x and y are two non-zero real numbers such that: x²-y²=15 and x+y=3√5. then x-y=
A. √15
B. √5
C. -3√5​

Answers

Answer 1

Answer:

[tex](x-y)=\sqrt{5}[/tex]

Step-by-step explanation:

[tex]We\ are\ given\ that:\\x^2-y^2=15\\x+y=3 \sqrt{5}\\Now,\\We\ know\ that,\\If\ x\ and\ y\ are\ two\ real\ numbers,\\Then:\\(x+y)(x-y)=x^2-y^2\\Here,\\Substituting\ (x+y)=3\sqrt{5}\ in\ the\ LHS\ and\ (x^2-y^2)=15\ in\ the\ RHS,\\(x+y)(x-y)=x^2-y^2\\3\sqrt{5} (x-y)= 15\\Hence,\\(x-y)=\frac{15}{3\sqrt{5} } \\(x-y)=\frac{5*3}{3\sqrt{5} }\\(x-y)=\frac{5}{\sqrt{5} } [Cancelling\ 3\ from\ the\ numerator\ and\ denominator]\\(x-y)=\frac{\sqrt{5}*\sqrt{5} }{\sqrt{5} }\\(x-y)=\sqrt{5}[/tex]


Related Questions

Hiiii Can someone please help me please
A, B, C, or D
F, G, H, or J
Ill give lots of points because there's two Please help me thank you BRAINLIEST ANSWER btw ❤️

Answers

Answer:

B, H

Step-by-step explanation:

The electrician charges 45 dollars per hour and 30 at the beginning. We are multiplying the hours, h, by 45 to get 45h. We add 30 to get C=45h+30

Jerome will always earn 75 dollars, but he also gets 10 percent commission, which is 0.10.

Answer:

B and H are the correct answers

A 24-foot ladder is placed 7ft from the wall, (as shown)
if the top of the ladder slips down 4 ft, how many feet will the bottom slide out?
a. 4 feet
b. 8 feet
c. 15 feet
d. 20 feet

anyone who answers this (first) will get 15 points!

Answers

I’m pretty sure it’s c.15 feet it’s the best answer
I would say d or c hope it helps

I get a 15% discount at Ann Taylor Loft. If I find a shirt I like for $20, how much will I have to pay for it?

Answers

The answer will be 17 dollar

4. The band at Jason's high school had a concert for charity. They raised $15000. Adult tickets were $5 each and student tickets were $3 each. The members of the band sold a total of 4000 tickets. Which of the following systems of equations can be used to determine how many adult, x, and student tickets, y. they sold? A. x + y = 4000 5x + 3y = 15000 C. x - y = 4000 5x - 3y = 15000 B. x + y = 15000 5x + 3y = 4000 D. 5x + 3y = 4000 3x + 5y = 15000 03 PO P MINE W 1 NY 19 C​

Answers

Answer:

A. x + y = 4000

   5x + 3y = 15000

Step-by-step explanation:

Total amount raised = $15000

cost of adult tickets = $5

cost of student tickets = $3

Total number of tickets sold = 4000

number of adult tickets sold = x

number of student tickets sold = y

Then we can say,

total number of ticket sold = number of adult tickets + number of student tickets

4000 = x + y

⇒ x + y = 4000 ............. 1

Also,

5x + 3y - 15000 ............. 2

the equations required are:

x + y = 4000

5x + 3y - 15000

Find the slope of the line y = 5/8x - 1/2

Answers

Answer:

slope = [tex]\frac{5}{8}[/tex]

Step-by-step explanation:

Slope-intercept form is the way in which an equation is written to easily identify the line's slope and y-intercept. It is represented by the equation y = mx + b, in which m represents the slope.

By looking at the equation, we can see that it takes the y = mx + b format - y is isolated - therefore it is in slope-intercept form. Remember that the number in place of the m would represent the slope - and in this case, that number is [tex]\frac{5}{8}[/tex].

Final Answer:

[tex]\sf{Slope = \dfrac{5}{8}}\\\sf{Y-intercept: -\dfrac{1}{2}}[/tex]

In-depth explanation:

The question is asking us to find the slope of the line, whose equation is;

[tex]\leadsto\quad\bf{y=\dfrac{5}{8}x-\dfrac{1}{2}}[/tex]

The format of this equation is: [tex]\boldsymbol{\sf{y=mx+b}}[/tex]. This is known as slope-intercept; it's the most common way of writing the equation of a line.

In y = mx + b, the variable "m" denotes the slope, or the rate of change, of a line; b denotes the y-intercept, or the point where the line intercepts the y-axis.

Also, the slope is the number before x, while b is the constant term.

Similarly, the slope is 5/8 and the y-intercept is -1/2.

[tex]\rule{350}{2}[/tex]

Help me i beg u


.Jessica is making metal sculptures to sell. A metal sculpture costs $24 to make and Jessica sells it to

a retailer for a profit of 175%. If the retailer then marks up the sculpture by another 120%, how

much will it cost someone to buy a sculpture in the shop?

Answers

Answer:

$50.40

Step-by-step explanation

The sculpture cost $24 to make so for her to make a 175% profit think of it as a decimal which is 1.75. So you do 24*1.75=$42. Then retailer marks up an additional 120% so then it'll be 42*1.20= 50.4

Which equation represents the slope-intercept form of the line below?
y-intercept = (0,3)
slope = 4
O A. y = 3x + 4
O B. y = 3x - 4
O C. y = 4x-3
D. y = 4x + 3
help asap

Answers

Answer:

D

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 4 and c = 3, then

y = 4x + 3 → D

Answer:

b

Step-by-step explanation:

Martin purchased a book. The receipt says that the total cost of the book is $11.65, including a 6% sales tax. What was the original price of the book without the tax?

Answers

Answer:

11.65$ : 100% = x : 94

94 because 100 - 6

Step-by-step explanation:

Do this:

11.65 x 94 = ?

divide the answer by 100

and that is your answer

Amy sells tote bags at a craft fair for a day. She pays $50 to rent a booth. The materials and labor cost on each tote bag is $3.50. Her expenses for the day depend on how many tote bags she sells. Write a linear function rule and identify the initial value and rate of change.​

Answers

Answer:

Let x= number of totebags sold

Cost=C(x)=50+3.5x

Please help

Leila will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $40 and costs an additional $0.13 per mile driven. The second plan has an initial fee of $53 and costs an additional $0.08 per mile driven

Answers

9514 1404 393

Answer:

260 miles$73.80

Step-by-step explanation:

The cost of each plan (y) is the sum of the initial fee and the product of the mileage charge and the number of miles (x).

First Plan: y = 40 +0.13x

Second Plan: y = 53 +0.08x

__

We can find when the costs are the same by solving this system of equations. A way to do that is to subtract the second equation from the first:

  (y) -(y) = (40 +0.13x) -(53 +0.08x)

  0 = -13 +0.05x

Multiplying by 20 gives ...

  0 = -260 +x

Adding 260, we have ...

  x = 260

The plans cost the same for 260 miles of driving.

__

The cost of the plans for that distance is ...

  y = 40 +0.13x = 40 +0.13(260) = 40 +33.80

  y = 73.80

The cost when the two plans cost the same is $73.80.

100 POINTS! I WILL MARK BRAINLIEST. ONLY ANSWER IF YOU KNOW HOW TO DO IT. RANDOM ANSWERS WILL BE REPORTED! :)

Answers

Answer:

the cords are 4 -2

Step-by-step explanation:

Answer:

First pic (4, -2) second pic (-3, 2)

what is the multiplicative rat of change of the function?
2/3
3/4
4/3
3/2

Answers

Answer:

3/4

Step-by-step explanation:

The "multiplicative rate of change" refers to the rate at which the function increases. The rate of exchange below is [tex]\frac{3}{4}[/tex] because if you multiply this to every value of y, the product is the next value of y.

[tex]\frac{3}{2}[/tex] x [tex]\frac{3}{4}[/tex] = [tex]\frac{9}{8}[/tex] [tex]\frac{9}{8}[/tex] x [tex]\frac{3}{4}[/tex] = [tex]\frac{27}{32}[/tex][tex]\frac{27}{32}[/tex] x [tex]\frac{3}{4}[/tex] = [tex]\frac{81}{128}[/tex]

If the function continues, the next value would be: [tex]\frac{243}{512}[/tex]

Such constant rate causes an "exponential growth."

Sarah and Eva took a road trip. Sarah drove two-fifths of the miles. If she drove 128 miles , how many total miles did they drive?


I need the answer without x being the equal. thanks!

Answers

Answer: 320 miles

Step-by-step explanation:

Let the miles that they drove be represented by x.

Since Sarah drove two-fifths of the miles which is 128 miles, then the total miles would be:

= 2/5 × x = 128

0.4 × x = 128

0.4x = 128

x = 128/0.4

x = 320

The total miles is 320 miles.

How do you graph g(x)=f(x)+5

Answers

Make a positive line going through (0, 5)

What is it called when you must give something up in order to get something else?

Answers

Answer:

NEVER GONNA GIVE U UP

Step-by-step explanation:

NEVER GONNA LET U DOWN

Match the vocabulary terms to the correct definitions.

1. the set of second coordinates in a relation, all possible y values in a function
linear function
2. a function which has one or two variables with no powers, this functions’ graph will always be a straight line
domain
3. the set of first coordinates in a relation, all possible x values in a function
range
4. a function which contains an expression within absolute value symbols
absolute value function

Answers

Answer:

Linear Function - A function that has one or two variables with no powers, this graph will always be a straight line.  Domain - the set of second coordinates in a relation, all possible y values in a function .                           Range -    the set of first coordinates in a relation, all possible x values in a function . Absolute Value function - A function which contains an expression within absolute value symbols .                                                                                                                   Step-by-step explanation: To be honest i guessed so if theses are wrong i am sorry . I really just wanted to help .  

Linear Function - A function that has one or two variables with no powers, this graph will always be a straight line.  

Domain - the set of second coordinates in a relation, all possible y values in a function .                          

Range -    the set of first coordinates in a relation, all possible x values in a function . Absolute Value function -

A function which contains an expression within absolute value symbols .                                                                                                                  

Step-by-step explanation: To be honest i guessed so if theses are wrong i am sorry . I really just wanted to help .  

i really need help please!!!

Answers

Answer:

5x-4y=0

Step-by-step explanation:

[tex]\frac{5-0}{4-0} =\frac{y-0}{x-0} \\ 5x-4y=0[/tex]

Which of the following represents the distributive property?

2x+3 = 2(x+3)
2(x +3) = 2x +6
2x+3 = 3(x+2)
2(x+3) = x +6

Answers

Answer:

2(x+3)=2x+6

Step-by-step explanation:

Because You multiply 2*x and 2*3.

The X is a variable and it actually equals to 1. so it's basically 2*1

After you multiply 2*x and 2*3 you will get 2x+6

B. 2(x+3)=2x+6

Have a nice day!

Mrs. Zimmerman’s students build the first letter of their names out of wood. Holly builds an H using rectangles with the dimensions shown.

How many square inches of wood does Holly use to create the letter H?

Answer Choices: A, 44 in.² B, 60 in.² C, 80 in.² D, 120 in.²

Answers

Answer:

Answer: 80in^2

Step-by-step explanation:

i got it right, so its right...

Find the measure of each angle

Answers

Answer: x=36°

Step-by-step explanation:

The four interior angles of a quadrilateral always equal 360°, so:

(x+16)+(4x-8)+(4x-8)+x=360

Combine like terms:

360=10x+0

360=10x

36=x

Answer:

In image below

Step-by-step explanation:

1, 4/3,16/9
Find the 9th term.

Answers

Answer:

The 9th term of the sequence is:

[tex]a_9=\frac{65536}{6561}[/tex]

Step-by-step explanation:

Given the sequence

1, 4/3,16/9

computing the ratios of all the adjacent terms

[tex]\frac{\frac{4}{3}}{1}=\frac{4}{3},\:\quad \frac{\frac{16}{9}}{\frac{4}{3}}=\frac{4}{3}[/tex]

The difference between all the adjacent terms is the same and equal to

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

A geometric sequence has a constant ratio 'r' and is defined by

[tex]a_n=a_1\cdot r^{n-1}[/tex]

As

[tex]a_1=1[/tex][tex]r=\frac{4}{3}[/tex]

so substituting [tex]a_1=1[/tex] and [tex]r=\frac{4}{3}[/tex] in the nth term of the equation

[tex]a_n=a_1\cdot r^{n-1}[/tex]

[tex]a_n=\left(\frac{4}{3}\right)^{n-1}[/tex]

Now, substitute n = 9 to determine the 9th term

[tex]a_9=\left(\frac{4}{3}\right)^{9-1}[/tex]

[tex]a_9=\left(\frac{4}{3}\right)^8[/tex]

[tex]a_9=\frac{4^8}{3^8}[/tex]

[tex]a_9=\frac{65536}{6561}[/tex]

Therefore, the 9th term of the sequence is:

[tex]a_9=\frac{65536}{6561}[/tex]

Which value of x satisfies the equation below

Answers

Answer:

20

Step-by-step explanation:

2x + 10 = 50

       -10  -10

2x = 40

x = 20

A standard six-sided die is rolled. What is the probability of rolling a number greater than 5 ? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

Answers

Answer:

the probability is one in 6

Step-by-step explanation:

there are 6 sides on a basic die and so the only number higher than 5 is 6. you have a 1/6 chance.

find rotational symmetry
sorry about the cringy drawing but y'all get the idea right​

Answers

Step-by-step explanation:

The rotational symmetry is 4

Answer:

Rotational symmetry is 4 and symmetry is 4

Joe’s Coffee is having a stained glass window installed on their front door. Approximately how much glass will be needed to create the stained glass window?
PLSS USE STEPSSS!!!!
A) 2.4
B) 9.6
C) 11
D) 38.5

Answers

Correct option :

[tex]\color{plum}\tt \: D) 38.5 [/tex]

Steps to derive correct answer :

Diameter of the stained glass window Joey needs = 3.5

Area of the window = quantity of glass Joey needs

Area of the window :

[tex] = \tt\pi {r}^{2} [/tex]

[tex] = \tt3.14 \times 3.5 \times 3.5[/tex]

[tex] =\tt 3.14 \times 12.25[/tex]

[tex] =\tt 38.46[/tex]

38.46 can be rounded off to 38.5.

Therefore, quantity of glass needed to make the stained glass window = 38.5

6z + 9 - 7 = 4z + 12

Answers

Answer:

z=5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

6z-4z=10

z=5

PlZ Make me brainliest

rotate the triangle through 180 degrees about the origin?

Answers

Answer:

Step-by-step explanation:

Uh can you give us a more clear question?

Can Somebody Please Help Me With This!!

Answers

Answer:

I think A

Step-by-step explanation:

sorry if it is not correct hope it helps

Answer:

I cant see the numbers clearly but I think its 24

Daniel works for 3 hours one day he gets paid $6 an hour.​

Answers

he’d get $18 dollars for working 3 hours

Which expression is equivalent to 3k + 5l + 6l + 2k?

A) 8k + 8l

B) 5k + 11l

C) 5k

D) 16

Answers

Answer:

B)5k + 11l

Step-by-step explanation:

3k + 5l + 6l + 2k collect like terms

3k + 2k + 5l + 6l

5k + 11l

hope it's helpful ❤❤❤❤

THANK YOU.

The expression is equivalent to the given expression is 5k+11l. Therefore, option B is the correct answer.

What is an equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is 3k+5l+6l+2k.

Group like terms and simplify, we get

(3k+2k)+(5l+6l)

= 5k+11l

The expression is equivalent to the given expression is 5k+11l. Therefore, option B is the correct answer.

To learn more about an equivalent expression visit:

https://brainly.com/question/28170201.

#SPJ5

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