The conversion of square feet to square yards can be represented by direct variation. Three square yards are equivalent to 27 square feet. Let y represent the number of square yards and x the number of square feet. Then y varies directly with x. What is the constant of variation? What is the equation representing the direct variation?

Answers

Answer 1

Answer:

Part 1) The constant of variation is [tex]k=1/9[/tex]

part 2) The equation is [tex]y=\frac{1}{9}x[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

Let

x -----> the number of square feet

y -----> the number of square yards

Three square yards are equivalent to 27 square feet

we have the point (27,3)

Part 1) What is the constant of variation?

The constant of variation or proportionality is equal to

[tex]k=y/x[/tex]

substitute the values

[tex]k=3/27[/tex]

Simplify

[tex]k=1/9[/tex]

Part 2) What is the equation representing the direct variation?

we know that

[tex]y=kx[/tex]

substitute the value of k

[tex]y=\frac{1}{9}x[/tex]

Answer 2

This equation shows that the number of square yards (y) is directly proportional to the number of square feet (x) with a constant of variation equal to 1/9.

In direct variation, the relationship between two variables can be represented by the formula:

y = kx

Where:

- y represents one variable (in this case, the number of square yards).

- x represents the other variable (in this case, the number of square feet).

- k is the constant of variation, which remains the same for all data points in the direct variation.

In this specific case, you've mentioned that 3 square yards are equivalent to 27 square feet. You can use this information to find the constant of variation (k). You can choose one of the data points to solve for k. Let's use the point (3, 27):

3 = k * 27

Now, solve for k:

k = 3 / 27

k = 1 / 9

So, the constant of variation (k) is 1/9. The equation representing the direct variation is:

y = (1/9)x

This equation shows that the number of square yards (y) is directly proportional to the number of square feet (x) with a constant of variation equal to 1/9.

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Related Questions

Word problem. Help (:

Answers

I just got 5 free points.

find the inverse of f(x) = 2x + 3

Answers

Answer:

f−1(x)=x−32

Explanation:

Follow the steps:

f(x)=2x+3

1- replace f(x) with y →y=2x+3

2- simply switch x and so the equation looks like x=2y+3

3- use algebra to solve for y. (isolate y)
x=2y+3

x−3=2y

x−32=y

This is the inverse function and is written as

f−1(x)=x−32

a patient is to take 2 4/5 tablespoons of medicine per day in 2 equally divided doses. how much medicine is to be taken in each dose?

Answers

Just divide 2 4/5 by 2:

Convert 2 4/5 into the improper fraction 14/5, and then divide this result by 2:

7/5, or 1 2/5, tablespoons of medication, twice per day (total 2 4/5 tablespoons)

With continuous compounding, a principal of P dollars accumulates to an amount A given by the equation
A = Pe^rt
where r is the interest rate and t is the time in years.
a) suppose you start with a principal of $1000 and an interest rate of 7%. how much work will you have in ten years
b)suppose you start with a principal of $1000 and an interest rate of 75. how long will it be until you have $2000? round to the nearest tenth of a year. PLEASE HELP

Answers

a)

[tex]\bf \qquad \textit{Continuously Compounding Interest Earned Amount}\\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to& \$1000\\ r=rate\to 7\%\to \frac{7}{100}\to &0.07\\ t=years\to &10 \end{cases} \\\\\\ A=1000e^{0.07\cdot 10}[/tex]

A ball is thrown downward from a window in a tall building. its position at time t in seconds is s = 16t^2 + 32t, where s is in feet. how long (to the nearest tenth) will it take the ball to fall 211 feet

Answers

so When S is equal to 211
S = 16t^2 + 32t
211 = 16t^2 + 32t
Then, turn into a quadratic equation
0= 16t^2 + 32t - 211

Afterwards, simply find the roots of the equation by using your calculator formula 01.
you will be getting two answers,
t = 2.7666.... (correct to 3 significant figures)
t = -4.7666...(reject this because of its negative sign)

therefore, it will take 2.78 for the ball to fall 211 feet.

The product of two consecutive positive even integers is 80. Find the integers

Answers

Greetings!

We can create an equation for this:
[tex](x)(x+2)=80[/tex]
Distribute the Parenthesis.
[tex]x^2+2x=80[/tex]
Add -80 to both sides.
[tex](x^2+2x)+(-80)=80+(-80)[/tex]
[tex]x^2+2x-80=0[/tex]
Factor the Simple Trinomial.
[tex]x^2+10x-8x-80=0[/tex]
Factor by Grouping.
[tex]x(x+10)-8(x+10)=0[/tex]
Factor the GCF.
[tex](x+10)(x-8)=0[/tex]
The Answer Is:
[tex](x+10)=0 \\ (x-8)=0[/tex]
[tex]x=-10 \\ x=8[/tex]

Either:
-10,-8 or 8,10
Can be the solution in this answer.

Hope this helps.
-Benjamin

What is the product of -2 1/2 and -3 1/3

A. -8 1/3
B. -6 1/6
C. 6 1/6
D. 8 1/3

Answers

-2 1/2 x -3 1/3
= -5/2 x -10/3
= 25/3
= 8 1/3

answer
D. 8 1/3

(A) negative 8 and 1/3

What is .16 repeating as a simplified fraction?

Answers

I'm assuming this is 0.1666666...

Which in that case is 1/6.

(Just from memory)

To do 0.161616161616...

First, assign 0.161616... a variable, say it's x.

Now say 100x, what is it.

16.1616161616...

Now subtract x from 100x.

16.161616161616... - 0.16161616...

Or, 99x

99x = 16 in this case right now

Divide both sides by 99

x = 16/99

So it really depends what's repeating, it's either 1/6 or 16/99.

Naomi has earned $54 mowing lawns the past 2 days. She worded 21/2 hours yesterday and 41/4 hourse today. If Naomi is paid the same amount for every hour she works, how much does she earn per hour to mow lawns?

Answers

she worked 2 and 1/2 hours yesterday, and today she did 4 and 1/4 hours.

first off, let's check how many hours she worked total, and divide 54 by it.

so, first off, let's convert the mixed fractions to "improper" and add them up.

[tex]\bf \stackrel{mixed}{2\frac{1}{2}}\implies \cfrac{2\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{5}{2}} \\\\\\ \stackrel{mixed}{4\frac{1}{4}}\implies \cfrac{4\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{17}{4}}\\\\ -------------------------------[/tex]

[tex]\bf \cfrac{5}{2}+\cfrac{17}{4}\impliedby \textit{our LCD will be 4}\implies \cfrac{(2\cdot 5)+(1\cdot 17)}{4} \\\\\\ \cfrac{10+17}{4}\implies \cfrac{27}{4}\implies \stackrel{total~hours}{6\frac{3}{4}} \\\\\\ \cfrac{\stackrel{wages}{54}}{\stackrel{hours}{6\frac{3}{4}}}\implies \cfrac{54}{\frac{27}{4}}\implies \cfrac{\frac{54}{1}}{\frac{27}{4}}\implies \cfrac{54}{1}\cdot \cfrac{4}{27}\implies \cfrac{216}{27}\implies 8~\frac{\$}{hr}[/tex]

ulia spends $6.25 on gas for her lawn mower. She earns $17.00 mowing her neighbor's yard. What is Julia's profit?

Answers

Profit = Income less expenses: $17.00 - $6.25 = $10.75 (answer)

Her profit is 10.75 hope this helped
17.00-6.25=10.75

Find an equation of the line that satisfies the given conditions. x-intercept 1; y-intercept −4

Answers

My make an equation in the form y=my+b
You already have the y intercept, -4

Y=mx-4

And you have the two points (1,0) and (0,-4)
To find the slope (rise over run) to get from the two points you go over one up 4

So the slope is 4/1 or 4

The equation is:

Y=4x-4

Hope this helps!

The equation which is representing x-intercept 1; y-intercept −4 is y = 4x - 4.

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say the equation is y = mx + c which is the standard form of the linear equation.

Now,

At x- intercept ⇒ (1,0)

So,

0 = m(1) + c

c = -m

And y- intercept ⇒ (0,-4)

-4 = m(0) + c

c = -4

So m = 4

Therefore,

y = 4x - 4 will be the equation.

Hence "The equation which is representing x-intercept 1; y-intercept −4 is y = 4x - 4".

For more about the equation,

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a choir needs new robes for each of its 46 singers. Each robe costs $32.00. What will be total cost for all 46 robes?

Answers

You would take 32 times 46 which equals 1,472

The total cost of robes for the 46 choir members would be $1472

46 * 32 = $1472

What is the value of the expression below?
−5+∣9−11∣

Answers

-5+|9-11|
first, you would find the absolute value
|9-11|= |-2|=2
then the problem looks like this
-5+2= -3
So, the answer is negative three

A local little league has a total of 60 players 80 percent are right handed. How many right handed players are there

Answers

Just find 80% of 60 players: 0.80(60 players) = 48 players are rt. handed.

There are 48 right handed players

A music download service charges a flat fee each month and $0.99 per download. The total cost for downloading 27 songs this month is $42.72. how much is the flat fee

Answers

I believe the answer is $15.45

Answer:

$15.99

Step-by-step explanation:

A music download service charges a flat fee each month and $0.99 per download.

Charge of downloaded 27 songs in this month = 0.99 × 27

= $26.73

The total cost for downloading 27 songs this month = $42.72

Therefore, the flat fee = 42.72 - 26.73 = $15.99

Flat fee for the month is $15.99.

G calculate the iterated integral. 8 −8 π/2 (y + y2 cos(x)) dx dy 0

Answers

[tex]\displaystyle\int_{y=-8}^{y=8}\int_{x=0}^{x=\pi/2}(y+y^2\cos x)\,\mathrm dx\,\mathrm dy=\int_{y=-8}^{y=8}(xy+y^2\sin x)\bigg|_{x=0}^{x=\pi/2}\,\mathrm dy[/tex]
[tex]=\displaystyle\int_{y=-8}^{y=8}\left(\dfrac\pi2y+y^2\right)\,\mathrm dy[/tex]
[tex]=\left(\dfrac\pi4y^2+\dfrac13y^3\right)\bigg|_{y=-8}^{y=8}[/tex]
[tex]=\dfrac{1024}3[/tex]

Final answer:

To solve the given iterated integral, integrate the function of x with respect to x and then integrate the resulting function with respect to y.

Explanation:

The given iterated integral can be solved by integrating the function of x with respect to x first and then integrating the resulting function with respect to y. The limits of integration are given as (-8, 8) for x and (0, π/2) for y.

Step 1: Integrate the function of x with respect to x.

Step 2: Integrate the resulting function of x with respect to y.

Step 3: Evaluate the iterated integral using the given limits of integration.

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Corinnes puppy eats 3 meals a day. How many meals does the puppy eat in 32 days

Answers

Corinne's puppies eat 92 meals in 32 days.

Corinne's puppy eats a total of 96 meals in 32 days.

To find out how many meals Corinne's puppy eats in 32 days, we need to multiply the number of meals per day by the number of days.

Determine the number of meals per day.

Since the puppy eats 3 meals a day, the number of meals per day is 3.

Calculate the total number of meals in 32 days.

Number of meals per day × Number of days = Total number of meals

3 meals/day × 32 days = Total number of meals

3 × 32 = Total number of meals

96 = Total number of meals

So, Corinne's puppy eats a total of 96 meals in 32 days.

Complete Question:

Corinnes puppy eats 3 meals a day. How many meals does the puppy eat in 32 days ?

Write an equation and solve. 21 is 35% of what number?

Answers

It's 35% of 60. You can create a ratio. I included the ratio but you can easily substitute 60 with the variable x.
(21/60)=(35/100)

If a grouping of numbers, variables, operators and/or functions used to represent a specific mathematical computation or connection is known as an expression. The expression 21 of 35% is 60.

What is the expression?

Let x represent the unknown number

The given data states that 21 is 35% of that unknown number.

Mathematically we can express this relationship as an equation:

0.35 * x = 21

To solve for x divide both sides of the equation by 0.35:

x = 21 / 0.35

Evaluating the expression on the right side of the equation:

x = 60

Therefore, 21 is 35% of 60.

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Which set of fractions is ordered from greatest to least? 11/12, 7/10, 5/6

Answers

The fractions ordered from least to greatest are 7/10, 5/6, and 11/12. This is because 5/6 = 11/12 and 7/10 equals closer to 2/3.

A Color printer will print 8 pages per min. How many mins. will it take to report that has 136 pages?

Answers

it will take 17 minutes to print 136 pages.

It will take 17 minutes hope this helps:)

if two positive fractions are less than 1, why is their product also less than 1?

Answers

The product of two positive fractions are also less than one because you are multiplying a number which is already less than 1.

For example.

1/ 2 = is 50% of a whole.

When you multiply 1/2 by 1/2 you do not get the 100% of the whole because you are only getting 50% of the 50% of the whole, which in turn is equivalent to 25% of the whole.

1/2 * 1/2 = 1/4 of the whole.

The only time you can get a result of 1 and above where two fractions are less than 1 is when you perform addition of these fractions.

1/2 + 1/2 = 1 - ALL CREDITS GO TO @TASKMASTERS!

When you multiply something (x) by a proper fraction ( less than 1 ), you always get something less than x, or the original number, because you're taking part of x and a part can't be larger than the whole.

Here's an example :
5 * 1/5 = 1
1<5

When you start with something that's less than 1 ( and positive), and you multiply it by a fraction, you get part of that positive fraction, so it will never be greater than 1.

Hope this helps!
I'm sorry if this is confusing ... it's too late for my brain to work at max level.

If it is sunny, then I will have a picnic.
Today it is sunny

1)I will have a picnic today
2)if I am having a picnic, it must be sunny
3)if it is not sunny, then I will not have a picnic
4)not possible

Answers

Answer:

Answer not possible

Step-by-step explanation:

invalid

the rest on you guys yw

honors geom

Simplify the expression.

1/4 n (-24+8m-100p)

A. –6n + 2mn – 25np

B. –6n – 2mn + 25np

C. –24n + 8mn – 100np

D. –6n + 2m – 25np

Answers

1/4 n (-24+8m-100p)
= -24n/4 + 8mn/4 - 100np/4
= -6n + 2mn - 25np

answer
A. -6n + 2mn - 25np

Kate is 17 years old, and Victor is 12 years younger. In how many years will Kate be twice as old as Victor?

Answers

10 to 12 years I'm sure

Answer:

In 7 years

Step-by-step explanation:

Victors age: 17-12=5

Kate's age:17+7=24

Victors age:5+7=12

24 divided by 2 equals to 12.

~~~~~~~

Check your answer

5+12=17

24-7=17

12-7=5

12*2=24

Find 20.25 + -15.711

Answers

20.25 - 15.711 = 4.539

hope this helps

4.539
Make sure if you have to show ur work line up the decimals and remember the rules to negative numbers

the cost (in dollars) of making n birthday cakes is represented by C=24n+35. How many birthday cakes are made when the cost is $395? explain your reasoning

Answers

395 = 24n +35
subtract 35 from both sides
360 =24n
divide both sides by 24
15=n

The sum of two numbers is 62. The smaller number is 18 less than the number.what are the numbers ?

Answers

hmmm assuming you meant "is 18 less than the larger number".

let's say the numbers are "a" and "b".

a = smaller number
b = larger number

a = b - 18

[tex]\bf \begin{cases} a+b=62\\ \boxed{a}=b-18\\ ----------\\ \left( \boxed{b-18} \right)+b=62 \end{cases} \\\\\\ 2b-18=62\implies 2b=80\implies b=\cfrac{80}{2}\implies b=40[/tex]

what's a? well, a = b - 18.

You have 120 pieces of fabric to make a blanket. Each piece of fabric is a square with a side length of 6 inches. You use as many squares as possible to make a square blanket. What is the area of the blanket? How many pieces are left over? How many more pieces of fabric would you need to increase the size of the blanket?

Answers

A. Since the blanket to be made is a square, therefore there should be equal number of fabric on all sides. So find the square root of 120.

number of fabrics = sqrt (120) = 10.95

Since number of fabrics cannot be decimal, therefore the largest number of pieces of fabric per side is 10 (length and width).

Since each fabric measures 6 inches, so total length per side is 60 inches. The area is therefore:

Area of blanket = 60 in * 60 in = 3600 square inches

B. Since the two sides, length and width, has same number of fabrics which is 10, so total number used is = 10 * 10 = 100

So the left-over are 120 – 100 = 20 fabrics left over

C. To create a bigger blanket, it would require 11 fabrics per side, so total number used would be = 11 * 11 = 121

Therefore only 1 additional piece of fabric is required.

A family has a monthly income of $3300 and plans to spend 11% of this amount on entertainment. How much will be spent on entertainment?

Answers

$363 just divide $3300 by 0.11

363 dollars is your answer
Hoped i helped

Jared is 10 years old and peter is 15 years old they are brothers . Together they run 150 yards . How far does each brother run

Answers

So, pretty much age would be a distractor, so if they both run 150 yards, they could possibly run 75 yards

Answer: About 70 yards :D.

Hope this helped

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