The diagram shows the construction of the perpendicular bisector of AB.

Answer:

[tex]\frac{1}{x-1}[/tex] - [tex]\frac{1}{x+2}[/tex] - [tex]\frac{3}{(x+2)^2}[/tex]

Step-by-step explanation:

Expressing as a partial fraction

[tex]\frac{9}{(x-1)(x+2)^2}[/tex] = [tex]\frac{A}{(x-1)}[/tex] + [tex]\frac{B}{(x+2)}[/tex] + [tex]\frac{C}{(x+2)^2}[/tex] ( A, B, C are numerical values to be found )

Multiply both sides by (x - 1)(x + 2)²

9 = A(x + 2)² + B(x - 1)(x + 2) + C(x - 1)

Choose value for x that are zeros of the factors and substitute into right side

x = - 2 : 9 = - 3C ⇒ C = - 3

x = 1 : 9 = 9A ⇒ A = 1

x = 0 : 9 = 4A - 2B - C , that is

9 = 4 - 2B + 3 = - 2B + 7 ( subtract 7 from both sides )

2 = - 2B ⇒ B = - 1, then

A = 1, B = - 1, C = - 3

Thus

[tex]\frac{9}{(x-1)(x+2)^2}[/tex] = [tex]\frac{1}{x-1}[/tex] - [tex]\frac{1}{x+2}[/tex] - [tex]\frac{3}{(x+2)^2}[/tex]

Answer: There are a total of 12 rocks

Step-by-step explanation:

Answer:

[tex] \huge \frac{4}{9 {x}^{4} {y}^{6} }[/tex]

Step-by-step explanation:

[tex] \huge \bigg( \frac{2 {x}^{ - 2} }{3 {y}^{3} } \bigg)^{2} \\ \\ \huge = \frac{ {2}^{2} ( {x}^{ - 2})^{2} }{ {3}^{2} ( {y}^{3} ) ^{2} } \\ \\ \huge = \frac{4 {x}^{ - 4} }{9 {y}^{6} } \\ \\ \huge = \frac{4}{9 {x}^{4} {y}^{6} } \\ [/tex]

Answer:

9x-6y+3xy+9

Step-by-step explanation:

firstly rearrange

9x-6y-6xy+9xy+9

then simplify those that can

-6xy + 9xy = +3xy

hence

9x-6y+3xy+9

Answer:

25/26 or 96.2%

Step-by-step explanation:

In the alphabets, we have 26 letters

If we remove Z, we have A -Y which is 25 alphabets

The question requires us to find the theoretical probability of choosing any other letter that is not Z

Probability= ratio of other alphabets that are not z to the number of letters in the alphabets.

Probability = 25/26 (as a fraction)

Probability = 0.9615 x 100 = 96.2% (as a percentage and to the nearest tenth)

Answer:

a. you cannot multiply both sides by x because you do not know what x is.

Step-by-step explanation:

Given:

[tex]\frac{1}{x} + 3 = \frac{3}{x}[/tex]

Required

Select which of the option that applies

Considering (a):

A is incorrect:

Because: Multiplying both sides by x has nothing to do with whether the value of x is known or not

Considering (b):

B is incorrect:

Substitute 0 for x in the given expression

[tex]\frac{1}{0} + 3 = \frac{3}{0}[/tex]

[tex]Und efi ned[/tex]

Both sides of the equation are undefined

However, you cannot assume x to be 0

Considering (c):

C is correct:

Start by multiplying both sides by x

[tex]x (\frac{1}{x} + 3) = \frac{3}{x} * x[/tex]

[tex]1 + 3x = 3[/tex]

Then, subtract 1 from both sides

[tex]1 - 1 + 3x = 3 - 1[/tex]

[tex]3x = 2[/tex]

Divide through by 3

[tex]x = \frac{2}{3}[/tex]

Considering (d):

D is incorrect;

Because, the equation is linear

Answer:

3+X=[3+X]4

Step-by-step explanation:

Let the number be X

we add x by three = 3+x

the sum of 3+x is 3+x

so we multiply the whole sum by 4 which is [3+x]4

so the ans is 3+x=[3+x]4

GOODLUCK ;]

Answer:

x=3

Step-by-step explanation:

1) get rid of the parenthesis by distributing the 2. You will get 8x-6-8=4+2x

2) Now combine like term on each side of the equal sign. You will get 8x-14=4+2x

3) Move the 14 to the right side of the equation making it +14 and move your 2x to the left side of the equation making it -2x. You will get 8x-2x=4=+14

4) calculate each side. You will get 6x=18

5) Divide both sides. You will get x=3

Answer:

Step-by-step explanation:

Since it's a triangle all it's interior angles sum up to 180°

The triangle is isosceles which means two of it's angles are equal

From the question

[tex]m\angle B = m\angle C = 41 \degree[/tex]

So to find [tex]m \angle A[/tex] add up all the angles and equate it to 180° and solve for A

That's

[tex]m\angle A + m\angle B + m\angle \: C = 180 \\ m\angle A = 180 -m\angle B - m\angle \: C \\ m\angle A = 180 - 41 - 41 \\ = 180 - 82[/tex]

We have the final answer as

[tex]m\angle A = 98[/tex]

Hope this helps you

Answer:

Domain: 1, 6

Range: 4

Step-by-step explanation:

The Domain is the first coordinate which is x

The Range is the second coordinate which is y

Hope This Helps :)

Answer:

its volume

Step-by-step explanation:

Answer:

Volume is the unit that measures space of an object

Answer:

Step-by-step explanation:

x^2 - 8x + 16 = (x - 4)^2

the first one

Answer:

1:4

Step-by-step explanation:

No of girls :3

No. Of boys:12

Hence 3:12

1:4

Answer:

The midpoint between 2 points is (1,2.5) .

Step-by-step explanation:

We have to apply midpoint formula :

[tex]midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]

[tex]let \: (x1,y1) \: be \: ( - 8,4)[/tex]

[tex]let \: (x2,y2) \: be \:(10 , - 9)[/tex]

[tex]midpoint = ( \frac{ - 8 + 10}{2} , \frac{4 + ( - 9)}{2} )[/tex]

[tex]midpoint = ( \frac{2}{2} , \frac{ - 5}{2} )[/tex]

[tex]midpoint = (1,2.5)[/tex]

Answer:

Yes.

Step-by-step explanation:

The sum of two odd numbers is always even. The product of two or more odd numbers is always odd. The sum of an even number of odd numbers is even, while the sum of an odd number of odd numbers is odd.

Answer:

Step-by-step explanation:

In this problem (word problem), we are examined on how to express equations from words.

let us initialize some variables

let the length of the first piece (the short piece) be x

and that of the second(the longer piece) be 5x

given that the total length is 96 cm

Also from the problem statement, the total length can be expressed as

5x+x= 96

6x= 96

divide both sides by 6 to solve for x

x= 96/6

x= 16

now the longer side = 5x

        the longer side= 5*6

       the longer side = 30 cm

Answer:

he got 4problems wrong

can you please give me brainliest

Answer:

Pete's: [tex]f(x) = 20x + 60[/tex]

Carla's: [tex]f(x) = 40x + 20[/tex]

Step-by-step explanation:

Let's assume that [tex]x[/tex] is the amount of rooms painted, and [tex]f(x)[/tex]

For Pete's Painting Company, they charge a flat fee of $60, so we will have a constant of 60.

They also charge 20$ per room, meaning that we will multiply 20 by [tex]x[/tex], the amount of rooms painted.

This gets us the function [tex]f(x) = 20x + 60[/tex]

For Carla's Creative Colors, they charge 20$ to hire the workers, meaning this will be our constant.

They also charge $40 a room, meaning we will multiply 40 by [tex]x[/tex], the amount of rooms painted.

So the function is  [tex]f(x) = 40x + 20[/tex].

Hope this helped!

Answer:

y+8 inches

Step-by-step explanation:

since it's eight inches taller we have to add 8 inches to niki's height

Answer:

the correct answer is 20 .

Step-by-step explanation:

x^2 - ( x + 4 ) - y = ?

6^2 - ( 6 + 4 ) - 6 = ?

36 - ( 10 ) - 6 = ?

26 - 6 = 20

Answer:

3x-20

Step-by-step explanation:

I had this test yesterday and this was the correct answer

The equation  D. y = 20 - 3x Megan use to find the amount of change.

An equation is is a tool that expresses two equality of two given expressions.

According to the given question Megan bought 3 pounds of apples that cost x dollars per pound. She gave the cashier a 20-dollar bill.

Let y denotes the change she received.

If 1 pound of apple cost x dollars then 3 pounds of apples will cos 3×x = 3x dollars.

∴ y = 20 - 3x.

learn more about equations here :

https://brainly.com/question/13795677

#SPJ2

Answer:

Length of the square poster = 6.1 in

Step-by-step explanation:

Area of a square poster = 37 in^2

Area of a square = length^2

37 = lenght ^2

Find the square root of both sides

√37 = √ length ^2

Length = 6.0828 in

Approximately

Length of the square poster = 6.1 in

Step-by-step explanation:

Let a, b, c be the measures of the interior angles and x, y, z be the measures of the exterior angles of the triangle. Where x and adjacent to a, y is adjacent to b and z is adjacent to c.

By interior angle sum postulate of a triangle:

a + b + c = 180°... (1)

Therefore, by remote interior angle theorem:

x = b + c.... (2)

y = a + c..... (3)

z = a + b.... (4)

Adding equations (2), (3) & (4)

x + y + z = b + c + a + c + a + b

x + y + z = 2a + 2b + 2c

x + y + z = 2(a + b + c)... (5)

From equations (1) & (5)

[tex]x + y + z = 2 \times 180 \degree \\ x + y + z = 360 \degree \\ x + y + z = 4 \times 90\degree \\ x + y + z = 4 \: right \: angles[/tex]

Thus, the sum of exterior angles so formed is equal to four right angles.

Proved.

Answer: Your answer is 7x-13.

Answer:

80

Step-by-step explanation:

6+4=10

10x8=80

Hope this helped!!! Have a nice day and please mark me brainliest!!!

UwU

Step-by-step explanation:

8(n + 6) = 4

8n + 48 = 4

8n = 4 - 48

8n = -44

n = - 5.5

Factors of 51: 1, 3, 17, 51

Factors of 68: 1, 2, 4, 17, 34, 68

As you can see the greatest common factor of both numbers is 17.

Therefore, the answer is C.

Best of Luck!

Answer:

b^a= 4^3 =64

Step-by-step explanation:

4^3

that is 4*4*4

hope this helped!

Answer:

1.1

Step-by-step explanation:

As we move left, we multiply by 10 to obtain the new place value.

Answer: 9^-16

Step-by-step explanation:

If an exponents have the same base and are  being multiplied together, all you do is just add the exponents and make the base stay the same

9[tex]9^{-53} * 9^{37} = 9^{-16}[/tex]

Negative exponents can be rewritten as positive exponents if you put them in the denominator.

[tex]x^{-a}=\frac{1}{x^a}[/tex]

Using this rule, we can rewrite the equation.

[tex]9^{-53}*9^{37}=\frac{1}{9^{53}}*9^{37}[/tex]

[tex]\frac{9^{37}}{9^{53}}[/tex]

Then, we can use exponent division rules.

[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

[tex]\frac{9^{37}}{9^{53}}=9^{37-53}[/tex]

[tex]9^{-16}[/tex] or [tex]\frac{1}{9^{16}}[/tex]

Hope this helps.

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