The following function represents an arithmetic sequence.
f(1)=−1.5
f(n+1)=f(n)+0.5
What is f(10)?

Answer:

At 7 hours from the visit telling the joke, everyone in town would have heard of it

Step-by-step explanation:

Exponential Grow

This is a good example of exponential growth, where the speed at which a rumor is spread out depends on the actual number of persons who already know it.

The visitor told the mayor a new joke at 10:00 am.

Total people who heard the joke=1

This person tells the joke to 3 people in one hour, so at 11:00 am, 1+3=4 persons heard the joke

Total people who heard the joke=4

Those persons take one hour to tell the joke to every 3 persons each. Thus at 11:00  

4 + 4*3 = 16 persons heard the joke. This succession grows very quickly. At 12:00

16 + 16*3 = 64 persons heard the joke

We can note the number of persons hearing the joke is an even power of 2, that is

[tex]2^0=1[/tex]

[tex]2^2=4[/tex]

[tex]2^4=16[/tex]

[tex]2^6=64[/tex]

We can predict the result for each hour since the exponent is double the number of hours passed since the joke started to spread. The number of persons who have heard the joke after t hours is

[tex]N=2^{2t}[/tex]

We can iterate until we find the value of t so that

[tex]2^{2t}<9800[/tex]

Let's better find the limit value of t

[tex]2^{2t}=9800[/tex]

Taking logarithms

[tex]log(2^{2t})=log9800[/tex]

[tex]2tlog(2)=log(9800)[/tex]

Thus

[tex]\displaystyle t=\frac{log(9800)}{2log 2}[/tex]

[tex]t=6.6[/tex]

So at 7 hours from the visit telling the joke (between 16:00 and 17:00), everyone in town would know it

Note that

[tex]2^{12}=4096[/tex]

[tex]2^{14}=16384[/tex]

Answer:

321.24 ft²

Step-by-step explanation:

If 3in = 5ft

   1in = x

5/3 = 1.6

So 1in = 1.67 ft

Actual dimensions will be;

L = 19.2*1.67 = 32.06ft

W = 6*1.67 = 10.02ft

Area = 32.06 * 10.02 = 321.24 ft²

To find the length and width of the actual studio, set up a proportion to convert the given dimensions from the scale to the actual dimensions. Then, find the area of the actual studio by multiplying the length and width.

To find the length and width of the actual studio, we need to convert the given dimensions from the scale to the actual dimensions. Since the scale is 3 in.: 5 ft, we can set up the proportion:

3 in / 5 ft = 19.2 in / x ft

Cross multiplying and solving for x, we get:

x = 32 ft

The length of the actual studio is 32 ft. Similarly, we can find the width:

3 in / 5 ft = 6 in / y ft

Solving for y, we get:

y = 10 ft

The width of the actual studio is 10 ft.

To find the area of the actual studio, we multiply the length and width:

Area = length x width = 32 ft x 10 ft = 320 ft²

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Answer:

  d.  about 9 years​

Step-by-step explanation:

There is a "rule of thumb" for doubling time* that says the product of the percentage rate of change per year and the doubling time in years is about 72. Here, that means the doubling time is about ...

  72/8 = 9 . . . . years

_____

You can write the exponential equation ...

  multiplier = (1 +.08)^n

and solve for multiplier = 2:

  2 = 1.08^n

  log(2) = n·log(1.08) . . . . . take logs

  log(2)/log(1.08) = n . . . . . divide by the coefficient of n

  9.00647 ≈ n

It will take about 9 years for the participation to double.

_____

* The farther away from 8% the rate of change is, or the more times per year it is compounded, the less accurate is the "rule of 72." When compounding is continuous, the "rule of 72" becomes the "rule of 69.4". For this problem, answer choices are sufficiently far apart that the rule of thumb is adequate for making a correct choice.

Answer:

Step-by-step explanation:

Let x represent the number of pounds of soap that she makes and eventually sells.

She intially spent $72 to purchase soap-making equipment, and the materials for each pound of soap cost $7. This means that the total cost of making x pounds of soap would be

7x + 72

Lisa sells the soap for $10 per pound. This means that her revenue for x pounds of soap would be

10 × x = 10x

If she eventually sells enough soap to cover the cost of the equipment, then

7x + 72 = 10x

10x - 7x = 72

3x = 72

x = 72/3 = 24

She would need to sell make and sell 24 soaps.

The cost would be

72 + 7 × 24 = $240

The total sales would be

10 × 24 = $240

Answer:

19 wrong answers.

Step-by-step explanation:

Given:

Sahil got 28 questions right.

Angelina got 7 more wrong answers than Sahil.

There where 40 questions on the test.

Question asked:

How many answers did Angelina get wrong on the math test ?

Solution:

Total questions on the test = 40

Number of right answers, Sahil got = 28

Number of wrong answers, Sahil got = 40 - 28 = 12

As Angelina got 7 more wrong answers than Sahil,

Number of wrong answers, Sahil got = 12

Then, number of wrong answers, Angelina got = 12 + 7 = 19

Therefore, 19 answers did Angelina get wrong on the math test out of 40.

Angelina got 35 wrong answers on the math test.

To find the number of wrong answers Angelina got on the math test, we need to know how many questions she got right. Since Sahil got 28 questions right and there were 40 questions on the test, we can subtract Sahil's score from the total number of questions to find Angelina's score. Sahil got 28 questions right, so Angelina would have gotten 40 - 28 = 12 questions right. And since Angelina got 7 more wrong answers than Sahil, we can subtract Sahil's wrong answers from Angelina's total wrong answers to find the specific number. If Sahil got 12 questions right, then he must have gotten 40 - 12 = 28 questions wrong. And since Angelina got 7 more wrong answers than Sahil, we can add 7 to Sahil's wrong answers to find Angelina's total wrong answers. Therefore, Angelina got 28 + 7 = 35 wrong answers on the math test.

The area of circle is 379.94 cm².

Step-by-step explanation:

Given,

Radius of circle = 11 centimeters

We have to calculate the area of circle.

We know that;

Area of circle = [tex]\pi r^2[/tex]

Here;

π = 3.14 , r = 11

Area of circle = [tex]3.14*(11)^2[/tex]

Area of circle = 3.14*121

Area of circle = 379.94 squared centimeters

The area of circle is 379.94 squared centimeters.

Keywords: area, circle

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Step-by-step explanation:

[tex]m \angle \: C = \frac{1}{2} (m \: arc \: AB)\\(By\:inscribed \:\angle\:theorem) \\ \\ \therefore \: (x + 5) \degree =\frac{1}{2} (4x)\degree \\ \\ \therefore \: x + 5=\frac{1}{2} \times 4x \\ \\ \therefore \: x + 5=2x \\ \\ \therefore \: x - 2x = - 5 \\ \\ \therefore \: - x = - 5 \\ \\ \: \: \: \: \: \huge \purple{ \boxed{\therefore \: x = 5}}[/tex]

Answer:

1. The vertical components decrease by 14 units while the horizontal component increase by 3 units

2.it therefore means that the vertical component decreases by 70units

Step-by-step explanation:

Slope of a graph is change in the vertical axis over the the change in the horizontal axis

in the above question, if the average rate of change is -14/7 it therefore means that the vertical components decrease by 14 units while the horizontal component inc rfease by 3 units

what does that mean if the waterslide from x=0, and x=15

it means that the vertical components decrease why there is an increment distance in the horizontal axis

mathematically, we say

-14/3=-y/[tex]s= \frac{dy}{dx} , slope=s\\-14/3=\frac{-y}{15-0}[/tex]

14/3=y/15

y=70

it therefore means that the vertical component decreases by 70units

Answer:

On average, the slide drops 14 feet for every 3 feet of horizontal distance.

On average, the slide drops about 4.7 feet for every 1 foot of horizontal distance.

Step-by-step explanation:

on edg... Good Luck!!!

Answer:

  85 m

Step-by-step explanation:

The diagonal of a square is √2 times the length of the side. The park will have a side length of 120/√2 m ≈ 84.85 m, about 85 meters.

_____

The relations are ...

  diagonal = (√2)×(side length)

  side length = diagonal/√2 . . . . . . . . . divide the above equation by √2

Answer: the system of equations are

a + c = 150

7.75a + 10.25b = 1470

Step-by-step explanation:

Let a represent the number of adult tickets that were sold.

Let c represent the number of child tickets that were sold.

The celluloid cinema sold 150 tickets to a movie. Some of these were child tickets and the rest were adult tickets. This means that

a + c = 150 - - - - - - - - - - - - - -1

A child ticket cost $7.75 and an adult ticket cost $10.25. If the cinema sold $1470 worth of tickets, it means that

7.75a + 10.25b = 1470 - - - - - - - - -2

The question can be answered by creating two linear equations, one representing the total number of tickets (a + c = 150) and the other representing the total earnings from the ticket sales (10.25a + 7.75c = 1470). Solving this system of equations will yield the number of adult and child tickets sold.

This problem can be solved using a system of linear equations, where one equation represents the total number of tickets sold and the other equation represents the total dollar value of the tickets sold.

The first equation is formed from the total number of tickets, which is the sum of adult tickets and child tickets: a + c = 150

The second equation is formed from the total cost of the tickets, where $10.25, the cost of an adult ticket, is multiplied by the number of adult tickets, and $7.75, the cost of a child ticket, is multiplied by the number of child tickets. This sum should be the total earnings from the ticket sales: 10.25a + 7.75c = 1470

Therefore, the system of equations to solve this problem is a + c = 150 and 10.25a + 7.75c = 1470.

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Answer:

  -6

Step-by-step explanation:

Take a couple of differences and see:

  11 -17 = -6

  5 -11 = -6

The common difference is -6.

Answer:

55% and 24%

Step-by-step explanation:

Firstly, we need an arbitrary number to serve as the number of students.

Let the total number of students be 120.

Firstly we need college-educated percentage.

Men are two-thirds, women are one-third

Men = 2/3 * 120 = 80

Women = 1/3 * 120 = 40

5/8 of men are college educated = 5/8 * 80 = 50

2/5 of women are college educated = 2/5 * 40 = 16

Total college educated = 50+ 16 = 66

% college educated = 66/120 * 100 = 55%

Percentage of college educated that are women.

Total college educated = 66

The % is 16/66 * 100 = 24%

Answer: he open the account 9 years ago.

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the amount deposited.

P represents the principal or amount deposited.

R represents interest rate

T represents the time for which the amount deposited was left in the account.

From the information given,

P = 400

R = 7.5%

I = 670 - 400 = $270

Therefore,

270 = (400 × 7.5 × T)/100 = 30T

T = 270/30

T = 9 years

Step-by-step explanation:

9 years thank you yw bubye

Part 1:

Replace "v0" in the given equation with the given velocity of 15 ft/sec:

y = -16t^2 + 15t +6.5

Part 2:

Now set the equation to 0 which would be when the basketball hits the ground:

-16t^2 +15t +6.5 = 0

A quadratic equation is solved using the formula:

t = -b +/- sqrt(b^2-4ac)/2a

Using the given equation: a = -16, b = 15 and c = 6.5

Replace the values and solve:

t = -(15)+/- sqrt(15^2 -4(-16)(6.5))/2(-16)

This solves to get both -0.32 and 1.26 seconds.

The time has to be a positive value so t = 1.26 seconds.

Part3:

Using the quadratic form at^2 + bt + c

The maximum is found using t = -b/2a = -15/2(-16) = = 0.47 seconds

The maximum height would be at 0.47 seconds

Part 4:

Replace t with 0.47 and solve for maximum height:

y = -16(0.47)^2 + 15(0.47) +6.5

Maximum height would be 3.52 feet

The function that represent cost is c(t) = 40 + 0.5(t -400).

For the first 400 minutes [tex](\(0 \leq t \leq 400\))[/tex], the cost is a flat rate of $40.

T represents the overall conversation time in minutes in the provided question.

Speed cell wireless offers a $40 package for the first 400 minutes.

Additional $0.50 per minute for remaining time

Time remaining = (t - 400) minutes

So, the cost for more beyond 400 minutes is 0.5(t -400). $

Thus, the entire cost, c(t), is 40 + 0.5(t -400).

The velocities of particles are given by the derivatives of their displacement functions. Equating the velocity functions of the two particles and solving numerically, we find that they have the same velocity for the first time at about t = 1.569 seconds.

The velocity of an object is given by the derivative of its displacement function. So, we need to first find the derivatives of the given displacement functions to find the velocities of the particles.

The derivative of e^(4cos(t)) is [tex]-4e^{(4cos(t))sin(t)[/tex]. The derivative of [tex]-(t^3)/(3) - (t^2)/(2) + 2 is -t^2 - t.[/tex] Now, we equate the two velocities and solve for t[tex].-4e^(4cos(t))sin(t) = -t^2 - t[/tex]

Unfortunately, this equation does not have a simple algebraic solution. However, it can be solved numerically using, for example, a graphing calculator or numerical software. By using these tools, we find the first positive time at which the particles have approximately the same velocity to be about t = 1.569 seconds. Therefore, the correct answer is A.) t = 1.569 seconds.

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Answer:

Step-by-step explanation:

Let t = flying time in seconds for each plane

Descending rate = 40 ft/s

Ascending rate = 60 ft/s

Descending height, hd= 19200 - 40t

Ascending height, ha = 60t

Equating hd = ha, therefore:

60t = 19200-40t

60t + 40t = 19200

100t = 19200

t = 19200/100

t = 192 seconds

h = 19200 - 192(40)

h = 19200 - 7680

= 11,520 ft.

After 192 seconds, the two airplanes will be at the same height, which is 11,520 feet.

To find the time it takes for the two airplanes to be at the same height, we need to set up an equation based on their rates of ascent and descent. Let's assume the height of the descending airplane is given by h1 and the height of the ascending airplane is given by h2. The descending airplane is descending at a rate of 40 feet per second, so its height after t seconds can be represented by the equation h1 = 19,200 - 40t. The ascending airplane is ascending at a rate of 60 feet per second, so its height after t seconds can be represented by the equation h2 = 60t. To find the time at which the two airplanes are at the same height, we can set h1 equal to h2 and solve for t: 19,200 - 40t = 60t. Simplifying this equation, we get 100t = 19,200, so t = 192 seconds. Therefore, after 192 seconds, the two airplanes will be at the same height.

To find the height at which the two airplanes are at, we can substitute the value of t into either the equation for h1 or h2. Let's use the equation for h1: h1 = 19,200 - 40(192) = 19,200 - 7,680 = 11,520 feet. Therefore, after 192 seconds, the two airplanes will be at a height of 11,520 feet.

Yo sup??

Since there is an x^2 term therefore this equation is of a parabola

By taking LCM and then cross multiplying it.

6y=x^2-9x+26

6y=x^2-9x+(9/2)^2+23/4

6y-23/4=(x-9/2)^2

we see that this is of the form

X^2=4AY

(x-9/2)^2=4(3y/2-23/16)

Hope this helps.

Answer:

[tex]f(x) =- \sqrt{x-1}+3[/tex]

Step-by-step explanation:

This looks like a square root function [tex]f(x) = \sqrt{x}[/tex]  but symmetric with respect to the x axis and shifted to the right for 1 and up for 3:

Lets take  [tex]f(x) = \sqrt{x}[/tex] . The function symmetric with respect to the x axis would be [tex]-f(x)[/tex], so now we have:

                                                [tex]f(x) = -\sqrt{x}[/tex]

Lets take [tex]f(x) = -\sqrt{x}[/tex] and shift it up for y = 3. Now we have:

                                               [tex]f(x) =- \sqrt{x}+3[/tex]

Lets take [tex]f(x) = -\sqrt{x}+3[/tex] and shift it right for x = 1. That means that instead of x we will have x-1:

                                            [tex]f(x) =- \sqrt{x-1}+3[/tex]

The measure of the first, second and third angles are 20°, 27° and 133°.

An exterior angle of a triangle is the sum of two opposite interior angles.

According to given question

The residents of a downtown neighbourhood designed a​ triangular-shaped park as part of a city beautification program.

Let us assume the first angle to be x°.

Therefore from the given data second angle is (x + 7)° and the third angle is (7x - 7)°.

We know that the sum of all the interior angles of a given triangle is 180°.

∴ x + (x + 7) + (7x - 7) = 180°

  9x = 180°

    x = 180°/9

    x = 20°.

So, The first angle of the triangular park is 20°, The second angle is 27° and the third angle is 133°.

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The solutions to the equations:

(a) x/3 = 6 => x = 18 (Verified)

(b) (5x + 9)/2 = 12 => x = 3 (Verified)

(c) x/4 = 9/6 => x = 6 (Verified)

(d) 5/x = 20/8 => x = 2 (Verified)

To solve the equation, follow these steps: identify the equation with one unknown, isolate x, substitute known values and solve, and check the solution.

The equations are

(a) x/3 = 6

(b) (5x + 9)/2 = 12

(c) x/4 = 9/6

(d) 5/x = 20/8

The answers to the question are

(a) x = 18

(b) x = 3

(c) x = 6

(d) x = 2

Step-by-step explanation:

(a) x/3 = 6

Therefore x = 3×6 = 18

x =18

Substituting the value of x in the above equation, we have

18/6 = 3 verified

(b) (5x + 9)/2 = 12

Multiplying both sides by 2 gives

(5x + 9)/2 × 2 = 12×2 = 24

5x + 9 = 24 or x = (24-9)/5 = 3

Substituting the value of x in the above equation, we have

(5×3 + 9)/2 = 24/2 = 12 verified

x = 3

(c) x/4 = 9/6

Multiplying both sides by 4, we have

x/4×4 = 9/6×4 = 6

x = 6

Substituting the value of x in the above equation, we have

(6/4 = 9/6 = 3/2 verified

(d) 5/x = 20/8

Inverting both equations, we have

x/5 = 8/20

Multiplying both sides by 20 we have x/5 × 20 = 8/20 × 20 or 4x = 8 and x = 2

Substituting the value of x in the original equation, we have

2/5 = 2/5 = 8/20 verified

x = 2

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Answer:

7y²

Step-by-step explanation:

First u group them like 4+3+y+y=7y²

Answer: the shipping and handling fee is 8 percent of the cost of the order.

Step-by-step explanation:

Shipping and handling fee of $35 is charged to all furniture orders over $250.

If the order is $437.50, it means that there would be a handing and shipping fee of $35 because the price of the order is above $250.

The percentage of the original price of the order that is the shipping and handling fee would be

35/437.5 × 100 = 0.08 × 100

= 8%

Final answer:

To find the percent that the shipping and handling fee is of the total order, divide the fee by the order amount and multiply by 100. For an order of $437.50 with a fee of $35, the shipping fee is 8% of the total order.

Explanation:

The question asks us to determine what percent the shipping and handling fee is of the total furniture order.

To calculate this percentage, we can use the formula:

Percentage = (Part / Whole)  imes 100

In this case:

Now, we insert the values into the formula:

Percentage = ($35 / $437.50)  imes 100

Percentage = 0.08  imes 100

Percentage = 8%

Therefore, the shipping and handling fee is 8% of the total order.

Answer:

The answer is 12

Step-by-step explanation:

t5 = 24 = a × r⁴

t8 = 3 = a × r⁷

We divide one by the other

r³= 1 / 8

r = 1 / 2

t6 = a × r⁵ = t5 × r = 24 × (1/2) = 12.

Therefore the sixth term of the geometric sequence is 12

Answer:

S = 128πx² + 64πx + 8π

Step-by-step explanation:

Suraface area of a cylinder is given by:

S = 2πrh + 2πr²

We know that the height is 3 times as big as the radius, hence:

h = 3r

so we can plug in the new h value and rewrite the S equation as:

S = 2πrh + 2πr²

S = 2πr(3r) + 2πr²

S = 6πr² + 2πr²

S = 8πr²

We're given in the question that the radius is ​(4x + 1​) inches, so plug that into r.

Given: r = 4x + 1​

Therefore,

S = 8πr²

S = 8π(4x + 1​)²

S = 8π(16x²+8x+1)

S = 128πx² + 64πx + 8π

Answer:

The answer to your question is 128πx² + 64πx + 8π

Step-by-step explanation:

Data

radius = (4x + 1)

height = 3(4x + 1)

Formula

Area = 2πrh + 2πr²

Substitution

Area = 2π(4x + 1)(3)(4x + 1) + 2π(4x + 1)

Simplification

Area = 6π(4x + 1)² + 2π(4x + 1)²

Area = 6π(16x² + 8x + 1) + 2π(16x² + 8x + 1)²

Area = 96πx² + 48πx + 6π + 32πx² + 16πx + 2π

Area = 128πx² + 64πx + 8π

Answer:

Fran was incorrect.

Correct representation: [tex]c \geq 15[/tex], where c is the number of customer during any time of day.

Step-by-step explanation:

We are given the following in the question:

Fran used the given inequality to represent the number of customers in a shop at any time.

[tex]c > 15[/tex]

where c is the number of customer during any time of day.

The least number of customers in a shop at any time during the day was 15.

Thus there could be 15 or greater than 15 customers in shop during any ime of day.

Thus, Fran was incorrect.

The correct representation is given by the inequality

[tex]c \geq 15[/tex]

where c is the number of customer during any time of day.

Answer:

Fran is incorrect.

The inequality is c ≥ 15

Step-by-step explanation:

Final answer:

By defining equations based on the relationships between Jen's, Carrie's, and Fran's numbers and solving them, we find that Carrie's number is 64, Jen's number is 73, and Fran's number is 70.

Explanation:

To solve for Fran's number, we need to use the information given: Jen's number is 9 more than Carrie's, and Fran's number is 3 less than Jen's number. Their total sum is 207. We can set up equations to solve this. Let Carrie's number be c, Jen's number be c + 9 (since it is 9 more than Carrie's), and Fran's number be c + 9 - 3 (since it is 3 less than Jen's).

The equation to express the sum of their numbers will be: c + (c + 9) + (c + 9 - 3) = 207.

Now let's solve the equation:

Now that we have Carrie's number, we can find Fran's number:

Therefore, Fran's number is 70.

Answer:

Step-by-step explanation:

The diagonals of the parallelogram are A(-5, -1), C(-1, 5) and B(-9, 6), D(3, -2).

Slope of diagonal AC = (5 - (-1)) / (-1 - (-5)) = (5 + 1) / (-1 + 5) = 6 / 4 = 3/2

Slope of diagonal BD = (-2 - 6) / (3 - (-9)) = -8 / (3 + 9) = -8 / 12 = -2/3

For the parallelogram to be a rhombus, the intersection of the diagonals are perpendicular.

i.e. the product of the two slopes equals to -1.

Slope AC x slope BD = 3/2 x -2/3 = -1.

Therefore, the parallelogram is a rhombus.

Answer:

Step-by-step explanation:

Let x represent the distance that the truck was driven.

Buck rented a truck for $39.95 plus $0.32 per mile. This means that the total cost of driving x miles with the truck would be

39.95 + 0.32x

Before returning the truck, he Filled the tank with gasoline, which cost $9.85. This means that the total amount that he spent is

39.95 + 0.32x + 9.85

If the total cost was $70.23, it means that

39.95 + 0.32x + 9.85 = 70.23

49.8 + 0.32x = 70.23

0.32x = 70.23 - 49.8 = 20.43

x = 20.43/0.32 = 63.8

Approximately 64 miles

The required equation in a standard form that represents the number of rooms Martin has left to clean (y) after x hours is 4x + 7y = 56.

To write the equation in a standard form that represents the number of rooms Martin has left to clean (y) after x hours, we can use the given information that there are 4 rooms left to clean after 7 hours.

Let's start with the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

We have the point (x₁, y₁) = (7, 4), which represents the number of rooms left after 7 hours.

Substituting the values into the point-slope form, we get:

y - 4 = m(x - 7)

Now, we need to find the slope (m) of the line.

The slope of a line can be determined by the change in y divided by the change in x. In this case, the change in y is -4 (4 rooms left to clean) and the change in x is 7 hours.

m = Δy / Δx = -4 / 7

Now, let's substitute the value of m into the equation:

y - 4 = (-4/7)(x - 7)

To eliminate fractions, we can multiply through by 7:

7y - 28 = -4(x - 7)

7y - 28 = -4x + 28

4x + 7y = 56

So, the equation in a standard form that represents the number of rooms Martin has left to clean (y) after x hours is 4x + 7y = 56.

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Final answer:

To express the relationship between the number of rooms left to clean and the hours spent cleaning in a linear equation, we use the slope of -4/7 and a y-intercept of 4, assuming 4 rooms are cleaned in 7 hours. This leads to the slope-intercept form y = -4/7x + 4. Multiplying by 7 and rearranging gives us the standard form 4x + 7y = 28.

Explanation:

To find the equation of the line that represents the number of rooms, y, Martin has left to clean after x hours, we start with the information that 4 rooms take 7 hours to clean. This means that every hour, a fraction of the total rooms are cleaned. To express this situation as a linear equation, we can use the slope-intercept form, which is y = mx + b. In this context, the slope (m) will be negative since the number of rooms left to clean decreases over time, and b is the y-intercept representing the initial number of rooms before any cleaning has started. Since there are 4 rooms to begin with and it takes 7 hours to clean all, the slope is -4/7 (the change in rooms left per hour).

The equation in slope-intercept form is y = -4/7x + 4. To convert this to standard form, we multiply the entire equation by 7 to eliminate the fraction: 7y = -4x + 28. Then we add 4x to both sides of the equation to get: 4x + 7y = 28. This is the equation in standard form, representing the number of rooms left (y) after x hours of cleaning.