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

PLZ HELP ME Solve -2z – 5 > 3 for z.

Answers

Answer:

z<-4

Step-by-step explanation:

-2z-5>3

Add 5 to both sides.

-2z>8

Divide both sides by -2.

Z<-4

The sign must change because you are dividing by a negative.

find the square root of 5.494
[tex] \sqrt{5.494} [/tex]

Answers

Answer:

the square root of 5.494 is 2.34

Step-by-step explanation:

The computation of the square root of 5.494 is as follows"

According to the question it is mentioned that

The number is 5.494

Now the square root of the above number is

[tex]\sqrt{5.494}[/tex]

= 2.34

Hence, the square root of 5.494 is 2.34

Therefore the same is to be considered

Nadia is asked to find a number such that the difference between five times the number and three less than twice the number is equal to eighteen. Her work and answer are shown below. 5n−(3−2n)5n−3+2n7n−37nn=====181818213 Is Nadia correct? If not, identify and correct her error.

Answers

Answer:

Nadia is incorrect, please check explanations for the correction to her work

Step-by-step explanation:

Here, we want to validate the wok of Nadia

Let the number be n

5 times the number is 5 * n = 5n

Difference between 5n and 3 less than twice the number

3 less than twice the number is 2n-3

So it should be 2n-3 ;

The solution is thus;

5n - (2n-3) = 18

5n - 2n + 3 = 18

3n + 3 = 18

3n = 18-3

3n = 15

n = 15/3

n = 5

Answer:

Nadia is incorrect; she did not translate the given information into an equation properly. The first equation should be 5n−(2n−3)=18.

Step-by-step explanation:

help asap
short its an MCQ
If the diameter of 3 circles is in the ratio 4: 2: 1. The perimeter of the smallest circle is 8 cm. Then the area of
the shaded region is

Answers

Answer:

216[tex]\pi[/tex]

Step-by-step explanation:

Given the figure.

And the perimeter in the ratio 4: 2: 1.

Perimeter of smallest circle = [tex]8\pi[/tex]

To find:

Area of shaded region.

Solution:

To find the area, we need to have radius first.

And radius can be calculated by the given perimeter.

Formula for Perimeter is given as:

Perimeter = [tex]2\pi r[/tex]

[tex]8\pi = 2\pi r\\\Rightarrow r = 4\ cm[/tex]

Radius of smallest circle = 4 cm

Ratio of perimeter is equal to the ratio of the radii.

Radius of 2nd smallest circle by the given ratio = 8 cm

Radius of largest circle = 16 cm

Area of a circle is given the formula:

[tex]A = \pi r^2[/tex]

Area of the smallest circle = [tex]\pi 4^2 = 16\pi\ cm^2[/tex]

Area of the 2nd smallest circle = [tex]\pi 8^2 = 64\pi\ cm^2[/tex]

Area of the largest circle = [tex]\pi 16^2 = 256\pi\ cm^2[/tex]

Area of the shaded region = Area of largest circle + 2 [tex]\times[/tex] Area of 2nd smallest circle + 3 [tex]\times[/tex] Area of smallest circle - 2 [tex]\times[/tex] Area of smallest circle - 3 [tex]\times[/tex] Area of 2nd smallest circle

Area of the shaded region = Area of largest circle - Area of 2nd smallest circle + Area of smallest circle = [tex]256\pi - 64\pi +16\pi = 216\pi[/tex]

I’ll give brainliest pls help

Answers

Answer:

The slopes of WX and XZ

Step-by-step explanation:

The singular factor that determines if the parallelogram is a rectangle are the angles at the edges

Mathematically, we can only have a rectangle if there are four right angles with one right angle each at the edges of the rectangle

So, by having the slope of the sides forming the width and that which forms the length, we can deduce if what we have is rectangle given that the slopes will yield a perpendicular product

Hence, the slopes of WX and XZ can be calculated to show this

Jerry is a judge. he hears 5 cases every 2 3/8 hours how many cases does he haer per hour

Answers

Answer:

2 2/19

Step-by-step explanation:

5 cases in 2 3/8 hours

The unit rate of cases per hour is calculated by dividing the number of cases by the number of hours.

5/(2 3/8) = 5/(19/8) = 5 * 8/19 = 40/19 = 2 2/19

Answer:

2 2/19 cases per hour

Step-by-step explanation:

5 ÷ 2 3/8

~Turn the fraction on the left into an improper one

5 ÷ 19/8

~Copy Dot Flip

5/1 * 8/19

~Multiply

40/19 or 2 2/19

Best of Luck!

I only need the answer to the question. Thank you!

Answers

Answer:

10

Step-by-step explanation:

refer attachment for detailed answer

The sum of the digits of a two − digit number is 11. The unit's digit is 7 less than the ten's digit. Find the number.

Answers

Answer:

Number = 92

Step-by-step explanation:

Let the unit digit is x and that of tens digit is y.

ATQ,

x+y = 11 ....(1)

The unit's digit is 7 less than the ten's digit

x = y-7 ...(2)

Put the value of x from equation (2) in (1)

y-7+y = 11

2x-7 = 11

2x = 11+7

2x = 18

x = 9

Put the value of x in equation (1)

9+y = 11

y = 2

Hence, the number is 92.

Somebody solve this plzz

Answers

Answer:

Not a function

Step-by-step explanation:

If you use the line/ pencil test ***I think that's what it's called...

you put a pencil flat on the graph and if it touches more than one point, it is not a function. This only works with some graphs.But it works with this one.  

6x=3-12x
how can i solve it
please tell the answer in a simple way

Answers

Answer:

x=0.16

Step-by-step explanation:

helicopter is flying at an elevation of 450 feet. It is within sight of the landing pad and the pilot finds that the angle of depression to the landing pad is 16∘. Find the distance between a point on the ground directly below the helicopter and the landing pad. Round your answer to the nearest whole number.

Answers

Answer:

138 feets

Step-by-step explanation:

Given that :

Angle of depression (α) = 16°

Elevation = height = 450 feets

Appling trigonometry :

From the picture attached :

Height / elevation = 450 feets (Adjacent)

Distance = d (opposite)

Tan α = opposite / Adjacent

Tan 17 = d / 450

450 tan17 = d

450 * 0.3057306 = d

d = 137.57880

Hence, distance between a point on the ground directly below the helicopter and the landing pad 138 feets

The distance between a point on the ground directly below the helicopter and the landing pad is 129.03 feet.

Given that,

The helicopter is flying at an elevation of 450 feet.

It is within sight of the landing pad and the pilot finds that the angle of depression to the landing pad is 16∘.

We have to determine,

The distance between a point on the ground directly below the helicopter and the landing pad.

According to the question,

The angle of depression =  16°,

Elevation = height = 450 feet

And d is the distance,

The angle of depression is an important component used in trigonometric operations.

The angle of depression is formed when the observer stands on a ground higher than the object which he is trying to observe.

Therefore, The angle of depression is,

[tex]Tan16 = \dfrac{d}{450}\\\\0.28 = \dfrac{d}{450}\\\\d = 450 \times 0.28\\\\d = 129.03 \ feet[/tex]

Hence, The distance between a point on the ground directly below the helicopter and the landing pad is 129.03 feet.

To know more about Trigonometry click the link given below.

https://brainly.com/question/13760328

If the maximum height of the tunnel is the same as its maximum width, 9.8 meters, determine a quadratic model to represent the tunnel.

State a geometric model that could be used to represent a truck passing through the tunnel. ​

Answers

Answer:

TUNNEL:

f(x) = -2/4.9  [tex]x^{2}[/tex]  + 9.8

TRUCK:

Width (m) < 9.8

Height (m) <  -2/4.9 ( [tex]Width^{2}[/tex] /4 - [tex]4.9^{2}[/tex] )

Step-by-step explanation:

Please see attachment

If the maximum height of the tunnel is the same as its maximum width, 9.8 meters, The quadratic model to represent the tunnel will be f(x)= (-2/4.9)x²+9.8.

What is a quadratic function?

Any function of the form[tex]\rm f(x) =ax^2+bx+c[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.

It is given that, If the maximum height of the tunnel is the same as its maximum width, 9.8 meters.

We have to determine a quadratic model to represent the tunnel.

The quadratic function is formed as,

f(x) =K(x-x₁)(x-x₂)

x₁=width/2

x₁=9.8/2 = 4.9

x₂= -x₁ = -4.9

Substitute the obtained value as,

f(x) = K(x-4.9)(x-(-4.9))

f(x) =K(x²-4.9²)

f(0)=9.8

The value of K is obtained as a result,

K=-2×4.9/(4.9)²

K= -2/4.9

Substitute the value of K as,

f(x) = -2/4.9(x²-4.9²)

f(x) = (-2/4.9)x²+2×4.9

f(x)= (-2/4.9)x²+9.8

Thus, if the maximum height of the tunnel is the same as its maximum width, 9.8 meters, The quadratic model to represent the tunnel will be f(x)= (-2/4.9)x²+9.8.

Learn more about quadratic function here:

brainly.com/question/17177510

#SPJ2

What are the answers to these aswell mb?

Answers

Answer:

4 is D = 23

Step-by-step explanation:

the coefficient is the number before the letter

The three consecutive terms
of an exponential sequence are
the second third and sixth terms
of a linear sequence. Find the
common ratio
the exponential
sequence.​

Answers

Answer:

1

Step-by-step explanation:

The nth term of an exponential sequence is expressed as ar^n-1

The nth term of a linear sequence is expressed as Tn = a + (n-1)d

a is the first term

r is the common ratio

d is the common difference

n is the number of terms

Let the three consecutive terms  of an exponential sequence be a/r, a and ar

second term of a linear sequence = a +d

third term of a linear sequence = a + 2d

sixth term of a linear sequence = a + 5d

Now if the three consecutive terms  of an exponential sequence are  the second third and sixth terms  of a linear sequence, this is expressed as;

a/r = a + d ..... 1

a = a + 2d ..... 2

ar = a+ 5d .... 3

From 2: a = a + 2d

a-a= 2d

0 = 2d

d = 0/2

d = 0

Substitute d = 0 into equation 1:

From 1: a/r = a + d

a/r = a+0

a/r = a

Cross multiply

a = ar

a/a = r

1 = r

Rearrange

r = 1

Hence the common ratio of the exponential sequence is 1

 

 

which system of inequalities is shown in the graph​

Answers

Answer:

The system of inequalities shown in the graph is x ≤ 4 and y > 1C

Step-by-step explanation:

The equation of a vertical line is x = a, where a is the x-coordinate of any point on the lineThe equation of a horizontal line is y = b, where b is the y-coordinate of any point on the line

In the given figure, there are 2 lines, let us find the equations of them, then write the inequalities which represent the shaded areas

∵ The purple line is a vertical line

∵ It is cross the x-axis at the point (4, 0)

→ By using the first rule above

∴ The equation of the purple line is x = 4

∵ The purple line is solid and the shaded area left the line

∴ The sign inequality is ≤

The inequality of the purple area is x ≤ 4

∵ The blue line is a horizontal line

∵ It is cross the y-axis at the point (0, 1)

→ By using the second rule above

∴ The equation of the blue line is y = 1

∵ The blue line is dashed and the shaded area above the line

∴ The sign inequality is >

The inequality of the blue area is y > 1

The system of inequalities shown in the graph is x ≤ 4 and y > 1

A motorcycle can travel 70 miles per gallon. Approximately how many gallons of fuel will the motorcycle need to travel 60 km?

[1 mile = 1.6 km]
0.2
0.5
0.8
1.4

Answers

We have the following given
mileage = 70 miles per gallon
distance = 60 km

Required: amount of fuel in gallons

First, we must convert the distance to miles, so
60 km (1 mi/1.6 km) = 37.5 mi

So, the amount of fuel is
37.5 mi / (70 mi/gal) = 0.54 gallons

Answer:

Step-by-step explanation:

if our motorcycle use 70 miles per gallon

and 1mile=1.6 km

the motorcycle travels 70*1.6=112 km per gallon

for 60 km it needs

60/112=0.54 gallons

I’m having trouble with this

Answers

Answer:

24 or 25, because of the max height it can reach on the graph, its reaching the maximum height it can go

-

Which expression can be used to find 80% of 120?


80% of 120
20%
20%
20%
20%
20%



(0.8) (24)
(0.2) (120)
(0.8) (120)
(0.2) (24)

Answers

Answer:

96

Step-by-step explanation:

80÷100×120

96 ,, , ,; , ,

Answer:

(0.8) (120)

Step-by-step explanation:

[tex]80\% \: of \: 120\\\\ = \frac{80}{100} \times 120 \\ \\ = (0.8)(120)\\\\=96[/tex]

A technician makes $34,400 a year and
a computer programmer makes $46,500 a
year. How much more does a computer
programmer make a year compared to a
technician.

Answers

a computer programer is making 12,100 more dollars than the technichan.

Krystal purchases a total of $120. If a 4% sales tax is added on, how much will her total purchase cost?    ​

Answers

120x.04 =4.8
Add to original 120

Final answer $124.80
It would be $124.80 hope it helped

which of the following shows the length of the third side, in inches, of the triangle below?

Answers

Answer:

20 inches

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

Step 1: Identify Variables

Leg a = x

Leg b = 15

Hypotenuse c = 25

Step 2: Solve for x

Substitute [PT]:                    x² + 15² = 25²Isolate x term:                      x² = 25² - 15²Exponents:                           x² = 625 - 225Subtract:                               x² = 400Isolate x:                               x = 20

Answer:

20 inches

Step-by-step explanation:

Step 1: Understanding Pythagorean Theorem

The Pythagorean Theorem is [tex]a^{2} +b^{2}+c^{2}[/tex]. It is used to find the side lengths of a right triangle.

Step 2: Using the Theorem

We can see that the triangle shown is a right triangle and we know two sides so we can solve for the last side.

We can denote -

a - 15

b - unknown

c - 25

(note, c is always the hypotenuse or the longest side of the triangle)

We can plug in the numbers -

[tex]15^{2} +b^{2} =c^{2}[/tex]

[tex]225 +b^{2}=625[/tex]

[tex]b^{2} =625-225[/tex]

[tex]b^{2} =400[/tex]

[tex]b=20[/tex]

Kara’s bedroom is in the shape of a rectangle. The perimeter of her room is 50 feet. The width of her room is 12 feet. What is the length of Kara’s room?

A

13 feet


B

25 feet


C

26 feet


D

38 feet

Answers

Answer:

13

Step-by-step explanation:

Ok so we will eliminate some numbers first. The width is 12, but the total on the perimeter is 24. 50-24 = 26

26 is not the length, so divide that by 2, and get 13

Proof:

x=2

13x=26

12x=24

24+26 = 50

The equation below has one solution.

9x - 10 = 3x + 2

What is the solution to the equation?

–2
–1
1
2

Answers

the solution is 2
( x = 2 )

Answer:

x=2

Step-by-step explanation:

The cost of a dvd in dollars can be represented by the expression 18-d where d is the discount amount. Use the distributive property to write and simplify an expression for the cost of 3 dvds

Answers

Answer:

54 - 3d

Step-by-step explanation:

In order to find the cost of 3 DVDs we would simply need to multiply the expression given by 3. In order to do so we must use the distributive property and distribute the 3 to both the initial price of the dvd and the discount price, like so...

3(18 - d)  ... in order to distribute we multiply 3 by 18 and then by d seperately

(3 * 18) - (3 * d)

54 - 3d

That would leave us the expression 54 - 3d

The fraction 24/28 in simplest form is

Answers

Answer:

6/7

Step-by-step explanation:

greatest common factor: 4

24/4=6

28/4=7

Please can y'all help me asp
flying with the wind a plane went 396km/h. Flying into the wind the plane only went 350 km/h. Find the speed of the wind and the speed of the plane in still air.​

Answers

Answer:

/

Step-by-step explanation:

A pie shop sold a total of 208 pies one day. The pies were apple, cherry, and blueberry. The ratio
of apple pies sold to cherry pies sold to blueberry pies sold was 6:4:3. How many of each type
were sold?
Plss step by steppp

Answers

Answer:

96 apple pies, 64 cherry pies, and 48 blueberry pies.

Step-by-step explanation:

6 + 4 + 3 = 13, and 208 / 13 = 16. Now multiply each number in the ratio by 16, so 6 x 16 = 96, 4 x 16 = 64, and 3 x 16 = 48. You can check your answer by adding all 3 numbers and making sure it adds up to 208. Hope that helps

A culture of bacteria triples by the end of each hour. If there were initially 40 bacteria in a culture, how many bacteria should there be after 3 hours?

Answers

Answer:

There would be 1080 bacteria in the culture.

Step-by-step explanation:

Initial number of bacteria = 40

Given that

culture of bacteria triples by the end of each hour

Number of bacteria after 1 hour = 40*3 (multiplying initial number of bacteria by 3)

Number of bacteria after 1 hour = 120

number of bacteria after 2 hours = 3*Number of bacteria after 1 hour = 3*120

number of bacteria after 2 hours =360

number of bacteria after 3 hours = 3*Number of bacteria after 2 hour = 3*360 = 1080

Thus,

there would be 1080 bacteria in the culture.

Answer:

1080 bacteria

Step-by-step explanation:

What is the value of 0.15 divided by
0.05?​

Answers

Answer:

0.3

Step-by-step explanation:

The answer is actually 3

O A. yis all real numbers.
O B. y> 0
C. O sys 8
D. -65 x<6

Answers

Answer:

C. 0 ≤ y ≤ 8

General Formulas and Concepts:

Algebra I

Range is the set of y-values that are outputted by function f(x)

Step-by-step explanation:

According to the graph, we see that the line's y-value span from 0 to 8. Since both are closed dots, they are inclusive in the range:

[0, 8] or 0 ≤ y ≤ 8

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