Why is the denominator of each fraction 12?
Pls help me

Answer: X^2 - 4x -12

1. Distribute :

(x−6)(x+2)

x(x+2)-6(x+2)

2. Distribute:

x(x+20-6(x+2)

X^2 +2x-6(x+2)

3. Distribute:

X^2+2x-6(x+2)

X^2+2x-6x-12

4. Combine like terms:

x^2+2x-6x-12

solution:X^2-4x-12

Answer:

Yes the triangles are congruent.

Step-by-step explanation:

You are going to move all the points 2 units to the left and  4 units up.

Look at the vertices of the triangle.  The points are (0,1) and (-5,0) and (2,-5).  If we moved all three of these points to places to the left and 4 up, they would be at (-2,4), (-7,4) and (0,-1)  This would make a image that is a congruent triangle.  You have just translated the original triangle 2 places to the left and 4 places up.

Answer:8

Step-by-step explanation:

2+6=8

Answer:

8 ghdhlhskgslhdlhskgz

Answer:

i think it is 5 feet

Step-by-step explanation:

i hope this helps

Answer:

c

Step-by-step explanation:

I definitely didn't searched it

[tex](5x^{4} )^{3} \\=5x^{4*3} \\=5x^{12}[/tex]

I used the law of exponents as indicated below:

[tex](x^{n} )^{m} \\=x^{n*m} \\=x^{nm}[/tex]

Answer:

S = ( P - 2L) / 2

Step-by-step explanation:

P = 2S + 2L

P - 2L = 2S

(P - 2L) / 2 = S

Hope this helps :D

The 'x' and 'y' variables and the 4 angles are highlighted in the boxes

Answer:

[tex]\frac{-1}{8}[/tex]

Step-by-step explanation:

To make the -3 positive, you put the power under 1.

[tex]\frac{1}{(-2)^{3} }[/tex]  This means [tex]\frac{1}{-2}[/tex] x [tex]\frac{1}{-2}[/tex] x [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{-8}[/tex]  Which means the same as[tex]\frac{-1}{8}[/tex]

radius = 30 in

Area = 900 in^2

To calculate the area of a circle, use the equation A = pi r^2

His mistake was that he did not multiplicate by pi (3.1416)

The actual area = (3.1416)(30)^2

A = 2827.44 in^2

Answer: [tex]y \geq 1[/tex]

Step-by-step explanation:

The range of a function is the set of y-values.

Answer:11

Step-by-step explanation: because 7+4=11

Imagine putting a mirror on the page and adding a reflection. You must identify the line in which the shape is mirrored when describing a reflection. The sum of the transformations can be referred to as a single transformation.

Imagine putting a mirror on the page and adding a reflection. You must identify the line in which the shape is mirrored when describing a reflection. Every point of a shape will be separated from the line of reflection by the same amount as the reflected point is separated from the line.

There are occasions when a shape is altered in more than one step, such as when a rotation is followed by a reflection. Typically, the sum of the transformations can be referred to as a single transformation.

Enlargements are a particular kind of transformation where the original shape's size is altered by multiplying it by a scale factor to make it bigger or smaller. To employ a center of enlargement, lines must be drawn from the center via the original shape's vertices. They are known as ray lines.

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Answer: D) there are no solutions.

Step-by-step explanation:

Answer:

It's (7, 13) not sure how to explain that

Given:

The objective is to find the number.

Explanation:

Consider the unknown number as x,

First, four times the number can be written as 4x.

Twenty more than 4 time the number will be,

Then, twice the number can be represented as 2x.

And the difference between 2 and twice the number will be,

Now, equate both the equations (1) and (2).

Hence, the unknown number is -3.

Since we are rolling a die twice

The possible out come of rolling a die is

Therefore, the probability of getting a 4 on every roll is

From the sample outcome above

P(of 4) = 1/6

Therefore

Therefore, thr porbability is 0.0278

Answer:

27

Step-by-step explanation:

f(x) = 5x + 7

f(4) = 5(4) + 7

= 20 + 7

f(4) = 27

The interest rate needed to make $3,472.32 from simple interest on a principal of $1,200.00 over 9 years is 21.04% per year.

Simple interest is expressed mathematically as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is rate and t is the time period.

Given the data in the question;

Plug the given values into the simple interest formula and solve for r

A = P( 1 + rt )

r = (1/t)(A/P - 1)

r = ( 1/9 )( $3472.3/$1200 - 1)

r = ( 1/9 )( 2.8936 - 1)

r = ( 1/9 )( 1.8936)

r = 0.2104

Convert to percentage

r = 0.2104 × 100%

Rate r = 21.04%

Therefore, the interest rate of the loan is 21.04%.

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Answer:

price ×time×rate/100 40000×6×14/100

33600

The area of rectangle in square inches is 8649 inches .

The subject of mathematics known as mensuration is concerned with measuring geometric shapes and their various characteristics, such as length, volume, shape, surface area, lateral surface area, etc. In fundamental mathematics, learn about mensuration.

Mensuration is the name given to the area, volume, and length of various geometric shapes in mathematics. These shapes can be found in either two or three dimensions.

Mensuration is the process of calculating various shape parameters, such as the perimeter, area, and volume, whereas geometry is the study of the characteristics and relationships between the points and lines that make up different shapes.

the area of rectangle will be =  length *  width

therefore just substituting the values given in the question

thus ,

area will be = 279 * 31

                    = 8649 square inches

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The pounds of the less expensive tea used in the mixture is 10 pounds.

The correct option is Option(1) 10.

Given:

Price of less expensive tea = $2.00

Price of expensive tea = $5.00

Price of custom-blended tea = $4.25

The total price of 40 pounds of custom blended tea = 40 × $4.25

                                                                                       = $170

Let the pounds of the less expensive tea used in the mixture be x pounds.

So, the pounds of expensive tea = 40-x

Now, the equation is

2x + 5(40 - x) = 170

2x + 200 - 5x = 170

3x = 30

x = 10 pounds

Therefore, there are 10 pounds of less expensive tea.

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Answer:

[tex] \frac{18}{4} [/tex]

Step-by-step

4.5

The linear equation is:

y = -6*x + 59

The slope is -6, and means that each hour the distance decreases by 6 miles.

The y-intercept is 59, and it is the initial distance to the waterfall.

A general linear equation in the slope-intercept form is:

y = a*x + b

Where a is the slope (also called the rate of change) and b is the y-intercept.

We know that if the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁).

Here we can define the variables:

y = distance

x = hours.

Then we have two points (8, 11) and (9, 5).

So the slope is:

a = (5 - 11)/(9 - 8) = -6

This means that the distance to the waterfall decreases by 6 miles each hour.

Then the linear equation is like:

y = -6*x + b

To find the value of b we can use any of the given points, I will use (9, 5), this means that:

5 = -6*9 + b

5 = -54 + b

54 + 5 = b

59  = b

This is the y-intercept, and gives the initial distance to the waterfall.

The equation is:

y = -6*x + 59

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Answer:60 =12

Step-by-step explanation:

The principal amount was invested for 8 Years.

In the given question, it is stated that when $314 was invested as the Principal amount, it got an Interest of $175.84 at an interest rate of 7%. We have to find out the total period of time the principal amount was kept and got interested in in order to complete the interest amount of $175.84.

To calculate the Interest, we know that the formula for Simple Interest is:

=> S.I. = (P*R*T)/100, where P = Principal amount, R = Rate of Interest, and T is the Time period. Now, putting values in the formula we get:

=> S.I. = (P*R*T)/100

=> 175.84 = (314*7*T)/100

=> T = 17584/2198

=> T = 8

Hence, we get Invested Time for 8 years.

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The amount for Kai's self employment taxes for the last month is  $407.745  .

In the question ,

it is given that

number of music lessons that Kai taught = 41

per music lesson charge = $65 .

the tax rate for self employment = 15.3%

So, the total amount earned is = (number of classes)*(per class charge)

= 41*65 = $2665  

According to the question .

Kai's self employment tax = 15.3% of total amount earned

On substituting the values , we get

Kai's self employment tax = 15.3% of 2665  

= 0.153*2665

= 407.745

Therefore , The amount for Kai's self employment taxes for the last month is  $407.745  .

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K = 1 is the value when x = - 1 is Factor of equation .

Why do we use the term factors?

f(x) = x^4+ kx³ + 2

x + 1 = 0

x = -1 put in equation

(-1)⁴ + k( -1)³ + 2 = 0

1 - k + 2 =0

k = 1

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