What is the equation of the line that passes through the points (-4, -6) and (2, 8)

Answers

Answer 1

The equation of a line is the mathematical function of a line thus the equation of the line that passes through the points (-4, -6) and (2, 8) will be y = (14/6)x + 10/3.

What is the equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

A linear equation or function is given as ;

y = mx + c

Here, m is the slope and is given as (y₂ - y₁)/(x₂ - x₁).

The slope of the line passing through (-4, -6) and (2, 8) will be,

m = (8 + 6)/(2 + 4)

m = 14/6

So, y = (14/6)x + c

Substitute,  (2, 8)

8 =  (14/6)2 + c

c = 8 - 14/3 = 10/3

Therefore, y = (14/6)x + 10/3

Hence "The equation of a line is the mathematical function of a line thus the equation of the line that passes through the points (-4, -6) and (2, 8) will be y = (14/6)x + 10/3".

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Related Questions

Solve the following equation for y. 3y - 7(y + 5) = y - 35 Also Show your work Describe and show each step taken.


A. y = 0

B. y = 1

C. y = 2

D. All real values for y are correct solutions.

Answers

The equation is,

→ 3y - 7(y + 5) = y - 35

Now the value of y will be,

→ 3y - 7(y + 5) = y - 35

→ 3y - 7y - 35 = y - 35

→ -4y - y = -35 + 35

→ -5y = 0

→ y = 0/-5

→ [ y = 0 ]

Hence, option (a) is correct.

Reflect the figure over the line y=1/3x+1

Answers

Answer:

  see the attachment

Step-by-step explanation:

You want a graph of the given figure reflected over the line y = 1/3x +1.

Line of reflection

The given line of reflection can be written in general form as ...

  y = 1/3x +1

  3y = x +3 . . . . . . multiply by 3

  x -3y +3 = 0 . . . . subtract 3y

This is in the general form ...

  ax +by +c = 0

where a=1, b=-3, c=3.

The line of reflection is the perpendicular bisector of the segment joining a point (x, y) with its reflection (x', y').

Reflected point

Using the formula in the second attachment, we find the reflection

  (x1, y1) ⇒ (x, y)

satisfies ...

  (x -x1)/a = (y -y1)/b = -2(ax1 +by1 +c)/(a² +b²)

or ...

  x = -2a/(a²+b²)·(ax1 +by1 +c) +x1

  y = -2b/(a²+b²)·(ax1 +by1 +c) +y1

Using the known values for a, b, c, we have ...

  x = -2(1)/(1² +(-3)²)·(x1 -3y1 +3) +x1 = (1/5)(4x1 +3y1  -3)

  y = -2(-3)/10·(x1 -3y1 +3) +y1 = (1/5)(3x1 -4y1 +9)

Rewriting the mapping in more conventional terms, we have ...

  (x, y) ⇒ ((4x +3y -3)/5, (3x -4y +9)/5)

It is convenient to let a spreadsheet do the repetitive tedious math. The third attachment shows the application of this mapping to the coordinates of the figure's vertices (clockwise from bottom).

__

Additional comment

The figure showing the reflected polygon was created by a geometry program using its "reflect over a line" feature.

15x+12=13x-15

…….?????

Answers

Answer:

x_6x=21_15_3x/. x+6x=21+15+3x

Step-by-step explanation:

Each page of a top-secret report on aliens requires 2 \text{ KB}2 KB2, start text, space, K, B, end text of space in digital format.
What is the maximum number of pages the report can have so that it can be completely stored on a USB drive that holds 4 \cdot 10^6 \text{ KB}4⋅10
6
KB4, dot, 10, start superscript, 6, end superscript, start text, space, K, B, end text?
Write your answer in scientific notation, and round to one decimal place.

Answers

The maximum number of pages the report can have, using scientific notation, is of:

2 x 10^6.

What is scientific notation?

A number in scientific notation is written as follows:

[tex]a \times 10^b[/tex]

With the base symbolized [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1.

For this problem, the maximum number of pages that the report can have is given by the following division:

Maximum number of pages = Total capacity/Size of page.

These variables, from the text, are given as follows:

Total capacity: 4 x 10^6 KB.Size of a page: 2 KB / page.

Hence the number of pages is obtained as follows:

Maximum number of pages = 4 x 10^6 KB / (2 KB/ page) = 2 x 10^6 pages.

When two numbers are divided in scientific notation, the bases are divided(4/2 = 2), while the exponents are subtracted (6 - 0 = 6).

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A 5-kilogram bag of cat food costs $14.85. What is the unit price?

Answers

Answer:

I believe the unit price would be $2.97

Step-by-step explanation:

Hope this helps! :))
Please let me know if its incorrect.

his table shows the ratio of the number of people to the number of pizzas needed. A 2-column table has 4 rows. Column 1 is labeled People with entries 5, 10, 15, 20. Column 2 is labeled Pizzas with entries 2, 4, 6, 8. Complete the statement about the equivalent ratios shown in this table. When the number of people is multiplied by 4, the number of pizzas is multiplied by .

Answers

When the number of people is multiplied by 4, the number of pizzas is multiplied by 4.

What is a ratio?

A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

What is a proportion?

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

Mathematically, a proportional relationship can be modeled by the following mathematical expression:

y = kx

Where:

x represents the number of people.y represents the number of pizzas needed.k represents the constant of proportionality.

If the x-value is multiplied by 4, we have:

x = 5 × 4

x = 20

From the corresponding y-value for 20 is equal to 8 and as such the number of pizzas needed should be multiplied by 4, in order to produce an equivalent ratio.

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How to solve and answer for IXLs

Answers

Answer: r = 77.3 degrees

Step-by-step explanation:

-Add both numbers together.

- 46.2

+ 31.1

= 77.3

-That is the value of "r".

Find the area of the circle. Give your answer to two decimal places . Please show work

Answers

Answer:

1256.64

Step-by-step explanation:

what is the probability that a positive integer not exceeding 100 selected at random is divisible by 5 or 7

Answers

Answer:

So, the probability of selecting a number from 1 to 100 that is divisible by 5 or 7 is 0.32.

Hope this helped!

The following sets of ordered pairs represent relations from the set X to the set Y. Which one is a function?

A (3, 4), (3, 5), (3, 6), (3, 7)
B (2, 5), (2, 8), (3, 7), (3, 9)
C (1, -1), (0, 0), (1, 1), (4, 2)
D (0, 0), (1, 1), (4, 2), (9, 3)

Answers

The set of ordered pairs that is a function is (d) (0, 0), (1, 1), (4, 2), (9, 3)

How to determine the ordered pair that is a function?

The list of options represents the given parameter

As a general rule, for an ordered pair to be a function;

The y values on the ordered pair must point to different x values

In (a) the y values 4, 5, 6 and 7 have the same x value of 3

So, it is not a function

In (b) the y values 5 and 8 have the same x value of 2

So, it is not a function

In (c) the y values -1 and 1 have the same x value of 1

So, it is not a function

In (d) all the y values have different x values

So, it is a function

Hence, the ordered pair that is a function is  (d)

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the radius of a sphere is increasing at a rate of 4 mm/s. how fast is the volume increasing (in mm3/s) when the diameter is 80 mm? (round your answer to two decimal places.)

Answers

Increase in volume is 802424.77 cubic mm/s when the diameter is 80 mm.

Let the radius of the sphere be R.

So, the volume of the sphere is given by,

V = [tex]\frac{4}{3}\pi r^3[/tex]

Differentiating the above relation with respect to time 't' we get,

dV/dt = 4[tex]\pi r^2[/tex]. dr/dt

Given that, the change of radius (dr/dt) = 4 mm/s

When the diameter is 80 mm, then the radius = 80/2 = 40 mm

So the volume change when the diameter is 80 mm is given by,

dV/dt [tex]=4\pi\times40^2\times4\approx 802424.77[/tex] cubic mm/s

Hence the volume increase in 802424.77 cubic mm/s.

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I need to find the equation for y=
For the format f(x)=|x|.

Answers

Answer:

[tex]f(x)=-|2x|[/tex]

Step-by-step explanation:

First, find the slope of the right side of the graph. It is -2. But because an absolute value always makes the value inside positive, we put the negative sign outside the absolute value.

The rule of thumb for absolute value graphs is: if it opens upwards, the absolute value is positive; if it opens downwards, the absolute value is negative.

So, the equation we can construct from this information is:

[tex]f(x)=-|2x|[/tex]

Dominic needs a new bike mirror. His old mirror was a square with a side length of 9 cm. He wants the new mirror to have an area as close as possible to his old bike mirror.
Which circular bike mirror should Dominic buy? Answer Choices: 8 cm , 7 cm , and 6 cm Answer ASAP FOR Brainlist.

Answers

Answer:

6 cm

Step-by-step explanation:

The circular mirror Dominic should buy is the mirror with a side length of

8 cm.

Option A is the correct answer.

What is a square?

A Square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is given as side².

We have,

Old mirror.

Side = 9 cm

Area = 9 x 9 = 81 cm²

New mirror.

Side = 8 cm

Area = 64 cm²

Side = 7 cm

Area = 7 x 7 = 49 cm²

Side = 6 cm

Area = 6 x 6 = 36 cm²

64 cm² is closer to 81 cm².

Thus,

A circular mirror with a side length of 8 cm should be bought.

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mike has 40 coins consisting of dimes and quarters. if the dimes were quarters and the quarters dimes he would have 90 cents more. how many quarters does he have?

Answers

In the word problem, if mike has 40 coins consisting of dimes and quarters and if the dimes were quarters and the quarters dimes, he would have 90 cents more, he has 17 quarters.

A word problem refers to a mathematical exercise where significant information on the problem is given in ordinary language and not mathematical notation.  Let x be the number of dimes (10 cents) and y be the number of quarters (25 cents). Hence, the total number of coins is:

x + y = 40

The amount of the total coins would be 0.1x + 0.25y.

If the dimes were quarters and quarters were dimes, he would have 90 cents more than the amount he has now.

Hence,

0.25x + 0.10y = 0.1x + 0.25y + 0.9

Solving,

0.25x – 0.1x = 0.25y – 0.1y +0.9

0.15x = 0.15y + 0.9

As x + y = 40, x = 40 – y

Substituting,

0.15 (40 – y) = 0.15y + 0.9

6 - 0.15 y = 0.15y + 0.9

0.15y + 0.15y = 6 – 0.9

0.3y = 5.1

y = 5.1/0.3 = 17

Hence, the number of quarters are 17.

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If x =-5, what is the value of 2x^+6x

Answers

2x^2+6x

2(-5)^2+6(-5)

2(25)+6(-5)

50+6(-5)

50+(-30)

50-30

20

3. Suppose that your calculator does not have a square root key. How could you still use your calculator to determine √144?

Answers

Answer

12

Step-by-step explanation:

click on square root

click on 144

then your answer will pop out below your equation

A football team loses 4 yards on each of 9 consecutive plays. Find the total change in yards from where the team started.

Answers

The total change in yards where the team started is 36 yards

How to determine the total change in yards?

The given parameters in the question are:

Yards per play = 4 yards

Number of plays = 9 consecutive plays

The total change in yards is the amount of yard per play multiplied by the number of plays

This is represented as

Total change = Yards per play * Number of plays

Substitute the known values in the above equation So, we have the following equation

Total change = 4 * 9

Evaluate

Total change = 36

Hence, the total change is 36 yards

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The length of a rectangle is twice its width.
If the perimeter of the rectangle is 42 in, find its length and width.

Answers

Answer: Width = 7 inches, Length = 14 inches

Step-by-step explanation:

Let the width be [tex]w[/tex]. Then, the length is [tex]2w[/tex].

Using the formula for the perimeter of a rectangle,

[tex]2(w+2w)=42\\\\w+2w=21\\\\3w=21\\\\w=7\\\\\implies 2w=14[/tex]

Given mn, find the value of x.
+
(8x-4)°
(6x-12)°

Answers

Answer:

The value of the equation will be 14

you are a contestant in a quiz show, answering a series of questions. you answer correctly with probability p, or incorrectly with proabaility q; you get $1 for every correct answer, and you are eliminated when you first give two consecutive wrong answers. the questions are indepdent. find the expecred number of questions you attempt, and your expecred total prize moeny

Answers

The expected total prize money is $2p/q.

Given that,

You participate as a participant in a game show and respond to questions. You receive $1 for each correct response, and you are disqualified if you first provide two consecutive inaccurate answers. You can answer properly with probability p or wrongly with probability q. Each question stands alone.

Let,

The probability of correctly answering a question is = p

The probability of incorrectly answering a question is = q

The number of failures after which you are eliminated is = 2

Let r = 2 =  No. of failures and

Let q = The probability of failure in a single question

Now, the number of questions that you will attempt will follow a negative binomial distribution whose parameters are r and q.

The expected value of a negative binomial distribution is given by

E[X] = r/q

So, the expected number of questions that you will attempt is = r/q = 2/q

Out of 2/q questions, the expected number of correct questions is = 2p/q

So, the expected total prize money is $2p/q.

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Please help me!!!!!!!!

Answers

277 bc 14 times 18 plus 25 is 277

A pediatrician prescribes 5 milliliters (ml) of a pain reliever for every 25 pounds of a child's weight. How many milliliters of
medicine will the doctor prescribe for a child who weighs 60 pounds?

Answers

If the child's weight is 60 pounds , then the doctor will prescribe 12 milliliter of medicine .

In the question, '

it is given that

the for every 25 pounds of weight 5 milliliter of pain reliever is required .

we need to find the amount of medicine for the child weighing 60 pounds

So , for 25 pounds =  5 milliliter is needed

for 1 pound = 5/25 ml is needed

hence for 60 pound = 60*(5/25) ml will be prescribed .

on simplifying further ,

we get

= 60*(5/25)

= 60*(1/5)

= 12 ml

Therefore , the doctor will prescribe 12 ml of medicines .

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Pls help due tomorrow!!!!!!!

Answers

We have : (a+b)^2 = a^2 + 2ab + b^2.

So, we can see here : the first term (3x) is a, the second term (a) is b.


For it to be expanded as such, the second term in the bracket must be equal to a^2 when it is squared.

Therefore, the missing term is a.

Recheck : (3x + a)^2 = (3x)^2 + 2.3x.a + a^2 = 9x^2 + 6ax + a^2.

The table shows the side
lengths and perimeters of
regular hexagons. Is the
relationship between the
perimeter and the side
length of the hexagons
proportional? Explain.

Answers

The relationship between the perimeter and the side length of the hexagons is proportional.

What is a proportional relationship?

A proportional relationship is one that illustrates the constant between the data that are given.

In this case, when the side length is 2, the perimeter is 12. The constant is:

= Perimeter / Length

= 12 / 2

= 6

Also, when the length is 3, the perimeter is 18. The constant will be:

= 18 / 3

= 6

Since they have 6 as constant, it's a proportional relationship.

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Determine the length of the line segment shown. line segment from negative 5 comma 5 to 3 comma negative 1 6 units 8 units 10 units 36 units
fist gets brainlyist and 35 points please help asap

Answers

The length of the line segment with points (-5, 5) (3, -1) is 10 units

How to find length of line

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points  (-5, 5) and (3, -1) is calculated as follows

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

d =√{(-5 - 3)² + (5 - -1)²}

d =√{64 + 36}

d = √100

d = 10 units

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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

maximum height = 32ft

Given function  h(t) = -16t^2+40t+7

known data:

[tex]h{0}[/tex] = 7 ft

[tex]v_{0}[/tex] = 40 ft/s

we equate the first derivation to zero

and solve for time.

h(t) = -16t^2 + 40t+7

[tex]\frac{dh}{dt} (t)[/tex] = -32t+40 = 0

t = [tex]\frac{40}{32}[/tex] = 1.25s

second derivative and evaluate:

[tex]\frac{d^{2}h}{dt^{2}}[/tex] [tex]\frac{}{}(t)[/tex] = -32

the maximum height of the rocket with the respect to

the ground can be obtained by evaluating the function

h(1.25) = - 16[tex](1.25)^{2}[/tex]+40(1.25)+7 = 32 ft

therefore the rocket reaches maximum height at  h = 32ft.

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p x 3,700=4,070
There was a % percent increase in the number of visitors.

Answers

There was 110%  percent increase in the number of visitors.

Percent:

Basically, percentage refers the number or ratio that can be expressed as a fraction of 100.

Given,

p x 3,700=4,070

There was a % percent increase in the number of visitors.

Here we need to find the increase in the percentage.

While we looking into the given question we have identified that,

The Old population = 3700

And the new population  = 4070

So, the value of P is calculated as,

=> p = 4070/3700

=> p = 1.1

When we convert this into percent then we get 110% as increase.

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TWO FRIENDS EARNED MORE THAN
$400 SELLING T-SHIRTS. THEY
PAID THEIR PARENTS $55 FOR
SUPPLIES AND DIVIDED THE REST
OF THE MONEY EQUALLY. WRITE AN
INEQUALITY TO FIND POSSIBLE
AMOUNTS EACH FRIEND EARNED.

Answers

what he said!!!!!!!!!!!! ^^^^^^^^

Graph the line that passes through the points (9,2) and (3,4) and determine the equation of the line ( I need it with graph)

Answers

The equation of the line that passes through the points  (9,2) and (3,4) is x + 3y = 15  and the graph  is shown below .

In the question ,

it is given that

the required line passes through the points (9,2) and (3,4)

in order to find the equation of  line we first need to find slope .

so , the slope(m) will be

m = (4-2)/(3-9)

m = 2/(-6)

m = -1/3

The equation of the line passing through the point (3,4) having slope -1/3 is

y - 4 = (-1/3)(x - 3)

3(y - 4) = -1(x - 3)

3y - 12 = -x + 3

x + 3y = 12 + 3

x + 3y = 15

the graph of the line is drawn below .

Therefore ,The equation of the line that passes through the points  (9,2) and (3,4) is x + 3y = 15  .

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A rectangle has an area of 50 square
centimeters. The width is 5 more than 1 times
the length. Find the length and width, in
centimeters, of the rectangle.
Show your work here

Answers

The measurements of the rectangle are 10 cm and 5cm.

What is rectangle?

A rectangle could be a quadrilateral with four right angles in geometer geometry. It may be outlined as an angulate quadrilateral as a result of all of its angles square measure equal; or a quadrangle with a right angle.

Main Body:

Let the width be x.

According to question :

width is 5 more than 1 times the length(l), so

length (l) = width -5

Area if rectangle = 50 cm²

Formula for area of rectangle = length * width

⇒50 = x*(x-5)

⇒50 = x² - 5x

⇒x² - 5x - 50 =0

splitting the middle term

⇒x²- 10x +5x -50 = 0

⇒x(x-10) +5(x-10)

⇒(x-10)(x+5)

Hence the value for x = 10 or -5 .

but length can never be -ve so x= 10.

Width = 10 cm

length = width -5

length = 10 -5

l = 5cm

Hence Measurements of rectangle are 10cm and 5cm.

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one day, amy walks into preschool and notices a little boy playing with the baby dolls. she compares that observation to her category for boys as well as her category for girls. if she has never previously experienced boys playing with baby dolls, this observation will not fit with her category for boys. however, the more exposure amy has to boys playing with baby dolls, she will start to incorporate baby dolls into her category for boys. which theory on gender role development is amy utilizing? question 4 options: 1) implicit associate theory 2) social learning theory 3) theory of mind 4) gender schema theory in purchasing a category is: a. represented by the strategic sourcing matrix b. a related group of items c. a standard grouping of materials that all companies use regardless of industry d. only a and b a person's blood glucose level and diabetes are closely related, let x be a measurement in milligrams of glucose per deciliter of blood, after 12-hour fast, the variable x will have a Distribution that is approximately normal with a mean of 85 and standard deviation of 25. this is only true for adults under 50. Use this information to answer the question that follow:what percentage of people have a blood glucose level between 100 and 125? 38132453123213 Which drug produces a dissociative state and can cause amnesia and profound loss of pain?. an economy that is undergoing industrialization, is growing faster than developed economies, and has capital markets that usually entail greater risk is referred to as a(n) Why do you think Battuta recorded this description of Mogadishu in his travels? Is it true or false a government in which the state has control over all aspects of society is called a totalitarian government. what are the four main catagoies used to develop a narritive Add.1 4/5 + (1/4) + (1/5) recall that hytex company is a direct marketer of technical products and that the file catalog marketing.xlsx contains recent data on 1000 hytex customers. a. identify all customers who are either (1) homeowners between the ages of 31 and 55 who live reasonably close to a shopping area that sells similar merchandise, and have a combined salary between $40,000 and $90,000 (inclusive) and a history of being a medium or high spender at hytex; or (2) homeowners greater than the age of 55 who live reasonably close to a shopping area that sells similar merchandise and have a combined salary between $40,000 and $90,000 (inclusive) and a history of being a medium or high spender at hytex. how many customers have you identified? hjwuowhsshsusbtsjstebeyudgdd the p plants that mendel used in his experiments were all homozygous for the trait he was observing. which genotypes could correctly represent the alleles of the p plants? the stock in net corporation sells for $25 per share and features cumulative voting. there are 24,000 shares outstanding. if five directors are up for election, how much does it cost to ensure someone a seat on the board? group of answer choices in horror movies, sexually arousing images of women are sometimes paired with violence against women. based on classical conditioning principles, what might be an effect of this pairing? for most breach of contract claims, the remedy at law will be awarded by the court to the nonbreaching party. Describe the diversity of language in sub-Saharan Africa. Be sure to use specific examples in your paragraph of at least five sentences.WILL GIVE 100 POINTS Simplify the expression:(5.5 + 2p)(2) = What is the solution of the inequality -8(x + 7.5) 10? following an instance of problem behavior in the tangible condition of a functional analysis the therapist should provide: