Write the equation for the following relation. Include all of your work in your final answer. Submit your solution. P = {(x, y): (1, 0), (2, 4), (3, 8), (4, 12), . . .}

Answers

Answer 1
First, we will notice that while the value of x increases by 1, the corresponding value of y increases by 4. This means that this is a linear relation.

The general equation for linear equations is : y = mx + c where m is the slope and c is the y-intercept

To get the slope, we will need to use two points. Let's take the first and the last points: (1,0) and (4,12)
The slope is calculated as: (y2-y1) / (x2-x1)
Use the chosen points to substitute in the equation and get the slope as follows:
m = (12-0) / (4-1) = 12/3 = 4

Now, the equation of the line became: y = 4x + c

The given points all satisfy the equation of the line, we can use any of them to substitute in the equation and get the value of c.
For instance, I will use the first point: (1,0)
y = 4x + c
0 = 4(1) + c
c = -4

The equation of the line is:
y = 4x - 4


Related Questions

Simplify three to the negative ninth divided by three to the negative twelfth.


Answers

(3^-9)/(3^-12) will give you 3^3, which can be further simplified to 27

Answer:

3^3

Step-by-step explanation:

What is 25.4067 to the nearest hundredth

Answers

I think it is 25.4100
25.0 because if it’s to the nearest hundredth then you Count 3 numbers and u see what u have to do because if it is 5 or more you increase the score but if its 4 or less u don’t mess!

Towing charge 30$ plus $3 per mile if I paid $117 how far was the car towed

Answers

117 - 30 = 87

87/3 = 29

The car was towed 29 miles

hope this helps

Use this equation to find dy/dx. 4y cos(x) = x2 + y2

Answers

Let's differentiate implicitly,
don't worry about solving for y explicitly before differentiating.

(4y)cosx = x^2 + y^2

Apply product rule on the left,
and power rule on the right-hand terms,

(4y)'cosx + 4y(cosx)' = (x^2)' + (y^2)'
4y'cosx + 4y(-sinx) = 2x + 2yy'
4y'cosx - 4ysinx = 2x + 2yy'

Let's get both y' terms on the left side,
and everything else on the right,

4y'cosx -2yy' = 2x + 4ysinx

Factor y' out of each term,

y'(4cosx - 2y) = 2x + 4ysinx

Solve for y' (which is dy/dx) by dividing by the stuff,

y' = (2x + 4ysinx) / (4cosx - 2y)

You can divide a 2 out of everything to simplify it down a little bit.

y' = (x + 2ysinx) / (2cosx - y)

HELP I WILL GIVE BRAINLIEST!
what value of x makes the equation true? 9x - 15 - 2x = -60 + 9x

Answers

The question is asking you to solve for x:

9x - 15 - 2x = -60 + 9x
-9x      +2x            -9x  +2x

-15              = -60 + 2x
+60                +60

45               = 2x
45/2 = x
Hope this helps!

What is the value of x?



Enter your answer in the box.
x =

Answers

3x + 50 = 6x -10

add 10 to each side

3x +60 = 6x

subtract 3x from each side

60 = 3x

x = 60/3 = 20

x = 20

In the accompanying diagram angle 1 and angle 2 are supplementary what is m angle 3

Answers

The M in angle three is complementary 

F(x)=5(3-x)^2 what is f(-4)

Answers

Plug in x = -4 and then use PEMDAS to simplify

f(x) = 5(3-x)^2
f(x) = 5*(3-x)^2
f(-4) = 5*(3-(-4))^2 ... replace every x with -4
f(-4) = 5*(3+4)^2
f(-4) = 5*(7)^2
f(-4) = 5*(49)
f(-4) = 245

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

Final Answer: 245

Earth's radius is about 261.4% of Mercury's radius.(2,440 km.)
what is the radius of Earth?

Answers

(C) 261.4/100 = 2.614 (your multiplier) 
2.614 x radius of mercury = 2.614 x 2440 = 6378.16 
therefore radius of earth is 6378.16 
Final answer:

Earth's radius is approximately 6,378.96 km.

Explanation:

To find the radius of Earth, we can use the information given in the question. We know that Earth's radius is approximately 261.4% of Mercury's radius, which is given as 2,440 km.

Let's set up an equation to solve for Earth's radius. Let x represent Earth's radius:

x = 261.4% * 2,440 km

Converting 261.4% to decimal form, we get 2.614. Multiplying this by 2,440 km, we find that Earth's radius is approximately 6,378.96 km.

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Identify the binomial A. x2 −4x + 2 B. x2 C. x2 − 4 D. 2x2 + 3x −1 + y

Answers

The Correct answer is C) x² - 4 .

A binomial is an expression that contains the sum of two distinct terms. In this case, the terms are x² and -4. 

A) Contains 3 terms: x², -4x, and 2. Notice that, since x and x² have different exponents, they are considered distinct terms (you can't simplify the expression any further, unless you know what the value for x is)

B) Contains only one term, x²

D) Contains 4 distinct terms, 2x², 3x, -1, and y

Write the percent as a fraction is lowest terms 65 1/2%

Answers

=5/8

Work:

62.5%=62.5/100
=0.625
= 0.625/1 x 1000/1000
= 625/1000=5/8

Trey has answered 15 E-mails.This is 20% of E-mails he must answer.How many E-mails does he need to answer?

Answers

Trey needs to answer 75 emails

What is the value of ▲ in the equation shown?

8 x 4 = ( ▲ x 7) - (▲ x 3)

= _____

Answers

the answer is 8 because
 8 times 4 = 32
 8 times 7 =56
 8 times 3 =24
 56 minus 24 = 32

Answer:

8

Step-by-step explanation:


P: grass is green or Q: 3 is the square root of 10 (P ∨ Q)

Answers

P v Q is a disjunction, which is true whenever P or Q is true or both are true. P v Q is false only when P and Q are both false.

You know that Q is false, because 3 is not the square root of 10, so the only possibility for P v Q be true is that P is true.

If that is the case, you have this relation:

T F ---> T

which means True and False imply True

Answer:

TFT

Step-by-step explanation:

Red jeans inc. sells jeans that cost $16.55 for a selling price of $35.99. The percent of markup based on cost is

Answers

This would be (35.99 - 16.55)  * 100
                      -------------------             =   117.5 %
                             16.55

Answer:

Markup percent = 117.50%

Step-by-step explanation:

Markup percent = (sales price - unit cost)/unit cos  *100

Given: Unit cost = $16.55, sales price = $35.99

Now plug in these given values in the above formula, we get

Markup percent = (35.99 - 16.55)/16.55 *100

= (19.44/16.55)*100

= 117.50%

Hope this will helpful.

Thank you.

In model trains, O scale means the models are made using a 1:48 scale. In the U.S., real train tracks have rails that are 4 ft 8 in apart.

a. If miniature train track was made using O scale, how far apart should the rails be? Round to the nearest hundredth of an inch.

b. The word gauge refers to how far apart the model rails are. For some reason, O gauge track does not exactly use O scale, and O gauge rails are 1.25 inches apart. Find the relative difference of the rail spacing on O gauge track compared to what it should be if it followed O scale. Round to the nearest tenth of a percent.

Answers

Final answer:

The correct O scale model train track spacing should be 1.17 inches. However, the actual O gauge spacing is 1.25 inches. The relative difference in the rail spacing is approximately 6.8%.

Explanation:

To solve for the correct O scale model train track spacing:

Convert the real train track gauge to inches: 4 feet x 12 inches/foot + 8 inches = 56 inches.

Divide the real gauge by the scale factor of 48 to find the model gauge: 56 inches / 48 = 1.1667 inches.

Round the result to the nearest hundredth of an inch: 1.17 inches.

Now to calculate the relative difference between O scale and the actual O gauge:

Determine the actual O gauge spacing: 1.25 inches.

Calculate the difference in spacing: 1.25 inches - 1.17 inches = 0.08 inches.

Find the relative difference by dividing the spacing difference by the O scale spacing and then multiply by 100 to get the percentage: (0.08 inches / 1.17 inches) x 100 = 6.8%.

Round the result to the nearest tenth of a percent: 6.8%.

one of the models of a dinosaur used in filming of a movie was only 15in tall. In the movie, the dinosaur appeared to have an actual height of 20ft. What is the Scale of the model?

Answers

well, keeping in mind there are 12 inches in 1 foot, 20 feet is 20 * 12, or 240 inches.

[tex]\bf \cfrac{model}{actual}\qquad 15:240\qquad \cfrac{15}{240}\implies \cfrac{1}{16}[/tex]

In how many ways can you receive four cards of the same face value and one card from the other 48 available cards?

Answers

There are 13 sets of 4 cards in a deck of card. So, there are 13 ways to get four cards of the same face value. The next card you pick will always be a different face value. So, essentially, you have 13 x 48 combinations of 5 cards that you can pick from the deck where you have 4 cards of the same face value and 1 card of a different face value.

13 x 48 = 624.


in the diagram below,point O is the center of the given circle.

Answers

yeah you right, it is the center of the given circle

Love them or hate them, they do be spitting straight facts

Julian is mixing drops of food coloring to create green frosting for a cake. He uses 18 drops of yellow dye and 12 drops of blue dye. Find the ratio of drops of blue dye to total drops of dye. Express as a simplified ratio.

Answers

Answer:

The ratio would be 2:5

Explanation:

The ratio of drops of blue dye to total drops of dye is got by dividing drops of blue dye  (12) by total drops, which is the sum of blue and yellow drops (12+18):

[tex]\displaystyle\frac{12}{12+18}=\frac{12}{30}[/tex]

Once we simplify the fraction by dividing both top and bottom by 6, we would get:

[tex]\displaystyle\frac{2}{5}[/tex]

Therefore, the ratio of drops of blue dye to total drops of dye is:  2:5

Final answer:

The simplified ratio of blue dye to total dye used by Julian is 2:5. This means that for every 2 drops of blue dye, there are 5 total drops of dye.

Explanation:

The question is asking for the ratio of blue dye to the total amount of dye. Julian used 12 drops of blue dye and 18 drops of yellow dye, making the total number of dye drops 30 (12 blue + 18 yellow). Therefore, the ratio of blue dye to total dye is 12 to 30. However, this ratio can be simplified by dividing each figure by their greatest common divisor (gcd) which is 6. So, the simplified ratio is 2:5.

This means for every 2 drops of blue dye, there are 5 total drops of dye. It's a useful way of comparing quantities in mathematics or in everyday life circumstances like this one, where Julian is mixing dyes.

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Help for C if anyone knows, thanks

Answers

i THINK the answer is 19 degres
well depending on the temperature it is at 10pm (which i do not know of the top of my head), you would subtract the temperature of noon from the temperature at 10pm and then it would equal the difference between the two temperatures.

hope this helps!
:D

For the given function sin−1(9x + 1), the "inside" function is 9x + 1 and the "outside" function is

Answers

Sin^-1 is inverse function of sin or it's sometimes called arcsin, that is the outside function.
Final answer:

In the function sin⁻¹(9x + 1), the 'outside' function is sin⁻¹(x). This is because it is the function performing an operation on the 'inside' function, which is 9x + 1.

Explanation:

For the function sin−1(9x + 1), the 'inside' function is indeed 9x + 1. The 'outside' function is sin⁻¹(x), also known as the inverse sine or arcsine function. In composite functions, the 'inside' function is the function that is being acted on, while the 'outside' function is the function carrying out the action on the inside function. So here, the action of sine inverse or arcsine is being performed on the 'inside' function 9x + 1.

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Brenda has a balance of d dollars in her piggy bank. Explain what value(s) d may have if d = 28

Answers

Not sure what you're asking!  
Brenda has a blance of 38 dollars in her piggy bank.  What exactly do you still need to learn / know?

She might have 3-$10 bills, 1-$5 bill and 3-$1 bills.  Other combinations are possible.

What is the sum and classification of 3/20 + sqrt of 10

A. 3.31227766..., irrational
B. 3.31227766..., rational
C.18.16227766..., irrational
D.18.16227766..., rational

Answers

Answer:

a

Step-by-step explanation:


Answer:

A. 3.31227766..., irrational

Step-by-step explanation:

We have been given two numbers. We are asked to find sum of given numbers and classify the type of number after addition.

[tex]\frac{3}{20}+\sqrt{10}[/tex]

[tex]0.15+3.1622776601683793[/tex]

[tex]3.3122776601683793[/tex]

We can see that [tex]\frac{3}{20}[/tex] is a rational number, while [tex]\sqrt{10}[/tex] is an irrational number as its digits are repeating infinitely after decimal.

We know that sum of a rational and irrational number is irrational, therefore the sum of given numbers is irrational and option A is the correct choice.

Darius and Matthew have three fruit bars. They are both hungry after playing football and decide to split the fruit bars evenly.

Answers

They each get one whole one and then half of one.

Dale cut a wire into 7 equal pieces. The wire was originally 7.84 meters long. How long is each piece?

Answers

7.84 / 7 = 1.12 meters per piece <=
each piece would be 1.12 meters each.

What is 100x100 I need help :(

Answers

100x100 is equal to 10,000, you only need to multiply

The solution is, the value is 100 x 100 =10000.

What is  multiplication?

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

given that,

100 x 100

i.e. we have to multiply 100 with 100

so, we get,

100 x 100

=10000

Hence, The solution is, the value is 100 x 100 =10000

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The planet Mercury has a diameter of 4,878 km whereas the Moon has a radius of 1736.5 km. Which object is larger and why?

Answers

First, to be able to compare these two things, you have to either find the radius of Mercury or find the diameter of the moon. I choose finding the diameter of the moon because it seems easier.

Diameter=radius*2
Diameter=1736.5*2=3473

The moon has a diameter of 3473 km.

Since Mercury's diameter, 4878km, is greater than the Moon's diameter, 3473km, Mercury is larger.

Hope this helps!

The planet Mercury is larger than the Moon, because the radius of Mercury is greater than the Moon.

Here,

Given that;

The planet Mercury has a diameter of 4,878 km.

And, The Moon has a radius of 1736.5 km.

We have to find the larger planet.

What is the relation between radius and diameter?

The radius is half or the diameter of the object.

Now,

The planet Mercury has a diameter of 4,878 km.

Hence, The radius of Mercury = 4,878/2 = 2,439 km

And,  The radius of the Moon = 1736.5 km

Clearly, 2,439 > 1,736.5

So, The planet Mercury is larger than the Moon, because the radius of Mercury is greater than the Moon.

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Find the slope of the tangent line to the parabola y=4x-x^2 at the point (1,3)

Answers

y=4x - x²
dy/dx = 4-2x
dy/dx | x=1 : 4-2(1) = 4-2= 2
gradient= 2

Samuel filled the glasses shown below completely with water. The total amount of water that Samuel poured into the glasses is 60 cubic centimeters. What is the height of glass 1? Round your answer to the nearest tenth. (Use π = 3.14.) Note that all measurements are in centimeters and images are not drawn to scale.
The possible answers are 0.2, 1.7, 3.9 or 5.6. When googled the answer always comes up 3.9. I always get 1.6527 which rounds up to 1.7. How about you?

Answers

volume of glass 2 = pi*r^2*h/3= 3.14 *2.5^2*6/3 = 39.25 cubic cm

60-39.25 = 20.75 cu cm was in 1st cup

volume of cylinder = pi *r^2 *h

20.75 = 3.14 *2^2 *h

20.75 = 3.14*4*h

20.75 = 12.56*h

h = 20.75 /12.56 = 1.652 round to 1.7

Answer:

The height of glass 1 is 1.7 cm.    

Step-by-step explanation:

We are given the following information in the question:

The total amount of water that Samuel poured into the glasses is 60 cubic centimeters.

Volume of glass 2 = Volume of cone =

[tex]\displaystyle\frac{1}{3}\pi r^2h\\\\\text{Putting value of r and h}\\\\= \frac{1}{3}\times 3.14\times \frac{5}{2}\times \frac{5}{2}\times 6 = 39.25\text{ cubic cm}[/tex]

Volume of glass 1 =

[tex]\text{ Total Volume } - \text{Volume of glass 2}\\= 60 - 39.25\\= 20.75\text{ cubic cm}[/tex]

Volume of glass 1 = Volume of cylinder =

[tex]20.75 = \pi r^2h\\\text{where r is the radius of cylinder and h is the height of cylinder}\\\\\text{Putting the values of r}\\\\  20.75 = 3.14\times \displaystyle\frac{4}{2}\times \frac{4}{2}\times h\\\\h = \frac{20.75}{3.14\times 2\times 2} 1.656 \approx 1.7[/tex]

Thus, the height of glass 1 is 1.7 cm.

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