac{12}{3},\:\frac{15}{3}\:\right)\:\:[/tex]

[tex]O\:=\:\left(4,\:5\right)\:\:[/tex]

Therefore, the coordinates of the centroid are:

[tex]O\:=\:\left(4,\:5\right)\:\:[/tex]

The diagram is also attached below.

We've been given with the co-ordinates of vertices of the triangle and asked to calculate the co-ordinates of the centroid.

★ Centroid of a triangle :-

[tex]\red{\boxed{ \sf{Centroid \: = \: \dfrac{x_1 \: + \: x_2 \: + \: x_3}{3} } \: , \: \dfrac{y_1 \: + \: y_2 \: + \: y_3}{3} }} \: \pink\bigstar [/tex]

We have :

x₁ = -1x₂ = 9x3 = 4y₁ = 7y₂ = 5y3 = 3

Substituting the values :

★ For x co-ordinate:-

[tex]: \: \implies \: \sf{x\: = \: \dfrac{x_{1} \: + \: x_2 \: + \: x_3}{3} } \\ \\ : \: \implies \: \sf{x\: = \: \dfrac{ - 1 \: + \: 9 \: + \: 4}{3}} \\ \\ : \: \implies \: \sf{x\: = \: \dfrac{ 8 \: + \: 4}{3} } \\ \\ : \: \implies \: \sf{x\: = \: \dfrac{ 12}{3} } \\ \\ : \: \implies \: \sf{x\: = \: \cancel\dfrac{ 12}{3} } \\ \\ : \: \implies \: \sf{x\: = \: 4 }[/tex]

★ For y co-ordinate:-

[tex]: \: \implies \: \sf{y\: = \: \dfrac{y_{1} \: + \: y_2 \: + \: y_3}{3} } \\ \\ : \: \implies \: \sf{y\: = \: \dfrac{ 7 + 5 + 3}{3}} \\ \\ : \: \implies \: \sf{y\: = \: \dfrac{ 10 \: + \: 5}{3} } \\ \\ : \: \implies \: \sf{y\: = \: \dfrac{ 15}{3} } \\ \\ : \: \implies \: \sf{y\: = \: \cancel\dfrac{ 15}{3} } \\ \\ : \: \implies \: \sf{y\: = \: 5 }[/tex]

★ Henceforth,

Co-ordinates are (4 , 5)

Additional Information :

★ Midpoint of two points:-

[tex]\boxed{ \sf{M \: = \: \dfrac{x_1 \: + \: x_2 }{2} \: , \: \dfrac{y_1 \: + \: y_2 }{2}}} \: \pink\bigstar[/tex]

★ Distance Formula :-

[tex]\huge \large \boxed{\sf{{d \: = \: \sqrt{(x _{2} - x _{1}) {}^{2} \: + \: (y _{2} - y _{1}) {}^{2} }}}} \: \red\bigstar[/tex]

★ Visit more :-

https://brainly.com/question/23658067

https://brainly.com/question/27354466

https://brainly.com/question/27354479

https://brainly.com/question/27354524

https://brainly.com/question/27354542

helpp

2^2 - (2)(-2) - (-2)^2​

Answers

Answer:

4

Step-by-step explanation:

2^2 - (2)(-2) - (-2)^2

=4+4-4

=4

2² - (2 × -2) - (-2²)

= 4 - (-4) - 4

= 4 + 4 - 4

= 8 - 4

= 4

HELPPPPPPPP T^T I NEED AN ANSWER!!!! IS THE QUESATIN A OR C

Answers

Answer:

Commutative

Please, mark as brainliest

the temperature at noon at an Antarctic weather center was –15 °C. At midnight it had fallen by 12 °C. What was the temperature at midnight?

Answers

Answer:

-27 °C

Step-by-step explanation:

-15 -12 = -27

Hem dibuixat tres rectangles. En el primer, la llargada mesura 3 cm més que l'amplada. El segon i tercer rectangle tenen unes dimensions augmentades, respectivament, en 1 cm i 2 cm respecte de les dimensions del primer. Si la suma dels tres perímetres és de 162 cm, quines són les dimensions de cada rectangle?

Answers

Resposta:

Primer rectangle:

Amplada = 11

Longitud = 14

Segon rectangle:

Amplada = 12

Longitud = 15

Tercer rectangle:

Amplada = 13

Longitud = 16

Explicació pas a pas:

Donat que:

Primer rectangle:

Amplada = x

Longitud = x + 3

2n rectangle:

Augment de la dimensió d'1 cm respecte al primer rectangle;

Amplada = x + 1

Longitud = x + 4

3r rectangle:

Augment de la dimensió de 2 cm respecte al primer rectangle;

Amplada = x + 2

Longitud = x + 5

Suma dels tres perímetres del rectangle:

Perímetre d'un rectangle: 2 (l + O)

Primer rectangle:

2 (x + x + 3) = 2 (2x + 3) = 4x + 6

2n:

2 (x + 1 + x + 4) = 2 (2x + 5) = 4x + 10

3r:

2 (x + 2 + x + 5) = 2 (2x + 7) = 4x + 14

Suma de perímetres = 162

(4x + 6 + 4x + 10 + 4x + 14) = 162

12x + 30 = 162

12x = 162 - 30

12x = 130

x = 11

Per tant,

Primer rectangle:

Amplada = 11

Longitud = 11 + 3 = 14

2n rectangle:

Amplada = 11 + 1 = 12

Longitud = 11 + 4 = 15

3r rectangle:

Amplada = 11 + 2 = 13

Longitud = 11 + 5 = 16

HELP MEEEE PLEASE i don't know how to do this

Answers

Answer:

5 hours

Step-by-step explanation:

35x+25 = 40x

25=5x

x= hours

Wykonaj mnożenie i zredukuj wyrazy podobne (x+5)(x+4)(x+3).

Answers

Answer:

.........................

b) How far does the car travel in 4 hours?

Answers

Answer:

70 miles per hour

Step-by-step explanation:

Answer:

A car can travel up to 240 km in 4 hours.

Step-by-step explanation:

A car travels 60 MPH meaning 60(miles) times 4(hours) is 240.

Two airplanes are carrying food and medical supplies to a country in needOne airplane is carrying 63 meals and 51 medical The total the supplies on that airplane is The other airplane is carrying 77 meals and 51 medical kitsThe cost for the supplies on that airplane Write and solve a system of equations to find the price of one meal and the price of one third airplane is carrying 70 meals and 62 medical , what is the total cost of supplies

Answers

Answer:374

Step-by-step explanation:

you add them all then get the total

9(p-4)=-189(p−4)=−18

Answers

Answer:

6

Step-by-step explanation:

Answer:

The Correct Answer is 2

Step-by-step explanation:

Trust me for I have the skills of a scientist

A car dealership sold 84 cars in April. The dealership wants to increase the number of cars sold by 25% in May. How many cars will the dealership need to sell to reach their goal?

Answers

Answer: 105 Cars

Step-by-step explanation: To get an increase of 25% you need to multiply 84 by .25 then add the product of that to 84 to get 105

The number of cars dealership need to sell to reach their goal is, 105 cars

What is the percentage?

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

A car dealership sold 84 cars in April,

The dealership wants to increase the number of cars sold by 25% in May

The number of cars dealership need to sell to reach their goal = ?

This represents a 25% increase, which is the same as adding one quarter to the original number of cars sold.

The car dealership wants to increase the number of cars sold by 25% in May, which means that they want to sell,

⇒ 84 x 1.25 = 105 cars

So, the dealership will need to sell 105 cars in May in order to reach their goal of increasing the number of cars sold by 25%.

To know more about Percentage check:

https://brainly.com/question/29306119

#SPJ6

please help i’ll give brainlest and lots of points !!

Answers

you should repost i’ll try and answer then

Explain why 186,426 Is diviable by both 3 and 9

Answers

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

A number is divisible by 9 if the sum of its digits is divisible by 9.

Look :

[tex] \frac{1 + 8 + 6 + 4 + 2 + 6}{9} = \frac{27}{9} = 3 \\ [/tex]

Thus 186,426 is divisible by 9 .

_________________________________

Also a number is divisible by 3 if the sum of its digits is divisible by 3.

Look :

[tex] \frac{1 + 8 + 6 + 4 + 2 + 6}{3} = \frac{27}{3} = 9 \\ [/tex]

Thus 186,426 is divisible by 3 .

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Slove the sum
-15 > - 16 + y

Answers

Answer:

Let's solve your inequality step-by-step.

−15>−16+y

Step 1: Simplify both sides of the inequality.

−15>y−16

Step 2: Flip the equation.

y−16<−15

Step 3: Add 16 to both sides.

y−16+16<−15+16

y<1

Answer:

y<1

helpppp
i need help quickly

Answers

Answer: 140?

I am not really sure but I think 140......

The answer is ————- 70

бx +7= 8х - 15
Pls help will mark brainliest

Answers

Answer:

X=11

Step-by-step explanation:

-6x both sides of = sign

+ 15 both sides of = sign

x=11

explain algebraic equations please

Answers

Answer:

: an equation obtained by equating to zero a sum of a finite number of terms each one of which is a product of positive integral powers (including the zero power) of the variables.

Step-by-step explanation:

includeing zero

add as brainleist plz

Answer:

An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign.

Step-by-step explanation:

Other Questions
Which of the following is NOT an appropriate result of healthy stretching?A. tension in the musclesB. a slight burning sensationC. muscle painD.increased range of motion Which of the following is a true statement about the sex of the newborn "male" child.The father determined the sex which is XXThe mother determined the sex which is XXThe father determines the sex which is XYThe mother determines the sex which is XYNone of the above are true Reasons why slavery was bad? I can't think of any. What is the three adjectives for the luggage was heavy and bulky so I struggle to put through the crowded airport What is the range of h if you have 12 pounds of food and you use 3/8 of that bag of food a day how long untill its all gone how many days Find the area of the parallelogram ABCD, where DC = 10cm, AD = 6cm, and angle A = 30 degrees Calculate the length of a regular hexagonof 62.50 cm. please answer i will give you brainiest!!!!!!!!!!!!!!!!!! SOMEONE PLS HELP ME PLS ITS DUE TMRW During the Lewis and Clark expedition,Sacagawea and her child helped smooth relations with American Indians.the explorers found a water route from the Atlantic to the Pacific.the explorers ignored the natural world and focused on American Indians.many skilled people of the frontier helped to smooth relations with American Indians. BRAINLIEST IF CORRECT HURRYWhich statements represent the relationship between y=3x and y=log3x ?a. The graphs of functions are symmetric about the line y = 0.b. The functions are inverses of each other.c. The graphs of functions are symmetric to each other over the line y = x.d. The equation y=log3x is the logarithmic form of y=3x . Mariah walks 6miles per hour. Bobby walks 4,400 yards in in a half-hour. Given that 1 mile = 1,760 yards, how much faster does Mariah walk than Bobby? Solve x^2 8x + 15 = 0 by completing the square.The solutions are x =and x= Sales to small businesses that typically purchase from dealerships represent almost __________ vehicles per year. solve this ...BABABOOEY 27Karim (22 years) tells his brother Ziad (8 years).l haven't given you a gift for your birthday, but I'll make it up to you. The year when my age will betriple yours. I'll give you a wonderful gift.After making his calculations, Ziad tells his brother :It will cost you nothing. Explain why.(solve it in an equation of 1 unknown) If an artist has been studying and practicing to apply design principles to her art, which of these will be the most likely result?Her emplover will trust her with jobs that must be done quickly. CORRECTShe will always have plenty of workShe will spend hours contemplating great art worksShe will invent new ways of using the principles Diane is a basketball coach. She has engaged a professional to advise her team on how to prevent injuries. Which professional would she have engaged? Whats the answers 1-7?