Lucy is knitting a blanket and needs to buy some more yarn. at her local craft store, 2 skeins of yarn cost $7 and 8 skeins of yarn cost $28. what is the constant of proportionality in this direct variation?

Answer:

y =  -x + 7.

Step-by-step explanation:

General form:-

y = mx + c where m = slope. So:

y = x + 2 has a slope of 1.

The line perpendicular to it has slope -1/1 = -1

To find the required line we use the point-slope form with m = -1, x1 = 3 and y1 = 4.

y - y1 = m(x - x1)

y - 4 = -1(x - 3)

y - 4 = -x + 3

y =  -x + 7.

Answer:

The amount of air in a leaky tire.

Step-by-step explanation:

The plot shows a decrease with time (I'll assume the x axis is time).

Which of the answer options would one expect a decrease over time.

A leaky tire?  YES

Hair length with soda?  NO

Cost of a meal when adding appetizers?  NO

Answer:

a. the amount of air in a leaky bicycle tire as time increases.

Step-by-step explanation:

since the scatter plot is descending(y), then we can infer whatever is being recorded is decreasing as time goes on (x)

a. is a great example, as you have a leak in a bicycle tire the air will decrease.

b. does not make any rational sense, since soda does not affect an individual's hair length.

c. does not make sense since the plot is getting smaller over time, therefore adding prices (of said appetisers) makes the cost go up not down.

therefore your answer is a. the amount of air in a leaky bicycle tire as time increases.

hope this helps:)

Answer:

23 min 30 sec

Step-by-step explanation:

First, you add 35 + 14 + 18 + 27 which is 94.
Next, you divide 94 by the number of deliveries there were. Which is 4.
94/4 = 23.5.
So your answer would be 23 minutes and 30 seconds.

I Hope This Helped :D

Answer:

23.5 minutes or 23 minutes and 30 seconds

Step-by-step explanation:

1. add all the minutes

35 minutes + 14 minutes + 18 minutes+ 27 minutes = 94 minutes

2. Divide the total amount of minutes by the number of deliveries

94 minutes =  23.5 minutes or 23 minutes and 30 seconds

4 deliveries

Answer:

Money made by tickets=

2753 x $5 = $13765

We have to subtract the cost of the concert from the money made by tickets to get our profit. Therefore,

$13765 - $8000 = $5765

An isosceles right angled triangle has two equal sides, and those two equal sides make 90 degrees (right angle) internally. The correct option is A.

An isosceles right angled triangle has two equal sides, and those two equal sides make 90 degrees (right angle) internally.

Since the two of the angles of the triangle are equal, therefore, the length on the opposite sides of this angle will be equal to each other. Hence, we can write that the length of the side s will be equal to 4.

Hence, the correct option is A.

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Answer:

overlapping congruent triangles:

ΔACE ≅ ΔBCD

Proof:

given: AC ≅ BC, angle A ≅ angle B

angle ACB ≅ angle BCA by the reflexive property

ΔACE ≅ ΔBCD by the ASA triangle congruence property

The domain that makes sense in this context will be (0, 10].

The domain means all the possible values of x and the range means all the possible values of y.

James can hike f(n) miles after building up n days of stamina, subject to a maximum of 10 days.

Then the domain that makes sense in this context will be (0, 10].

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Answer:

C

Step-by-step explanation:

A quadratic has to have an exponent of 2 somewhere. The only one of these functions that does is C

The quadratic parent function is f ( x ) = x²

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

f ( x ) = x²

The graph of the function f(x) = x² is a parabola that opens upward, symmetric with respect to the y-axis, and its vertex is at the origin (0, 0)

Now , the value of y is the square of x

Hence , the parent function is f ( x ) = x² and graph is plotted

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Answer:

b is your answer

Step-by-step explanation:

Answer:

E.  5

Step-by-step explanation:

Let's rewrite the equation in the form of y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).

2x + y = 5

y = -2x+5

M, the slope, is -2

5, b, is the y-intercept

See attached graph.

The number of cubes needed to fill the rectangular prism 4608 cubes.

volume of rectangular prism = lwh

where

Therefore,

volume of the rectangular prism = 8 × 4 × 9 / 4 = 72 inches³

volume of the cube = l³

where

Therefore,

volume = (1 / 4)³

volume of the cube = 1  / 64 inches³

Therefore,

The number of cubes needed to fill the rectangular prism = 72 ÷ 1 / 64

The number of cubes needed to fill the rectangular prism = 72 × 64 = 4608

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Answer:

The product xy is constant, so the relationship is an inverse variation.

Step-by-step explanation:

Inverse variation is the mathematical relationship between two variables which can be expressed by an equation in which the product of two variables is equal to a constant.

inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases.

Here, the product xy is constant and gives the product as 960.

The relationship is inverse relationship.

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Step-by-step explanation:

Hi There! Let me help you :)

Known

[tex] = \frac{ {6}^{ - 10} }{ {6}^{ - 4} } [/tex]

[tex] \: [/tex]

Asked

Simplify form.

[tex] \: [/tex]

Answer

[tex] = \frac{ {6}^{ - 10} }{ {6}^{ - 4} } [/tex]

[tex] = {6}^{ - 10 - ( - 4)} [/tex]

[tex] = {6}^{ - 6} [/tex]

[tex] = {6}^{ - 6} \: \text{or} \: \frac{1}{ {6}^{6} } [/tex]

There are 2 answers, it's A and C.

The domain over which the bacteria population Increases is [tex]d \ge 3[/tex]

The function is given as;

[tex]d = \sqrt{5.2d - 15.6} + 2[/tex]

Set the radicand greater than or equal to 0

[tex]5.2d - 15.6 \ge 0[/tex]

Add 15.6 to both sides

[tex]5.2d \ge 15.6[/tex]

Divide both sides by 5.2

[tex]d \ge 3[/tex]

Hence, the domain over which the bacteria population Increases is [tex]d \ge 3[/tex]

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Answer:

150.04

Step-by-step explanation:

144.12

5.92

+ 150.04

Answer:

13/28

Step-by-step explanation:

using pemdas we can determine that the equation is directly solves from left to right

so

first

we have

3/8 + 1/8

which is 4/8

you can simplify this to 1/2

then you have 1/2 - 2/7

you must make them have the same numerator

you can multiple 1/2 by 7/7 and 2/7 by 2/2

7/14 - 4/14 = 3/14

now you must add 3/14 and 1/4

but you to make them have the same numerator

so you multiply 3/14 by 2/2 and 1/4 by 7/7

6/28 + 7/28 = 13/28

that is your final answer

Answer:

y=10

Step-by-step explanation:

Since this triangle has equal length sides, it is equilateral and also has equal measured angles. This means that each angle is 180/3=60 degrees.

To solve for y, we can do 5y+10=60. Simplifying, we get

5y=50

y=10.

Answer:

4

Step-by-step explanation:

So all the angles will have the same value. In a triangle all the angles will add up to 180, so each angle would have to be 60 degrees. So to know Y we need 6x+6=5y+10.  So subtract 10 from each side, then subtract 6x from each side to get 4=x

Let's take this problem step by step:

To find the ordered pair of the system:

⇒ must set both equations equal to each other

    ⇒ and solve for 'x'

Let's solve:

 [tex]x^2-2x+3=-2x+19\\x^2-2x+2x+3-19=0\\x^2-16=0\\(x+4)(x-4)=0[/tex]

Let's find the x-values:

   [tex](x-4)=0\\x=4\\\\(x+4)=0\\x=-4[/tex]

Let's find f(x)'s value for each 'x':

 [tex]x=4\\f(4)=-2(4)+19=-8+19=11\\\\x=-4\\f(-4)=-2(-4)+19=8+19=27[/tex]

Answer: (4, 11), (-4,27)

Hope that helps!

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Step-by-step explanation:

x | y

-2.| 13

-1. | 15

0. | 17

1. | 19

2. | 21

just start with the y-intercept and then add 2 or subtract two depending on whether your increasing x or decreasing x. as x increases 1 y increases 2.

Answer:

Answer:

Step-by-step explanation:

cost of 25 kg =262.50x25

                      =6562.5

The box plot that represents the data is the first option.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. The end of the first whisker represents the minimum number and the end of the second whisker represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

Minimum value = 30

Maximum value = 57

1st quartile = 1/4 (n + 1)

1/4 x 10 = 2.5th term = 35

Third quartile = 3/4 x (n + 1 )

3/4 x 10 = 7.5 term = 53

Median = 46

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The value of y will be -4 when the value of x is 4.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

The equation of the given condition will be given as:-

y = [tex]\dfrac{k }{x}[/tex]

At y = 8 when x = -2 so

8 = [tex]\dfrac{k}{-2}[/tex]

k = -16

The value of y at x = 4 will be calculated as:-

y = [tex]\dfrac{-16}{4}=-4[/tex]

Therefore the value of y will be -4 when the value of x is 4.

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Answer:

jackson sold 27 pounds of bananas and 12 pounds of grapes :D

Step-by-step explanation:

Taking into account the definition of a system of linear equations, the number of pounds of bananas and grapes sold are 36 and 16 respectively.

A set of two or more first-degree equations with two or more connected unknowns is referred to as a system of linear equations.

Finding the value of each unknown in order to satisfy all of the system's equations constitutes the process of solving an system of equations. To put it another way, it is necessary to find the values of the unknowns, as they must be replaced with values that, when used to solve the equations, is the process of solving a system of equations

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

x +y= 52

x + 2.25y= 72

There are several methods to solve a system of equations, it is decided to solve it using the graphical method. The system's equations are graphically represented by graphs in the graphical method. The solution of the system is the point of intersection between the graphs, since the coordinates of said point satisfy both equations.

Graphically, it can be seen that the intersection point is (36; 16). That is, the value of x is 36 and the value of y is 16.

Finally, the number of pounds of bananas sold are 36 and the number of pounds of grapes sold are 16.

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Answer:

y = 2x - 1

Step-by-step explanation:

Given equation: 2x - y = 1

We're being asked to solve for y. This is also known as the Slope-Intercept Form. It is represented by the following formula:

y = mx + b

where:

Steps:

1. Subtract 2x from both sides:

[tex]\sf 2x-2x - y = 1-2x\\\\\implies-y=-2x+1[/tex]

2. Divide both sides by -1:

[tex]\sf \dfrac{-y}{-1}=\dfrac{-2x+1}{-1}\\\\\implies y=2x-1[/tex]

This equation has a slope of 2, and a y-intercept of -1.

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A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of objects. The coordinates of c' are (a+4, b-1).

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

Let the coordinates of c be represented by (a,b). Now, if the shape x is translated by 4 units to the right and 1 unit down. Then, the coordinates of c' are:

c = (a, b)

c' = (a+4, b-1)

Hence, the coordinates of c' are (a+4, b-1).

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It is possible that a small sample size contributed to the 82% (±24%) estimate at a 95% confidence level.

A proportional confidence interval is provided by

[tex]\pi \pm z \sqrt{\frac{\pi (1-\pi )}{n} }[/tex]

Where π is the sample proportion, z is the critical value and n is the sample size.

The margin of error is represented by

[tex]z \sqrt{\frac{\pi (1-\pi )}{n} }[/tex]

As a result, smaller sample sizes result in wider margins of error. Option A has the greater margin of error in this scenario, so it most likely employed the smallest sample size.

Therefore we can conclude It is possible that a small sample size contributed to the 82% (±24%) estimate at a 95% confidence level. Option A is correct.

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Answer:

VQU =58°

Step-by-step explanation:

angle QUV is 61 because of F angles (I don't know what they call them in ur country)

triangle QUV is an isosceles triangles so base angles are the same

61+61=122

180-122=58

Answer:

The responses for the seniors are reversed.

Hope this helped!