if x2=18x+y and y2=18y+x, then find the value of root

If X2=18x+y And Y2=18y+x, Then Find The Value Of Root

Answers

Answer 1

Answer:

[tex]\sqrt{x^2+y^2+1}=18[/tex]

Step-by-step explanation:

We are given:

[tex]x^2=18x+y\qquad\qquad[1][/tex]

[tex]y^2=18y+x\qquad\qquad[2][/tex]

Subtracting [1] and [2]:

[tex]x^2-y^2=18x+y-(18y+x)[/tex]

Operating:

[tex]x^2-y^2=18x+y-18y-x[/tex]

Recall:

[tex]x^2-y^2=(x-y)(x+y)[/tex]

Substituting:

[tex](x-y)(x+y)=18x+y-18y-x[/tex]

Rearranging:

[tex](x-y)(x+y)=18x-18y-(x-y)[/tex]

[tex](x-y)(x+y)=18(x-y)-(x-y)[/tex]

Dividing by x-y (recall x≠y):

[tex]x+y=18-1=17[/tex]

[tex]x+y=17\qquad[3][/tex]

Now we add [1] and [2]:

[tex]x^2+y^2=18x+y+18y+x[/tex]

Rearranging:

[tex]x^2+y^2=18x+18y+x+y[/tex]

[tex]x^2+y^2=18(x+y)+(x+y)[/tex]

[tex]x^2+y^2=19(x+y)[/tex]

Substituting from [3]

[tex]x^2+y^2=19*17=323[/tex]

Adding 1:

[tex]x^2+y^2+1=324[/tex]

Taking the square root:

[tex]\sqrt{x^2+y^2+1}=\sqrt{324}=18[/tex]

Thus:

[tex]\mathbf{\sqrt{x^2+y^2+1}=18}[/tex]


Related Questions

simplify the product. write (x + 2)(x − 5) in standard form. Show your work

Answers

Answer:

x^2-3x-10

Step-by-step explanation:

Answer:

The answer is x²-3x-10

Step-by-step explanation:

(x + 2)(x − 5)

x²-5x+2x-10

x²-3x-10

Write an equation of the line that passes through (5,9) and is perpendicular to the line y=-1/3x+1

Answers

Perpendicular = opposite sign and reciprocal slope
Slope would be 3
Y = 3x + b, plug in point
9 = 3(5) + b, b = -6
Solution: y = 3x - 6

48 people attended the Sunday matinee to watch a film. .Three over 8 of the people went to see a romantic comedy. .One over six of the people went to see an action movie. .The remaining people saw a horror movie. How many people saw a horror movie?

Answers

Answer:

22 people saw an horror movie

Step-by-step explanation:

Total people who attended the Sunday matinee = 48

People who saw romantic comedy = 3/8 of 48

= 3/8 × 48

= (3*48) / 8

= 144 / 8

= 18 people

People who saw action movie = 1/6 of 48

= 1/6 × 48

= 48/6

= 8 people

People who saw horror movie = x

Total people who attended the Sunday matinee = People who saw romantic comedy + People who saw action movie + People who saw horror movie

48 = 18 + 8 + x

48 = 26 + x

Subtract 26 from both sides

48 - 26 = 26 - 26 + x

22 = x

x = 22 people

22 people saw an horror movie

My teacher can grade 25 homework assignments in 20 minutes. Is she working at a faster rate or slower rate than Ms. Jones, who is grading 36 homework assignments in 30 minutes?

Answers

Answer:

Ms.Jones is faster

Step-by-step explanation:

59.5 is what percent of 17 ?

Answers

350%.................

Answer:

350%

Step-by-step explanation:

59.5÷17=3.5

3.5•10=350

350%

Two sides of a triangle are two consecutive number, whose area is 17.5cm². Find the numbers

Answers

Answer:

The numbers associated with the triangle are 5.437 and 6.437 centimeters, respectively.

Step-by-step explanation:

Two numbers are consecutives, when their difference is equal to 1. The area of the triangle is determined by the following formula:

[tex]A = \frac{1}{2}\cdot n \cdot (n+1)[/tex]

[tex]A = \frac{1}{2}\cdot (n^{2}+n)[/tex]

[tex]A = \frac{n^{2}}{2}+\frac{n}{2}[/tex]

[tex]n^{2}+n = 2\cdot A[/tex]

Where [tex]n[/tex] is the shortest length of the triangle, measured in centimeters.

And we get the following second-order polynomial:

[tex]n^{2}+n -2\cdot A = 0[/tex] (1)

If we know that [tex]A = 17.5\,cm^{2}[/tex], then the shortest length of the triangle is:

[tex]n_{1} = 5.437\,cm[/tex] and [tex]n_{2} \approx -6.437\,cm[/tex]

Since length is a positive variable, the only possible solution is:

[tex]n\approx 5.437\,cm[/tex]

Then, the numbers associated with the triangle are 5.437 and 6.437 centimeters, respectively.

The next model of a sports car will cost 4.7% less than the current model the current model cost 31000. How much will the price decrease in dollars? What will be the price next model?

decrease in price $_
price of next model $_


please help me !​

Answers

Step-by-step explanation:

decrease value is 1353

value 31,647

Round 639,121 to the nearest ten thousand.

Answers

Answer:

640,121

Step-by-step explanation:

Explain the difference between equilateral and equiangular :) ​

Answers

An equilateral polygon has congruent sides, like a rhombus.

An equiangular polygon has congruent interior angles, like a rectangle.

In other words: Equilateral doesn't necessarily have congruent INTERIOR angles while equiangular does have/need congruent interior angles.

what number makes the equation true? 6 equals 30 divided

Answers

Answer: 5

Step-by-step explanation:

This question is basically asking:

6 = 30 ÷ ?

We can use a fact family to find the value.

30 ÷ 6 = 5

The answer is 5.

y-28=95
y-28+ ? =95+28
y=?

Answers

Answer:

Step-by-step explanation:

y -28 = 95

y-28 + 28 = 95 +28

y=123

dummy ;)

99-45f+36b in factored form

Answers

9(4b-5f+11)

hope this helps

The scale drawing of a building has a width of 6 inches and a height of 8 inches. If the height of the actual building is 48 feet, what is the width?

Answers

Answer:

36 feet

Step-by-step explanation:

48/8=6 so you need to multiply the 6 by 6 as well which gives you 36

A building in a shape of a cube has a width of 100 ft., a length of 100 ft., and a height of 100 ft. An architect wants to build a scale model of the building that is 10% smaller in volume. What is the height of the new building? Round to the nearest hundredth.

A) 90.75 ft.
B) 95.25 ft.
C) 96.55 ft.
D) 99.25 ft.

Answers

Answer: A) 90.75 ft.

Step-by-step explanation: because if we cut 10 from 100 we will get 90

Write an equation of the line that passes through (–2, 8) and (–4, –4).
PLEASE HEEEELP MEEE! PLEASE ACTUALLY PROVIDE AN EXPLANATION! BEST EXPLANATION AND ANSWER GETS BRAINLIEST! THANKS

Answers

Answer:

sorry bro

Step-by-step explanation:

Answer:

Y=6x+20

Step-by-step explanation:

A company has a monthly profit, or gain, of $6,400. The next month they have a loss of $4,700.

What expression would you use to find the difference in profit between the two months?

-4,700 - 6,400
6,400 - 4,700
6,400 - (-4,700)
4,700 - 6,400

Answers

Answer:

6,400-4,700

Step-by-step explanation:

5x + 2x + 2 = 9x + 4​

Answers

Step-by-step explanation:

Given

5x + 2x + 2 = 9x + 4

9x - 5x - 2x = 2 - 4

9x - 7x = - 2

2x = - 2

x = - 2 / 2

Therefore x = -1.

therefore lhs is equal to rhs

the first blanks options are -2 , -1/2 , 2 , 1/2
The seconds are -5 , -3 , 5, 3
the thirds are -2, -1, 2, 1
and the fourths are -2, -1, 2, 1

Answers

Answer:

equation 1

y = -2x

equation 2

y = x-3

Solution to both

(1,-2)

Step-by-step explanation:

We need to get the equations of both lines

General form is;

y = mx + c

where m is slope and c is the y-intercept

Table 1

since we have a point 0,0; the y-intercept here is zero

Let us get the slope. We can do this by selecting any two points

m = (y2-y1)/(x2-x1)

m = (2-10)/(-1+5) = -8/4 = -2

So the equation of the first line is;

y = -2x

Table 2

we get the slope

m = (4+2)/(7-1) = 6/6 = 1

The partial equation is;

y = x + c

To get c, we select any two point and substitute

4 = 7 + c

c = 4-7

c = -3

So the equation is;

y = x-3

To get the solution to both systems, we equate the y

-2x = x - 3

-2x-x = -3

-3x = -3

x = -3/-3

x = 1

To get y, we substitute;

recall; y = -2x

y = -2(1)

y = -2

Solution to the system is;

(1,-2)

BRAINLIEST TO RIGHT WITHOUT WORK
If you increase the length of a rectangle by 50% and the width by 100% by what percent will the area of this rectangle increase

Answers

Answer:

200%

Step-by-step explanation:

if you substitute in numbers you'll find this as the answer.

as an example:

suppose the sides of the rectangle was 1 unit long.

area before change: 1 * 1 = 1

then, the length gets increase by 50% making it 1.5 ( 50% of 1 is 0.5, then you add it onto 1, 1 + 0.5 = 1.5 )

the width gets increased by 100% making it 2 ( 1 + 1 = 2 )

new area: 1.5 * 2 = 3

1 increased by 200% is 3, therefore the answer is 200%

Daisy is reading a 47 pg book. She read the first 20 pgs in 6 minutes. How long will it take her to read the entire book?

Answers

Answer:

About 15 minutes

Step-by-step explanation:

It takes her 6 minutes to read 20 pgs. If she reads 20 more pages (which will be 40 now) she will have been reading for 12 minutes. This leaves you with 7 pages left, about 3 or 4 minutes.

by the definition of supplementary angles, the base angles of the top isosceles triangle have the measure of

Answers

Answer:

128

Step-by-step explanation:

Top Triangle

Let the base angles of the top triangle = y

y + 102 = 180

y = 78

The vertex

Is found by adding the two base angles together and subtract that from 180

y + y + vertex = 180

78 + 78 + vertex = 180

156 + vertex = 180

vertex = 180 - 156

vertex = 24 degrees

Bottom Triangle

Because the base angles are connected by a vertically opposite angle on the bottom triangle, both base angles are 26

Therefore 26 + 26 + x = 180

52 + x = 180

x = 180 - 52

x = 128

HELP ME WITH MATH HOMEWORK

Answers

Step-by-step explanation:

Only option B shows a proportional relationship (y = 3x).

Answer:

D

Step-by-step explanation:

Y=3x-1 is written as the slope-intercept form y=mx+b don't let the -1 confuse you.

Jamal drew angle bisector AD with D on the line segment BC. If BD=3, DC=9 and AB+AC=28 find AB and AC.

Answers

Answer:

  AB = 7

  AC = 21

Step-by-step explanation:

Because AD is an angle bisector it divides the triangle into proportional parts. That is ...

  AC/DC = AB/BD

  (28 -AB)/9 = AB/3 . . . . use AC = 28 -AB

  28 -AB = 3AB . . . . . . . . multiply by 9

  28 = 4AB . . . . . . . . add AB

  AB = 28/4 = 7 . . . . divide by 4

  AC = 28 -7 = 21

The lengths AB and AC are 7 and 21, respectively.

_____

Additional comment

The triangle ABC cannot exist. The reason is that its side measures are 7, 12, and 21. The sum of 7 and 12 is not greater than 21, so the side measures do not satisfy the triangle inequality.

For the triangle to exist, the sum of AB and AC cannot exceed 24 for the given values of BD and DC.

Imani is taking apart a beaded necklace to make 4 identical bracelets. The necklace has 48 beads. How many beads will Imani use for each bracelet?

Answers

Answer:12 beads

Step-by-step explanation: If she has 48 beads and wants to make 4 bracelets, you will have to divide 48 by 4 which gives you 12

Please help ASAP 15 points

Answers

Answer:

B

Step-by-step explanation:

The answer is B because it tells you the letter atound triangle.

Answer:

b

Step-by-step explanation:

Solve the equation below for the value of x.

−314x + 25 = 214x − 1312

Answers

Answer:

x=1337/528

Step-by-step explanation:

-314x-214x=-1312-25

-528x=-1337

x=1337/528

Answer:

Step-by-step explanation:

add 314x to both sides

-314+25=214x-1312

+314x     +314x

add 1312 to both sides

25=528x-1312

+1312       +1312

1337=528x

x=1337/528

i dont thing you can simplify to a whole number...hopefully this helps a little :)

Please answer!!

During what times is Ann driving a consistent speed? Give a reason to support your answer

Answers

Answer:

There are 3 intervals where Ann is driving a consistent speed

Between 1 and 4 minutes, Between 6 and 8 minutesBetween 9 and 11.5 minutes

==========================================================

Explanation:

When she drives a consistent speed, this means her speed is the same.

This happens exactly when there are flat portions of the graph. This is because the speed y is not going up or down during these intervals.

The intervals where the graph is flat are mentioned at the top in the answer portion.

Any time the graph goes uphill, from left to right, Ann is increasing her speed. So she is accelerating.

In contrast, any time the graph goes downhill, she is decreasing her speed (or decelerating).

Side note: I'm not including the portion from roughly 4 to 5 minutes because during that time, she is stopped and the car isn't moving.

Use the information provided to write the equation of each parabola in vertex form and intercept form.

Answers

I think it’s B
Hopefully this helps!!

Please help I have searched this question and have not found it yet so please help me answer this, I am bad at math

You want to go to Africa for a photo safari. You need $2,800. You can get $1,000 from your savings and family and you can save $30 per week. How many weeks will it take you to save up the money for the trip?

A. 127 weeks

B. 60 weeks

C. 93 weeks

D. 84 weeks

Please select the best answer from the choices provide

Answers

Answer:

B 60

Step-by-step explanation:

because 30x60=1800 and since you already have 1k you add the 1800 to get 2800.

In 2008, the number of tourists visiting France was 7.94 x 10^7. The number of tourists visiting Italy was 4.27 x 10^7. Find the difference in the number of visitors.​

Answers

Answer:

[tex]36700000[/tex]

Step-by-step explanation:

Difference between tourists visiting France and Italy = [tex](7.94 - 4.27)[/tex] ×[tex]10^{7}[/tex]

[tex]= 3.67[/tex] × [tex]10^{7}[/tex]

[tex]= 36700000[/tex]

[tex]\therefore[/tex] Difference between population of tourists in France and Italy are [tex]36700000[/tex] people.

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