The table below models the cost, y, of using a high-efficiency washing machine and a standard washing machine over x number of years.





Which equation represents the cost of the high-efficiency washing machine over a given number of years?

Which equation represents the cost of the standard washing machine over a given number of years?

After how many years of use would the washing machines cost the same amount?

Which washing machine would be the more practical purchase if kept for 9 years?

Q1:  y = 25x + 500

Q2: y = 30x + 400

Q3: 20 years

Q4: Standard washing machine

"Which equation represents the cost of the high-efficiency washing machine over a given number of years?"

NOTE: There will be a lot of reading at first, however, it covers the process of the first question and the second.

1.1 - Pinpointing key terms

This is a useful skill that never stops being practiced. The trick to it in this situation is to cross-examine information which, in our case, is the word problem and the graph.

Doing this we will notice this;

"Which equation represents the cost of the high-efficiency washing machine over a given number of years?"

For further clarification, we will look specifically at these two columns in our chart to answer the first problem

1.2 - Deciding which formula would best represent the data

The slope-intercept formula is used to measure data trends, and as such we can use it, and its rules, here. (Technically f(x) in general is universally recognized for this.)

1.3 - Determine which column to assign as the x values and which to assign as y values

Our y-axis is what we're measuring for, and that we want to find, and our x-axis is for the values that which our y values change in correlation to.

We want to find the high-efficiency cost, we'll as a result assign that column as the y values, at any given year, which in this case was given

1.4 - Find the slope

To do this we'll use the slope formula

[tex]Slope = m = \frac{rise}{run} = \frac{change~in~y}{change~in~x} = \frac{y_2~-~y_1}{x_2~-~x_1}[/tex]

1.4.1 - Defining variables of slope formula

[tex]x__1[/tex] means the first x value of two consecutive points

[tex]x__2[/tex] second x value

(Must be to the right of the first point on a graph, greater than)[tex].^{*Note~1}[/tex]

NOTE: [tex]y__{2}[/tex] [tex]is~derived~from~the~y~value~that~corresponds~with~x__2[/tex]; [tex]and[/tex] [tex]y__1[/tex] [tex]from~x__1[/tex]

Further help in understanding this concept

To help you visualize I'll convert the variables to points

[tex]\left[\begin{array}{ccccc}Number~of~years&|&high-efficiency~cost&|&point\\1&|&525&|&(1, 525)\\2&|&550&|&(2, 550)\\3&|&575&|&(3,575)\end{array}\right][/tex]

1.4.2 -Putting it all together

In this case, we'll use (1, 525) and (2, 550)

As a result of defining of variables section, our x1 and y1 is (1, 525) and our x2 and y2 is (2, 550)

So, now lets plug and solve

(y2-y1)/(x2-x1)

On top:

y2 - y1 = 550-525 = 25

On the bottom

x2 - x1 = 2 - 1 = 1

Therefore our slope is 25/1 which is 25

1.5 - Finding our y-intercept, b, for y = mx + b

All we need to do now that we know the slope, and that we have a chart, is continue the trend in reverse to find y

because our slope was 25/1 that means that y increases by 25 for every increase of 1 that occurs in our x;

The reverse is for every decrease of 1 x, y decreases by 25

Using that we'll need to decrease our x and y accordingly until x equals 0

 (1, 525)

- (1, 25)

 (0, 500)

Our y intercept, b, in this case is 500

Therefore now we have the needed information to complete the formula

y = mx + b

y = 25x + 500

"Which equation represents the cost of the standard washing machine over a given number of years?"

2.1-2 - Assigning x and y

y = Standard Cost

x = Number of years (given)

y = mx + b

2.3 - Find the slope

[tex]Slope = m = \frac{rise}{run} = \frac{change~in~y}{change~in~x} = \frac{y_2~-~y_1}{x_2~-~x_1} = \frac{460~-~430}{2~-~1} = \frac{30}{1} = 30[/tex]

2.4 - Find the y-intercept, b, using the slope

 (1, 430)

- (1, 30)

(0, 400)

y-intercept = b = 400

2.5 - Plug it in slope-intercept form

y = mx + b

y = 30x + 400

"After how many years of use would the washing machines cost the same amount?"

We need to set the two equations equal to each other, and thanks to the fact they're both equal to y, this allows us to do so through substitution

3.1 - Write the equations

y = 25x + 500

y = 30x + 400

3.2 - Substitute an equation in for the y of the other and simplify and solve algebraically

30x + 400 = 25x + 500

       - 400             -400

-25x            -25x            .

           5x = 100

             x = 20

After 20 years they will be equal

"Which washing machine would be the more practical purchase if kept for 9 years? "

To answer this we just plug in 9 for x in each equation and see which is cheaper

4.1 - Rewrite

High Efficiency

y = 25x + 500

Standard

y = 30x + 400

4.2 - Plug in

High Efficiency

y = 25(9) + 500

Standard

y = 30(9) + 400

4.3 - Solve

High Efficiency

y = 25(9) + 500

y = 225 + 500

y = 725

Standard

y = 30(9) + 400

y = 270 + 400

y = 670

In this case the standard would cost less therefore our answer is the standard washing machine

14. Define a Variable

Guests at a pizza party are seated at three tables. The small table has 8 seats and 3 pizzas. The medium table has 10 seats and 4 pizzas, The large table has 14 seats and 6 pizzas. The pizzas at the table are shared equally. At which table does a guest get the most pizza? the medium? large? or small?

Which set of expressions below does not represent equivalent expressions?

a. 8(3x + 7) and 8(3x) + 8(7)

b. 3(8x + 7) and 11x + 10

c. 7(3x + 8) and 7 · 3x + 7· 8

d. 3(7x + 8) and 21x + 24

Jonathan looked at the picture frame below and computed the following sum:
8 3/4 + (-4) what value did he find?

a. x
b. 2x
c. y
d. 2y

At Christmas a woman received from one person 2/9 of a ton of coal, from another 5/9 and from a third 7/9. How much coal did she receive in all ?

Circle the function types that have an absolute maximum or minimum. Choose all that apply.
linear functions
constant functions
quadratic functions
exponential functions
linear absolute value functions

ASAP!
Lesson 4 Problem-Solving Practice

Add and Subtract Unlike Fractions

MARBLES For Exercises 1–4, use the table showing colors of marbles.

Color
Fraction
Red
350
Blue
325
Green
310
Yellow
125
Pink
110
Purple
15
White
950



1. What fraction of the marbles are red or blue?

2. What fraction of the marbles are green or purple?

3. What fraction represents how many more purple marbles there are than yellow ones?

4. What fraction represents how many more white marbles there are than pink ones?

5. GRADES If13of the students got an A and25of them got a B, what fraction of the students got an A or a B?

6. WATER AEROBICS If 58of the people in a water aerobics class are over age 65 and 14 of the people in the class are under age 40, what fraction of the people in the class are either over 65 or under 40?

Need helpp fastt plss will give brainliest to who is correct plss helpp
PLSSS HELPP I NEED THE ANSWER CORRECT

Explain in detail how to divide 3 2/3 by 3/4!



*Explain step by step*

During a special sales event, the dealership offers a 10%
discount off of the retail price ($15840). After the discount, how much will
a customer pay for this vehicle?

what is the LDC of 11/12 and 1/8

need the answer to this question quick please!!!!!!!!!

What goes in the table?

Pls help I’m begging u it’s due in 30 min

please help ill give whoever answers best brainliest xx

Duffy completed a 50-meter dash in 36 seconds. That was 90 percent of the time it took Paul to complete it. What was Paul's time?


A. 36 seconds

B. 42 seconds

C. 40 seconds

FIND WHAT DID I DO WRONG
(-2)(-3)(-4)=(-6)(-4)=24

Need helpp fastt plss will give brainliest to who is correct plss helpp

PLSSS HELPP I NEED THE ANSWER CORRECT

answer this question, thx for the help

If you explain properly I'll give you branliest.

Ron is planning for the back-to-school rush at his store. Last year he estimated that he would need 168 notebooks, but he sold 200 notebooks. Explain how Ron can find the percent error of his estimate.

Eric and Shiloh each have a savings account. The ratio of Eric’s account balance to Shiloh’s account balance is 4:3. Together they have a total of $140 in their accounts. Use the tape diagram below to help you determine the balance of Eric’s account. [Type your answer as a number.]

FYI: there are seven bars down below, i dunno how to put the pictures there bc im on comupter

Determine the rule for the sequence. Then find the unknown term. 56.38, 51.28, 46.18, ____
Rule: _____

A football reaches its maximum height in y divided by 9.8 seconds. A football is kicked at a 62 degree angle. At the same time, another football is kicked at 27 degree angle. which reaches its maximum height first? Explain.

answer plz
and god bless you

A triangle has vertices A (-2, 3), B (0, 0), and C (1, 2). What are the coordinates of the vertices of the triangle if it is dilated by a scale factor of 3?



A.
A’ (-6, 9); B’ ( 3, 3); C’ (3, 6)

B.
A’ (1, 6); B’ ( 3, 3); C’ (4, 5)

C.
A’ (-6, 9); B’ ( 0, 0); C’ (3, 6)

D.
A’ (1, 6); B’ ( 0, 0); C’ (4, 5)

Your grandparents give you $1000 for your tenth birthday to invest for your college education. You research some investment companies around town and find one that pays you 4.2% and compounds quarterly. If you leave the money in your account until your 18th birthday, how much money will you have? Show all your work.

If a 6-ounce bottle of salad dressing costs $3.99, what is the cost per ounce?

Erik pays $225 in advance on his account at the athletic club. Each time he uses the club, $9 is deducted from the account. Write an equation that represents the value remaining in his account after x visits to the club. Find the value remaining in the account after 7 visits. a. V=225 -9x,• $162 b. v=9-225x,• $162 c. 225-9x,• $2032 d. 225 •x; $2046

Which of the following letters drawn on a coordinate plane would represent a function?

A) T
B) F
C) B
D) V

What is the ratio of the corresponding side lengths?
4:9
4:2
26:26
4.5:2