How many pairs of positive integers (x,y) satisfy x^2-y^2=51?

Answer:

Look below :)

Step-by-step explanation:

1. To find the slope of a line, we can use this expression: [tex]\frac{y2 - y1}{x2 - x1}[/tex]

In order to use that expression, we need to use two points. The graph given only provides you with two complete points, so we'll use those.

(4, 4) = (x1, y1)  (12, 20) = (x2, y2)

Now we can input the values into the expression:

[tex]\frac{y2 - y1}{x2 - x1}[/tex] = [tex]\frac{20 - 4}{12 - 4}[/tex]

Let's solve for the slope:

20 - 4 = 16

12 - 4 = 8

[tex]\frac{16}{8}[/tex]

To simplify 16/8 divide both the numerator and the denominator by 8:

16/8 = 2

8 = 1

You get 2/1 or just 2.

The slope of the line is 2.

2. To make an equation for the line, we'll use slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. We already know the value of the slope is 2, so now we need to find the y-intercept. We can find the y-intercept using a given point and the slope. In this example, I'll use the point (4, 4). Let's input the values into the equation:

y = mx + b

4 = 2(4) + b

Now let's solve for b:

4 = 8 + b

Subtract 8 from both sides to isolate the b:

4 - 8 = 8 - 8 + b

-4 = b

The y-intercept of the equation is -4.

Now that we know the values for the slope and y-intercept, we can write the equation:

y = 2x - 4

3. To find the values of a and b, we can use the equation we made in the previous question.

First we'll find a:

The point we are given is (a, 16). We know the y-value is 16, so we can put that into our equation. We can also replace x with a:

y = 2x - 4

16 = 2a - 4

Now we can solve for a:

First, add 4 to both sides to isolate the 2a:

16 + 4 = 2a - 4 + 4

20 = 2a

Then divide both sides by 2 to isolate a:

20/2 = 2a/2

10 = a

The value of a is 10.

Now let's find b:

This is similar to finding a. The point we are given is (8, b). We know the value of x is 8, and we can replace y with b in the equation:

y = 2x - 4

b = 2(8) - 4

Let's solve:

b = 2(8) - 4

b = 16 - 4

b = 12

The value of b is 12.

4. Finally, to find the y- coordinate when x=0, all we have to do is input 0 in for x in the equation and then solve for y:

y = 2x - 4

y = 2(0) - 4

y = 0 - 4

y = -4

When x = 0, y = -4.

The answer for what the y-coordinate is when x = 0 will always be the value of the y-intercept.

I hope this helps!

The answer issssssss C

The constant of proportionality(k) between a yard and a foot is 0.33.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

The variable feet and yards are in direct proportion.

Let,

yard = k(feet).

1 = 3k

k = 1/3 = 0.33.

learn more about proportion here :

https://brainly.com/question/7096655

#SPJ2

Answer:

30,52,69

Step-by-step explanation:

Answer: 12/30

and 40 percent

Step-by-step explanation:

Well it’s 12 to 30 so just put a fraction bar

and 12 divided by 30 is .4

Answer:

The answers are 12/30 and 10%

Step-by-step explanation:

It's 40% because the ratio of males to total students is 12 to 30, or 12:30, which is equal to 12/30.

The other answer is 10% because the ratio of males to total students is 3 to 30, or 3:30, which is equal to 1/10. Then you would do 100 divided by 10 which would give you 10 so it's 10%.

Hope this helps!

Answer:

22

Step-by-step explanation:

0.8 --> 1 * 22 = 22

Hope this helped! Have a nice day!

Answer:

i believe the answer is 7/6 or 1[tex]\frac{1}{6}[/tex]

Answer:

1.5

Step-by-step explanation:

Answer:

slope=1/2 and y-interception=3

Step-by-step explanation:

mx+b where m is the slope and y- inersception is b

Answer:

A C D

Step-by-step explanation:

Answer:

4.64c

Step-by-step explanation:

Step-by-step explanation:

=1.52c+3.12c

=4.64c

hope it help u.

Answer: For the first question, m = 1.5 and y-intercept = 5, so your equation for the first one should be, y = 1.5x + 5.

And for the second question, m = -1.75 and y-intercept = 4, so your equation for the second one should be, y = -1.75x + 4.

Step-by-step explanation: For the 1st one, subtract 3x to get -2y = -3x - 10, then divide by -2 to get y = 1.5x + 5.

For the 2nd one, subtract 7x to get 4y = -7x + 16, then divide by 4 to get y = -1.75x + 4.

Hope this helps you! :)

Answer: 7/8x - 7

Step-by-step explanation:

1/4x +2 = -5/8x - 5

Let me know if this is right

Answer:

Multiply the cost of an item or service by the sales tax in order to find out the total cost. The equation looks like this: Item or service cost x sales tax (in decimal form) = total sales tax. Add the total sales tax to the Item or service cost to get your total cost.

Step-by-step explanation:

Answer: The volume can be found using the fomula (pi)(r)^2(h).

(3.14)(3.8)^2(3)

136.0248

Step-by-step explanation:

In miles per hour, 4/3 speed represents the flow of water in the river, and its calculation can be defined as follows:

Distance = [tex]\frac{1}{3}[/tex] miles

Time= [tex]\frac{1}{4}[/tex] hours

speed=?

Speed Definition:

An object's speed is indeed the pace at which it moves along a path in time, whereas its velocity is the rate and direction of travel.

The formula for calculating the speed:

[tex]\to[/tex] speed =[tex]\bold{\frac{Distance}{time}}[/tex]

               [tex]=\frac{\frac{1}{3}}{\frac{1}{4}}\\\\={\frac{1}{3} \times \frac{4}{1}}\\\\={\frac{4}{3}}\\\\[/tex]

Therefore, the calculated speed of water flow is [tex]\frac{4}{3}[/tex] miles per hour.

Find out more about the speed calculation here:

brainly.com/question/26822909

Answer:

y= 10/3x + 20

Step-by-step explanation:

the slope is 10/3 because from one point to another (on the line) it moves up 10 (from 20 to 30) and to the right 3 (from 0 to 3)

the y intercept is 20 because when x = 0, y = 20 which we can see on the graph

Answer:

y=10/3x +20

im too late to be first again :(

Answer:

y = 4x + 3

Step-by-step explanation:

Answer:

You have 3 cookies and need to divide them between you and a friend.

Step-by-step explanation:

Answer:

3 div 1/2 or 1/2 div 3 = 1.5 or 1.50

Step-by-step explanation:

dsffsgfduntydgfjghfu,dryfujyftmhgjghjg,kgytugjhyghkbgk

Answer:

Hiiiii

I'm okay, how about you?

thanks for the free points! :)

Answer:

192 baskets

Step-by-step explanation:

Answer: your answer  is 2.4

Step-by-step explanation:

Answer:

240

Step-by-step explanation:

20% of the students like rock and 40% like hip-hop. That means that 60% of the 360 students would be expected to choose one of the two. Because you don't know the other 10%, you would assume that they would have the same ratio of students who like the country to those who like rock and hip-hop. 60 is 2/3 of 90, so you would expect 2/3 of the students to like hip-hop or rock. 2/3 of 360 is 240.

(this is not my handlely work; I not very good at explaining)

Answer:

-38

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:because train a reaches a higher distance in a faster rate

Answer:

im only doing this for the points sorry :/

Step-by-step explanation:

Answer:

p on the -3 line

Step-by-step explanation:

Answer:

5.9..... there are a bunch of numbers after that but you would round it to 6.0

Step-by-step explanation:

Answer:

5. Noah and Diego has the same amount of money which is $7.5

Step-by-step explanation:

Noah=75% of $10

75÷100×10=7.5

Noah has $7.5

Diego=25% of $30

25÷100×30=7.5

Diego=$7.5

Therefore Noah and Diego has the same amount of money

Answer:

Can I please have Brainliest I want to level up

Step-by-step explanation: