y = x + 3
y = x² - 2x + 3

Answer: (y-(-43))=-7(x-6) and y=-7x-1

Step-by-step explanation:

1) Pick two points. I'll choose (3,-22) and (6,-43)

2) Next set it up in a rise-over-run function

-43 - (-22)

-------------

6    -  3

3) Solve

-21/3

-7

The slope is -7

4) Find the starting value.

You can do this by substituting two points in a slope-intercept equation(y=mx+b)

y=-7x+b

-22=-7(3)+b

-22= -21+b

-1=b

The starting value is -1.

5) Slope intercept form

We can put all the info together to find that the slope-intercept is:

y=-7x-1

6) Point-slope form:

Point slope form equation is this: y-y1=m(x-x1)

y1 and x1 are one of the points while keeping x and y as variables

So our final equation is (y-(-43))=-7(x-6)

Answer:

786

Step-by-step explanation:

Answer:

Helena',s savings... h=78+6

If the dining hall is located at (-12,6) and the stables are located at (20,6), then the dining hall is 32  units apart from the stables

The location of the dining hall = (-12,6)

The location of the stables = (20,6)

The distance between the two points d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Where d is the distance between the two points

[tex](x_1,y_1)[/tex] is the coordinates of the first point

[tex](x_2,y_2)[/tex] is the coordinates  of the second point

Substitute the values in the equation

d = [tex]\sqrt{20-(12))^2+(6-6)^2}[/tex]

= [tex]\sqrt{1024}[/tex]

= 32 units

Hence, if the dining hall is located at (-12,6) and the stables are located at (20,6), then the dining hall is 32  units apart from the stables

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In linear equation , 2,932.25 * ( 1.0316)¹²t = (1)t is value of t .

What are a definition and an example of a linear equation?

275000 = 3001 - ( 1 + 0.38/12)⁻¹²t/0.038/12

275000 = 3001 - ( 1 + 0.38/12)⁻¹²t/0.0025

275000 * 0.0025 = 3001 - ( 1 + 0.38/12)⁻¹²t

 68.75 = 3001 - ( 1 + 0.38/12)⁻¹²t

3001 - 68.75 =  ( 1 + 0.38/12)⁻¹²t

2,932.25 = ( 1 + 0.0316)⁻¹²t

2,932.25 = ( 1.0316)⁻¹²t

2,932.25 = 1/ ( 1.0316)¹²t

2,932.25 * ( 1.0316)¹²t = (1)t

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The length of the each side of the square garden of Jessica is found as 10.77 ft.

For the given question,

Jessica is making a square garden in her backyard.

The compost bought is to cover the area of the 116 ft².

The formula for the area is given as;

A = s² , where s is the length of the side of the square.

Put the values.

116 = s²

Taking square root both side.

s = √116

s = 10.77

Thus, the length of the each side of the square garden of Jessica is found as 10.77 ft.

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Answer:

Step-by-step explanation:

Aryon is left with $9.25 of money after he has paid for his lunch.

According to the question,

We have the following details:

Total amount Aryon has = $20

The cost of 1 coke = $1.50

So, the cost of 2 cokes = $(2*1.50)

The cost of 2 cokes = $3

The cost of a sandwich = $5.50

The cost of a bag of chips = $2.25

So, the total cost of all the materials = the cost of 2 cokes + the cost of a sandwich + the cost of a bag of chips

The total cost of all materials = $(3+5.50+2.25)

The total cost of all materials = $10.75

Now, the money Aryon has = Total money he has - the total cost of all materials

The money Aryon is left with = $(20-10.75)

The money Aryon is left with = $9.25

Hence, the money Aryon is left with is $9.25.

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Chords and arcs

YM is the chord of the circle and it has a length of 12 in

The perpendicular VL bisects the chord in V.

To prove the above statement, please note that triangles VYL and VLM are similar because they have one side in common and the second side of the same length (the radius of the circle).

Let's work with any of those triangles, for example, VLY. It's a right triangle in V. The hypotenuse of the triangle is the radius, one leg is the given distance of 5 in and the other leg is half the length of the chord (6 in).

Thus, applying Pythagora's Theorem:

Thus, the radius is

r=7.8 in

Option b.

The two rectangles that is R3 and R4 have the greatest difference in the area.

How to calculate the area of the rectangle?

In mathematics, the rectangle is a closed polygon shape which has four vertex as well as four sides. And the opposite side are parallel to each other. To calculate the area, multiply the length and breadth. Similarly, for the perimeter means add all the sides.

According to the question, the given data in the form of the area of the rectangle is as follows:

Area of Rectangle1 = 60.81 square centimeters

Area of Rectangle2 = 61.44 square centimeters

Area of Rectangle3 = 35.52 square centimeters

Area of Rectangle4 = 47.88 square centimeters

Now, to calculate the greatest difference in the area of the rectangles:

Difference(Rect2 - Rect1) = 61.44 - 60.81 = 0.63

Difference(Rect1 - Rect3) = 60.81 - 35.52 = 25.29

Difference(Rect1 - Rect4) = 60.81 - 47.88 = 12.93

Therefore, the two rectangles that is R3 and R4 have the greatest difference in the area.

And the differences are as follows:

Area(Rect1 - Rect3) = 60.81 - 35.52 = 25.29 square centimeters

Area(Rect1 - Rect4) = 60.81 - 47.88 = 12.93square centimeters

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$134 is the amount paid by grandparents every month.

Percentage as the name suggests is a ratio of some particles to 100. In order to get the value of the required amount one has to divide the value by 100.

It is given that the  tuition fee is $180 per week = $720 per month

It is also provided that she receives an honour rule of $50 per month.

So, her fees per month is $720- $50= $670.

It is given that 20% of the fees is paid by grandparents.

So, percentage share = 20% of $670 =20/100 x $ 670 = $134

So, $134 is paid by the grandparents every month.

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Based on the mathematical statement, the unit rate is 3/4 books per hour

The mathematical statement is given as

"rewrite 1/4 book 1/3hour as a unit rate"

The above means that

Book = 1/4

Time = 1/3 hour

The unit rate is then calculated as

Unit rate = Book/Time

Substitute the known values in the above equation

So, we have the following equation

Unit rate = (1/4)/(1/3)

Evaluate

Unit rate = 3/4

Hence, the solution is 3/4 books per hour

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Answer:the 2nd choice

Step-by-step explanation:

Please find attached the dilated image of triangle ΔXYZ obtained by using a scale factor of 1.5, with the center of dilation at (0, 0), giving the coordinates of the vertices at the points X'(-6, 3), Y'(9, 0) and Z'(-3, -6).

A dilation transformation is one in which the lengths of a figure are scaled up or down.

From a similar question online, we have:

The vertices of the triangle ΔXYZ are: X(-4, 2), Y(6, 0), and Z(-2, -4)

The given center of dilation is (0, 0)

The scale factor of the dilation is 1.5

The coordinates of the points on the image following a dilation of the point (x, y) by a scale factor of k about the origin is given by the formula:

(x, y) [tex]\underrightarrow{R_k}[/tex] (k·x, k·y)

Therefore, the coordinates of the vertices of the image of the triangle ΔXYZ following a dilation by a scale factor of 1.5 are:

X(-4, 2) [tex]\underrightarrow{R_k}[/tex] X'(1.5×(-4), 1.5×2) = X'(-6, 3)

Y(6, 0) [tex]\underrightarrow{R_k}[/tex] Y'(1.5×6, 1.5×0) = Y'(9, 0)

Z(-2, -4) [tex]\underrightarrow{R_k}[/tex] (1.5×(-2), 1.5×(-4)) = (-3, -6)

The vertices of the dilated image of ΔXYZ, which is ΔX'Y'Z' are; X'(-6, 3), Y'(9, 0), Z'(-3, -6)

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The solution to given inequality 12 > w + 3 is w < 9

In this question, we have been given an inequality 12 > w + 3

We need to solve the inequality for w.

Consider given inequality,

12 > w + 3                              ............(Given)

12 - 3 > w + 3 - 3                    ...........(Subtract 3 from each side)

9 > w

This means, w is less than 9.

Therefore, the solution to given inequality 12 > w + 3 is w < 9

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Based on the reflexive property of congruency, the other pair of sides that we know are congruent is: 1. QS = SQ.

The reflexive property of congruency states that a line will always be a congruent to itself. This means it will always be equal in measure to itself.

In the diagram given showing triangle QSP and triangle SQR, we are given that sides PQ and RS are congruent so also are angles PQS and RSQ.

However, we can also see that both triangles share a common side, side QS. Therefore, side QS is congruent to side SQ by the reflexive property of congruency.

This implies that another pair of sides would be: 1. QS = SQ.

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Rafael is fertilizing his garden. The garden is in the shape of a rectangle. Its length is 16 feet and its width is 13 feet. Suppose each bag of fertilizer covers 26 square feet. How many bags will he need to cover the garden?​

step 1

Find the area of the garden

Remember that the area of a rectangle is equal to

A=L*W

we have

L=16 ft

W=13 ft

substitute

A=16*13

A=208 ft^2

step 2

we know that

each bag of fertilizer covers 26 square feet

so

Applying proportion

1/26=x/208

solve for x

x ----> number of bags

x=(1/26)*208

x=8 bags

therefore

The surface and of the cone is

The volume of the cone is

What is a cone?

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.

We are given that radius of the cone as 5yd and slant height as 13yd

We first find the height using pythagoras theorem

Let height be h

by Pythagoras theorem we have

[tex]r^{2}+h^{2}=13^2\\ 5^2+h^2=169\\ h^2=144\\h=12[/tex]

Height of the cone is 12yds

Now volume of the cone is given by

[tex]V=[/tex]π[tex]r^{2}\frac{h}{3}[/tex]

Substituting the values in the equation we get

[tex]V=100[/tex]π yd^3

Now we find the surface area

The formula for surface area is

[tex]A=r(r+\sqrt{r^2+h^2} )[/tex]π

Substituting the values in the equation we get

[tex]A=90[/tex]π yd^2

Hence the surface area of the cone is 90π yd^2

And the volume of the cone is 100π yd^3

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The credit hours that a student has to take for the two tuition costs to be equal is A. 250 + 200h = 300 + 180h

From the information, the tuition costs, C, for a local community college are modeled by C(h) = 250 + 200h

h = the number of credit hours taken.

The local state university has tuition costs, S, modeled by the function S(h) = 300 + 180h.

Therefore, the credit hours that a student have to take for the two tuition costs to be equal will be:

250 + 200h = 300 + 180h

200h - 180h = 300 - 250

20h = 250

h = 250/20

h = 12.5 hours.

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By converting to slope-intercept form to graph and solving this equation we are get -x/2 +2

What is slope intercept ?

The slope indicates the steepness of a line and the intercept indicates to the  location where it intersects are in an axis. The slope and that the  intercept define to  the linear relationship between the two variables, and can be the used to the estimate an average rate of change.

The slope, m, represents the steepness of a line. The slope of the line is also the  termed as gradient, sometimes .and  the y-intercept, b, of a line, represents the  y-coordinate of the point to where the graph of the line intersects the y-axis.

Sol-

Re write 2x+4y=8 in slope intercept form we are get-

y= -x/2+2

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Answer:

1a. 4/6

1b. 6/9

1c. 8/12

2. [tex] \frac{6}{12} [/tex]

3. 8/16

Step-by-step explanation:

1a. Multiply top and bottom value by 2

1b.multiply top and bottom value by 3

1c. multiply top and bottom value by 4

2.To get your denominator to twelve you multiply it by 2. and if you multiply by two at the bottom you also multiply by two on top.

3.to get your denominator to 16 multiply the denominator by 8. If you multiply the bottom you should multiply the top with the same value as well.

Answer: The answer is A) There are no solutions to the system because the equations represent parallel lines.

Step-by-step explanation: got it on edge 2022

Answer:

There are no solutions to the system because the equations represent parallel lines

Step-by-step explanation:

Answer:

I am 99% certain that the answer is c. because it has defiantly been reflected. and if you look at the points in order for them to be moved like that it would have had to have been rotated first.

hope this helped!

The value of the expression |-10+6|-|3²-5| = 0

The expression given is |-10+6|-|3²-5|.

This contains absolute value which needs to be evaluated.

We will go through the definition of absolute value.

Absolute value for x = x, when x is a positive integer.

i.e., |x| = x, when x >0

Absolute value of (-x) = x, when -x is a negative integer.

So absolute value always gives the positive value of the number inside it.

Now |-10+6|-|3²-5| = |-4| - |9-5|

                              = 4 - |4|    [Since |-4| = 4]

                              = 4 - 4      [Since |4| = 4]

                              = 0.

So the value of the expression |-10+6|-|3²-5| = 0

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"y is a function of x." The input value, or independent variable, is represented by the letter x. The dependent variable or output value is denoted by the letter y, or f(x).

f(x) = 2x + 5.

f(x+3) = 2(x+3) + 5.

f(x+3) = 2x + 11.

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The number of gigabytes that Mayerlin can use while staying within her budget is 5.

The first step is to determine the appropriate inequality sign to use. Here are the inequality signs:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The sign that would be used is <

The form of the inequality is:

flat cost + (cost per gigabyte x number of gigabytes) < total budget

$55 + $5x < $70

5x < $70 - $55

5x < 25

x < 25 / 5

x = 5

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Answer:dsa

Step-by-step explanation:

sadfdfsaf

The value of the Constant of Proportionality will be $2.19.

In the given question, it is stated that 3 pounds of grapes cost $6.57. We have to calculate and find out the Constant of Proportionality.

The constant of Proportionality is a constant term in the equation that does not vary and has a fixed value that represents a certain quantity in a given situation.

Here, we know that 3pounds cost $6.57. Taking:

y = Total Cost

x = Number of Pounds

c = Constant of Proportionality

We get the equation to represent the Total cost with respect to the number of pounds where c will be the proportionality constant which defines the unit price of a pound. The equation will be:

=> y = c*x

=> 6.57 = 3c

=> c = 2.19

Hence, we get the Constant of Proportionality $2.19

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Answer:

26 total questions

Step-by-step explanation:

6 * 2 = 12

7 * 2 = 14

14 + 12 = 26