Paula has a large ball of yarn that she is going to use to knit a scarf for the winter. Every square inch on the scarf requires a certain number of yards of yarn from the ball. A linear model of this situation contains the values (11 , 352.99) and (30 , 126.7), where x represents the number of square inches knitted on the scarf, and y represents the number of yards remaining on the ball of yarn. How many yards of yarn did Paula start with?

Answers

Answer 1

Answer:

She started with 484 yarns

Step-by-step explanation:

Given

[tex](x_1,y_1) = (11,352.99)[/tex]

[tex](x_2,y_2) = (30,126.7)[/tex]

Required

Number of yarns she started with

The interpretation of this question is to calculate the y intercept.

We strt by calculating the slope (m)

[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]

[tex]m = \frac{352.99 - 126.7}{11 - 30}[/tex]

[tex]m = \frac{226.29}{-19}[/tex]

[tex]m = -11.91[/tex]

Next, we calculate the linear equation as follows;

[tex]y - y_1 = m(x - x_1)[/tex]

Where

[tex](x_1,y_1) = (11,352.99)[/tex]

[tex]m = -11.91[/tex]

[tex]y - 352.99 = -11.91(x - 11)[/tex]

[tex]y - 352.99 = -11.91x + 131.01[/tex]

Make y the subject

[tex]y= -11.91x + 131.01 + 352.99[/tex]

[tex]y= -11.91x +484[/tex]

A linear equation has the form

[tex]y=mx + b[/tex]

Where

[tex]b = y\ intercept[/tex]

By comparison.

[tex]b = 484[/tex]

Hence, she started with 484 yarns


Related Questions

Pls help, The graph of a proportional relationship contains the point (20, 4) .

What is the corresponding equation?

Enter your answer as a fraction in simplest form by filling in the boxes.

y = ?/? x

Answers

Answer:

y = 1/5 x

Step-by-step explanation:

Answer:

1

--

5

Step-by-step explanation

Can you give jasmynpurifoy branliest

WILL GIVE BRAINLIEST if you spin the following spinners how many outcomes are possible

Answers

Answer: 30 OR C

Step-by-step explanation:

C will be the correct answer! Hope this helps!

10000000000000000000x0 + 111111111111111111111111111111111111111111111111111111

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Answer:

111111111111111111111111111111111111111111111111111111

Step-by-step explanation:

a. (x+2) (x2 +x+2) + 2(x3 + x2)

Answers

Answer:

3x³ + 5x² + 4x + 4

Step-by-step explanation:

Given

(x + 2)(x² + x + 2) + 2(x³ + x²)

To expand the product, each term in the second factor is multiplied by each term in the first factor, that is

x(x² + x + 2) + 2(x² + x + 2) + 2(x³ + x²) ← distribute the parenthesis

= x³ + x² + 2x + 2x² + 2x + 4 + 2x³ + 2x² ← collect like terms

= 3x³ + 5x² + 4x + 4

A school has 1,000 students on Wednesday, 300 students went on a field trip. What percent of students did not go on the field trip?

Answers

Answer:

%70

Step-by-step explanation:1,000=%100  300+%30  1000 - 300 = 700 so 700 + %70

A person walked x feet and half that length again

Answers

Answer:

3/2x

Step-by-step explanation:

x feet and half x = x+1/2x or 3/2x

Hope this helps plz hit the crown :D

Ahmad’s father is 4 times as old as Ahmad. After 5 years, father will be three times as old as Ahmad. Find their present ages

Answers

The present age of Ahmed and Ahmed's father is 12 and 36 respectively.

Step-by-step explanation:

Given : Ahmed's father is thrice as old as Ahmed. After 12 years, his age will be twice that of his son.

To Find : Their present age ?

Solution :

Let the Ahmed's age be 'x'.

Ahmed's father is thrice as old as Ahmed.

i.e. Ahmed's father age is '3x'

After 12 years, his age will be twice that of his son.

i.e. 3x+12 = 2(x+12)3x+12=2(x+12)

Solving the equation,

3x+12 = 2x+243x+12=2x+24

x=12x=12

So, Ahmed's age is 12.

Ahmed's father age is 3\times 12=363×12=36

Therefore, The present age of Ahmed and Ahmed's father is 12 and 36 respectively.

There is 3 times in space of 4 times please mark as brainlist

Amitas kitchen is rectangular with an area of 3 3 4 square meters the width of the kitchen is 1 1 2 meters what is the length in meters of amitas kitchen

Answers

Answer:

2 1/5 meters

Step-by-step explanation:

Given that:

Area of kitchen = 3 3/4

Width of kitchen = 1 1/2

Length = x

Recall : Area of rectangle = Length * width

Area of kitchen = length * width

3 3/4 = x * 1 1/2

15 / 4 = x * 3/2

x = 15/4 ÷ 3/2

x = 15/4 * 2/3

x = 30/12 = 2 6/30

x = 2 1/5

EXPLAIN HOW TO PARTITION SHAPES (sorry for caps lock)

Answers

Answer:

Partition shapes is to create equal shares by partitioning one whole area into small same-size areas.

WILL MARK BRAINLIEST !!!
find the indicated value for each of the figures shown or described

Answers

Answer:

10. 9

In the first question we can solve using the Pythagorean theorem. It states that the hypotenuse in a right triangle or the longest side of the triangle, squared is equal to the other 2 sides, squared. Its expressed as so: C^2 = A^2 + b^2 where c is the hypotenuse and a and b are the other sides oft eh triangle.

Therefore,

15^2 = 12^2+x^2

225=144+x^2

81=x^2

x=9

__________________________________________________________

11. x=12

In this figure, there are 2 right triangles on the sides of the square. If we can find the lengths of the base of both triangles then we can find x using the Pythagorean theorem. the total base is 21 and the square is 11. 11+a+b=21. We can assume that both triangles are congruent and therefore we can solve this equation:

11+a+b=21

a+b=10

5+5=10

b=5

a=5

The bases of the two triangles are 5 and the hypotenuse is 13. Now we can solve using the Pythagorean theorem:

c^2 = a^2+b^2

13^2=5^2+x^2

169=25+x^2

144=x^2

144= 12 x 12

x=12

__________________________________________________________

12.

The diagnol of a triangle is the hypotenuse and since the length is the square root of 3, we have all the information we need.

c^2 = a^2+b^2

2^2 = (square root of 3)^2+b^2

4=3+b^2

1=b^2

b=1

Step-by-step explanation:

Expand and simplify 5(3x+2)-2(4x-1)

Answers

Answer:

15x+10-8x+2

7x+12

Step-by-step explanation:

Answer:

7  x  +  12

Step-by-step explanation:

pleaseee help me answer this!!! it is my last question help!!!

Answers

20° as they are alternate angles forming the Letter Z (from B to c, c to a, a to d)

Which number sentence is true?
A. -1/12 times 6/7 = -1/14
b. -1/12 times (-6/7)= -1/14
c. 1/12 times 6/7 = -1/14
d.1/12 times (-6/7) = 1/14

Answers

Answer:

We conclude that:

[tex]-\frac{1}{12}\cdot \frac{6}{7}=-\frac{1}{14}[/tex]

Hence, option (A) is true.

Step-by-step explanation:

Let us solve the expression

-1/12 times 6/7 = -1/14

Let us solve the L.H.S to check whether it becomes equal to R.H.S

[tex]-\frac{1}{12}\:\times \frac{6}{7}[/tex]

Factor the number: 12=6×2

[tex]-\frac{1}{6\cdot \:2}\cdot \frac{6}{7}[/tex]

Cross - cancel the common factor

[tex]-\frac{1}{2}\cdot \frac{1}{7}[/tex]

[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}[/tex]

[tex]-\frac{1\cdot \:1}{2\cdot \:7}[/tex]

Multiply the number: 7×2 = 14

[tex]-\frac{1}{14}[/tex]

Therefore, we conclude that:

[tex]-\frac{1}{12}\cdot \frac{6}{7}=-\frac{1}{14}[/tex]

Hence, option (A) is true.

Answer:

a

Step-by-step explanation:

12. You are at a carnival and you can spend no more than $15 on games. If you spent $8.75 already, how much money do you have left to spend? Write an inequality and solve.​

Answers

15-8.75= 7.25

That is the answer

8.75+x (less than or equal to sign) 15

8.75 is the amount you already spent
x is the amount you have left to spend
15 is the total number you can spend

4 • (2)3 equals???????

Answers

Answer:

24

Step-by-step explanation:

4*6=24

Given 2x (x + 1) - 3 (x + 1), what can be done to simplify for factoring?
A.
Subtract 2x.
B.
Factor out (x+ 1).
C.
Add 3.
D.
Multiply by (x + 1).

Answers

Answer:

Im not sure but i think its b

Find the measure of side JK

Answers

Answer:

In ΔIJK, the measure of ∠K=90°, JK = 90 feet, and KI = 54 feet. Find the measure of ∠I to the nearest tenth of a degree.

Step-by-step explanation:

In Louisville, 40% of the population is female and 60% are males. 36% of Louisville's population is under 18. The ratio of males to females who are under 18 is 2:1. If there are 1,176 males who are under 18, what is the population of females who are over 18.

Answers

Answer:

1411 females

Step-by-step explanation:

Given that:

Male population = 60%

Female population = 40%

36% of total population are under 18

Ratio of male to female under 18 = 2 : 1

Males under 18 = 1176

Females over 18 =?

The population of females under 18:

If males under 18 = 1176

Then female under 18 = 1176 / 2 = 588

Hence number of population under 18 = (1176 + 588) = 1764

1764 = 36% of the entire population

Hence, (100 - 36)% = 64% of the entire population are over 18

1764 = 0.36

x = 0.72

x = (0.72 * 1764) / 0.36

x = 3528

Hence, 40% of the population above 18 are female

0.4 * 3528 = 1411.2

= 1411 females are over 18

which is a mathematical property shown here
8(x+7)
1 commutative property
2 distributive property
3 identity of addition

Answers

it is distributive property. you would need to distribute the 8 onto the x and 7, making it 8x+56
Distributive property

-write each product using an exponent 6 x 6 =

Answers

6^2
An exponent describes a number being multiplied by itself. 6 * 6 is basically saying they’re are two sixes multiplied so 2 is the exponent (6 is the base)

The product is expressed as an exponent as 6 x 6 = 6².

Given data:

To write the product 6 x 6 using an exponent, we can express it as 6².

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

When we multiply a number by itself, we can represent the repeated multiplication using an exponent. In this case, we have 6 multiplied by 6, which is the same as saying 6 raised to the power of 2 (6²).

The exponent 2 indicates that we are multiplying 6 by itself 2 times.

Hence, the product 6 x 6 can be written as 6².

To learn more about exponents click :

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Jessica is looking at the blueprints for her new apartment. In the blueprints,
the length of the master bedroom is 2.5 inches. What is the actual length of
the master bedroom in feet?

Answers

Answer: 20 feet

Step-by-step explanation: you want to do 2.5 x 8

Can someone solve this problem with work please? :)

Answers

I hope the attachment over here helps!!!

Cookies are on sale! Today each cookie costs \$0.75$0.75dollar sign, 0, point, 75 less than the normal price. Right now if you buy 777 of them it will only cost you \$2.80$2.80dollar sign, 2, point, 80!Write an equation to determine the normal price of each cookie

Answers

Answer:

The equation to determine the normal price of each cookie is

7(x - 0.75) = 2.80

The normal price of each cookie = $1.15

Step-by-step explanation:

Let us represent the normal price of a cookie as : x

We are told that:

Today each cookie costs \$0.75less than the normal price.

The price of a cookie today is

x - 0.75

Right now if you buy 7 of them it will only cost you \$2.80$

Hence:

7(x - 0.75) = 2.80

Solving for x

7x - 5.25 = 2.80

7x = 2.80 + 5.25

7x = 8.05

x = 8.05/7

x = $1.15

The normal price of each cookie = $1.15

Answer:

$ 1.15

Step-by-step explanation:

7(c-0.75) = 2.80 is the equation

$1.15 is the total for C

I did this khan before and this is correct

Hope this helps!

;)

WILL MARK BRAINLIEST!!!! BRAINLIEST!
Write 206 in base 7

Answers

206 in base 7? jndjd

Answer:

104

Step-by-step explanation:

Complete the ratio table.

9 1
18 2
27 3
36
45 5

Answers

Answer:

9:1, 18:2, 27:3, 36:4, 45:5 or 1,2,3,4,5

Step-by-step explanation:

This is the answer because:

1) We can see that eah ratio is being multiplied with the next number. We can say this because 9 x 2 = 18 and 1 x 2 = 2 which is 18:2 just like that 9 x 3 = 27 and 1 x 3 = 3 which makes the ratio 27:3.

2) If we keep on doing this, 9 x 4 = 36 and 1 x 4 = 4 which makes the ratio 36:4.

Therefore, the answer is 4.

Hope this helps! :D

If the price is the same for each yard, how much money would 12 yards of fabric cost? $18.00 $21.00 $24.75 $26.25

Answers

Answer:

The answer is $21

Step-by-step explanation:

The amount of money for 12 yards of fabric is $ 21.00

Given data:

To determine the cost of 12 yards of fabric, we can use the information provided in the table. We observe that the cost of fabric increases linearly with the number of yards.

The table shows that 3 yards of fabric cost $5.25. To find the cost per yard, we divide the total cost by the number of yards:

$5.25 / 3 = $1.75

On simplifying the equation:

Now we can use this cost per yard to calculate the cost of 12 yards:

$1.75 × 12 = $21.00

Hence, 12 yards of fabric would cost $21.00.

To learn more about equations click :

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The complete question is attached below:

The table below shows the amount of money needed to buy certain amounts of fabric.Fabric Cost

Yards of Fabric

Total

Cost

3

$5.25

6

$10.50

9

$15.75

12

?

If the price is the same for each yard, how much money would 12 yards of fabric cost?

$18.00

$21.00

$24.75

$26.25

Evaluate this expression when x is 50

-6x+150

Answers

Plug in 50
-6(50) + 150
-300 + 150 = -150
The solution is -150

Answer:

-150

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Step-by-step explanation:

Step 1: Define

-6x + 150

x = 50

Step 2: Evaluate

Substitute in x:                    -6(50) + 150Multiply:                               -300 + 150Add:                                     -150

Graph the linear equation y= -1/2x-1

Answers

Answer:

thetht

Step-by-step explanation:jtejr

-3x + 1 – 3 – 6x what is the awnser

Answers

Answer:

-9x-2

Step-by-step explanation:

Answer:

-9x -2

Step-by-step explanation:

-3x + 1 – 3 – 6x

Combine like terms

-3x -6x  +1 -3

-9x -2

if A # B means the same thing as 2 A- B, then 1 # ( (2 # 3 ) # 4) equals:

Answers

By definition of #,

2 # 3 = 2•2 - 3 = 4 - 3 = 1

(2 # 3) # 4 = 1 # 4 = 2•1 - 4 = 2 - 4 = -2

1 # ((2 # 3) # 4) = 1 # (-2) = 2•1 - (-2) = 2 + 2 = 4

The 1 # ( (2 # 3 ) # 4) equals to 4.

Given that,

if A # B means the same thing as 2 A- B.

Based on the above information, the calculation is as follows:

By definition of #,

= 2 # 3

= 2(2) - 3

= 4 - 3

= 1

Now

=(2 # 3) # 4

= 1 # 4

= 2(1) - 4

= 2 - 4

= -2

Now

=1 # ((2 # 3) # 4)

= 1 # (-2)

= 2(1) - (-2)

= 2 + 2

= 4

Learn more: brainly.com/question/16911495

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