The sum of two number is 22 and difference is 8. Find the numbers.

Answer:

y = 14/3 and 2

x = -13/3 and 1

(-13/3, 14/3) and (1, 2)

Step-by-step explanation:

[tex]x + 2y = 5 - - - (a) \\ {x}^{2} - {y}^{2} = - 3 - - - (b)[/tex]

for equation (a)

make x the subject of the formular:

[tex]x = 5 - 2y - - - (c)[/tex]

for equation (b)

[tex] {x}^{2} - {y}^{2} = - 3[/tex]

substitute for x as 5 - 2y in equation (b):

[tex] {(5 - 2y)}^{2} - {y}^{2} = - 3 \\ (25 - 20y + 4 {y}^{2} ) - {y}^{2} = - 3 \\ 25 - 20y + 3 {y}^{2} = - 3 \\ {3y}^{2} - 20y + 28 = 0 \\ (3y - 14)(y - 2) = 0[/tex]

therefore,

[tex]y = \frac{14}{3} \: \: and \: \: 2[/tex]

substitute for all values of y in equation (c):

for y = 14/3:

[tex]x = 5 - 2( \frac{14}{3} ) \\ \\ x = 5 - \frac{28}{3} \\ \\ x = - \frac{13}{3} [/tex]

for y = 2:

[tex]x = 5 - 2(2) \\ x = 5 - 4 \\ x = 1[/tex]

Answer:

(1, 2)

(-13/3, 14/3).

Step-by-step explanation:

x + 2y = 5

x² - y² = -3​

From the first equation x = 5 - 2y

Substitute for y in the second equation:

(5 - 2y)^2 - y^2 = -3

25 + 4y^2 - 20y - y^2 = -3

3y^2 - 20y + 28 = 0

Factoring:-

(3y - 14(y  -  2)   = 0

y = 2, 14/3.

So when y = 2, x = 5 - 2(2) = 1.

When y = 14/3, x = 5 - 2(14/3) = -13/3.

Checking the results in the second equation:

(1, 2):-

1^2 - 2^2 = -3    Correct.

(-13/3, 14/3):-

(-13/3)^2 - (14/3)^2 = -3   Correct.

Answer:

1. 32

2. 100

3. 36

..........................

Answer:

32

100

36

Step-by-step explanation:

Answer:

20 weeks

Step-by-step explanation:

200-1.5w=180-0.5w

You can double-check by substituting 20 for w (weeks), if it is equal, then the equation is correct.

Answer:

sum is -(10x + 1)

Step-by-step explanation:

[tex]( - x - 7) + ( - 9x + 6) \\ = ( - x - 9x) + (6 - 7) \\ = - 10x - 1 \\ = - (10x + 1)[/tex]

Answer:

[tex]( - x - 7) + ( - 9x + 6) \\ = - x - 7 - 9x + 6 \\ = - 10x - 1 \\ thank \: you[/tex]

Answer:

D

Step-by-step explanation:

x + 5 > 11

is the same as

x > 6

and because it is ">" and not ">=", the solution point is not included.

therefore the right graph is D and not C. an empty little circle means "excluded", while a filled, black circle means "included".

Here is your answer. Hope this helps you.

Answer:

51

Step-by-step explanation:

15= a/3 -2

17= a/3

51=a

x - 1 is the total number of weeks minus the first  

Answer: x-1 is number of weeks-1st week

Step-by-step explanation:

x represents the number of weeks bring the first.

-1 is to remove the first week that costs $300

Answer:

Step-by-step explanation:

Given:

Rewrite it as:

Since all A, B, C are integers from 0 to 9, A can be 1 only, then we have:

or

It gives us:

The equation is:

Answer:

ABC=198

Step-by-step explanation:

If you do 11+99+88 then you get 198 which is true to the problem that you have.

Answer:

720

Step-by-step explanation:

He has 8 books. He knows the placement of 2... so

8 - 2 = 6

To find the total... 6!

6*5*4*3*2*1 = 720

The required number of the ways the book is arranged on the shelf is 720 ways.

Given that,
Kareem is putting 8 books in a row on his bookshelf. He will put one of the books, Pride, and Prejudice, in the first spot. He will put another of the books, Little Women, in the last spot. In how many ways can he put the books on the shelf is to be determined.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

here,
There are 8 books to be arranged, 1st and last place is fixed,
now remaining books = 8 - 2 = 6
now, a number of combinations can be formed with the number 6,
= 6!
= 6×5×4×3×2×1
= 720

Thus, the required number of the ways the book is arranged on the shelf is 720 ways.

Learn more about permutations and combinations here:

https://brainly.com/question/2295036

#SPJ5

Answer: The angles are 36 and 144.

Step-by-step explanation:

Let the linear pairs be 4x and x

so

4x + x = 180 (being linear pair)

or, 5x = 180

or, x = 180/5

so, x = 36

so, 4x = 4*36 = 144

Answer:

A) y = 3x – 2

Step-by-step explanation:

Just check the results: when you put the numbers of the x-colum from the table, the result will be the corresponding numbers of the y-colum. and that means this is the right equation

Answer:

[tex]The\,\,derived\,\,equation\,\,is\\6x+2y=-8[/tex]

Step-by-step explanation:

Given, equation of line

[tex]6x+2y = 10......(i)\\\\Parallel\,\,line\,\,of\,\,the\,\,equation\,\,(i),\\6x+2y=k.....(ii)\,\,;[here,\,\,k\,\,is\,\,a\,\,constant]\\\\The\,\,line\,\,(ii)\,\,passes\,\,through\,\,the\,\,point\,\,(-3,5),\\6*(-3)+2*(5)=k\\So,\,\,k=-8\\\\Therefore,\,\,the\,\,derived\,\,equation\,\,is\\6x+2y=-8[/tex]

Hope you have understood this.....        

ask me if you have any confusion.....        

if you liked it pls mark it as the brainliest

Step-by-step explanation:

hope it helps you check it if there is a mistake sorry!! for that

Answer: Yes, the set of real numbers is closed under addition.

Explanation:

Let x and y be two real numbers. Their sum x+y is some other real number. This is what it means when we say the set of real numbers is closed under addition. Taking any two numbers and adding them will get us some other real number.

There is no way to have x+y be nonreal while x,y are both real.

Answer:

635.75

Step-by-step explanation:

90π + 2π(7.5)²

~Simplify

90π + 2π(56.25)

~Multiply

282.5 + 2(176.625)

~Simplify

282.5 + 353.25

635.75

All this was simplified using PEMDAS.

Best of Luck!

Answer:

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

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Given

[tex]\sqrt[3]{\sqrt{729} }[/tex]

Evaluate from the ' inside- out ' , that is

[tex]\sqrt{729}[/tex] = 27 , then

[tex]\sqrt[3]{27}[/tex]

= 3

Answer:

3

Step-by-step explanation:

[tex] \sqrt[3]{ \sqrt{729} } [/tex]

[tex] = \sqrt[3]{ \sqrt{ {27}^{2} } } [/tex]

[tex] = \sqrt[3]{27} [/tex]

[tex] = \sqrt[3]{ {3}^{3} } [/tex]

[tex] = 3[/tex] ✅

the one on the left is (2,2) the one on the right is (8,2)

Answer:

Population of Africa in 2003 is 22.5 million

population of Africa in 1950 is 1 million - 22.5 million /5

21.5million / 5

21500000/5

4300000

4.3 million people

Given Polynomial

[tex]\\ \sf\longmapsto x^2y^3+a^3b^4-7[/tex]

Calculate degrees of all variables

B has highest degree

Hence degree of polynomial is 4

It is a tetranomial

Answer:

Step-by-step explanation:

In reality it is :  [tex](x-\frac{1}{x} )^5\\[/tex]

[tex]Pascal'sTriangle\\\\\begin{array}{cccccc}1\\1&1\\1&2&1\\1&3&3&1\\1&4&6&4&1\\1&5&10&10&5&1\\\end{array}\\\\\\(x-\frac{1}{x} )^5\\\\=x^5+5*x^4*\frac{1}{x} *(-1)+10*x^3*\frac{1}{x^3}*(-1)+5*x*\frac{1}{x^4} +\frac{1}{x^5} *(-1)\\\\\\\boxed{(x-\frac{1}{x} )^5=x^5-5x^3+10x-\frac{10}{x} +\frac{5}{x^3} -\frac{1}{x^5} }[/tex]

Answer:

[tex]2^{1} + 3^{1}[/tex], [tex]2^{3} - 2^{1}[/tex], [tex]3^{2}[/tex]

Step-by-step explanation:

[tex]3^{2}[/tex] = 9

[tex]2^{3} - 2^{1}[/tex] = 6

[tex]2^{1} + 3^{1}[/tex] = 5

Step-by-step explanation:

Simplify the expressions

[tex]2 {}^{3} - 2 {}^{1} = 2 {}^{3} - 2 = 8 - 2 = 6[/tex]

[tex]2 + 3 = 5[/tex]

[tex] {3}^{2} = 9[/tex]

So the expressions from least to greatest is

[tex]2 {}^{1} + 3 {}^{1} < 2 {}^{3} - 2 {}^{1} < 3 {}^{2} [/tex]

Hi! I'm happy to help!

First, we need to get our two equations, so we need to look at what facts we have throughout the equation. It tells us that x is 3 times as much as y. We can use this to write our first equation:

3y=x

All of the interior angles inside of a triangle add up to 180°, and because we already have 3 angles, we can use this information to make our second equation:

x+y+45=180

Now, we have to use these equations together to get our answer.

Since we can replace 3y for x (first equation) we can replace it in our second equation:

3y+y+45=180

We edit both sides of the equation in the same way to get the same outcome, but to simplify. Since we are solving for y, let's isolate it by subtracting 45 from both sides:

3y+y+45=180

       -45  -45

3y+y=135

Let's combine the 3y and y to make things simpler:

4y=135

From here, we divide both sides by 4, to isolate y:

y=33.75

Now that we have our y value, we can use our first equation to solve for x:

3y=x

3(33.75)=x

101.25=x

We used our equations to get both our x and y values: 33.75, and 101.25.

I hope this was helpful, keep learning! :D

Answer:

5/4 or 1 . 1/4

Step-by-step explanation:

3/4 + 1/2 = 5/4 or 1 . 1/4