Factor the expression. 8+27 x³

The subtraction of the expression 10√27 - 4√12 is 22√3.

Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more integers together.

In mathematics, subtraction involves removing anything from a group or a number of objects. What is left in the group gets smaller when you subtract.

Consider the expression,

y = 10√27 - 4√12

Now, the number in the root can also be written as:

27 = 3 × 3 × 3

12 = 2 × 2 × 3

Therefore,

y = 10√27 - 4√12

y = 10[ √(3 × 3 × 3) ] - 4[ √( 2 × 2 × 3 ) ]

y = 10 × 3√3 - 4 × 2√3

y = √3 ( 10 × 3 - 4 × 2 )

y = √3 ( 30 - 8 )

y = 22√3

The value of the expression 10√27 - 4√12 is 22√3.

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Explanation:

[tex]g_3 = 6.25[/tex] tells us that the third term is 6.25

The common ratio r = 5/4 = 1.25 tells us how to get the next term. We multiply the third term by 1.25 to get the next term

4th term = (3rd term)*(r) = (6.25)*(1.25) = 7.8125

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To go backwards and find the second term, we will divide by r, which is the inverse operation of multiplication.

2nd term = (3rd term)/r = (6.25)/(1.25) = 5

Use the same idea to find the 1st term

1st term = (2nd term)/r = 5/(1.25) = 4 is the final answer

The number of bottles collected by the high school is 1922 bottles since the total collected bottles is 3627.

The total number of bottles collected by both elementary and high schools is 3627 bottles, which means that the number of bottles collected by the high school can be determined as the total bottles minus the ones collected by the elementary school:

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The logarithm statement log₃ 3 / 2 = 1 / 2 log₃ 3 is a false statement as 1 / 2 log₃ 3 is equal to log₃ √3 and not log₃ 3 / 2.

We are given the logarithm as:

log₃ 3 / 2 = 1 / 2 log₃ 3

We need to tell if it is true of not.

We get that, it is false as 1 / 2 log₃ 3 is equal to log₃ √3 and not log₃ 3 / 2.

So, the statement given will be a false statement.

Therefore, we get that, the logarithm statement log₃ 3 / 2 = 1 / 2 log₃ 3 is a false statement as 1 / 2 log₃ 3 is equal to log₃ √3 and not log₃ 3 / 2.

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Answer:

x=-7

Step-by-step explanation:

Divide both sides by 4: 4(3x+2)/4=-76/4

Simplify; 3x+2=-19

Subtract 2 from both sides: 3x+2-2=-19-2

Solve:3x=-21

divide side by 3: 3x/3=-21/3

simplify: x=-7 B)

Answer:

x = -7

Step-by-step explanation:

Given equation:

[tex]4(3x+2)=-76[/tex]

Distribute:

[tex]\implies 4 \cdot 3x+4 \cdot 2=-76[/tex]

[tex]\implies 12x+8=-76[/tex]

Subtract 8 from both sides:

[tex]\implies 12x+8-8=-76-8[/tex]

[tex]\implies 12x=-84[/tex]

Divide both sides by 12:

[tex]\implies \dfrac{12x}{12}=\dfrac{-84}{12}[/tex]

[tex]\implies x=-7[/tex]

The solution of the equation is the final answer to the problem , $ 240 .

Calculating Simple Interest :

Simple Interest = ( P * R * N ) / 100

where P = Principal Amount

              R  = Rate of Interest

         and N = No. of years for which investment is done

According to question :

P = 1000

R = 6

N = 4

Hence ,

Simple Interest = ( 1000 * 6 * 4 ) / 100

                          = 240

Therefore , after college graduation in 4 years the interest received would be $240 .

The solution of the equation is the final answer to the problem .

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The slope and y-intercept of the line are  -3 and -6 respectively.

The graph is a linear function.

The graph can be represented in a slope intercept form as follows;

y = mx + b

where

Therefore, using (1, -9)(-4, 6)

m = 6 - (-9) / -4  - 1

m = 6 + 9 / -5

m = 15 / -5

m = -3

Therefore,

slope = -3

Let's find the y-intercept as follows;

(1, -9)

y = -3x + b

-9 = -3(1) + b

b = -9 + 3

b = -6

Therefore, the slope and y-intercept of the line are -3 and -6 respectively.

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Answer:

I don't think any are parrallel.

Step-by-step explanation:

If you look at the angles, they are different. Just slightly. So the rays making the angles would be at different angles. If they were the same angles the rays making the angles would be the same not allowing them to touch making them parallel. But since they are not I don't think they are parallel.

Answer:

No

Step-by-step explanation:

The correct answer is -406,726

A negative minus a negative is the same as a negative plus a positive

-621,044 + 214,318 = -406,726

Answer:

(8w+8x)(8w+8x)+(3w+10y)(3w+10y)+(4y+8x)(4y+8x)

Step-by-step explanation:

The sequence of transformations that take quadrilateral ABCD to quadrilateral A'B'C'D' is given by:

Examples of transformations are given as follows, along with explanations on the changes caused by the transformations.

As a dilation changes the side lengths the figure, a dilated figure is not congruent to the original figure, hence a dilation does not happen for this problem.

The first change was in the inclination and orientation of the figure, hence it underwent a rotation. From the movement of the vertices, for example, A to the bottom to the top, B from right to left, the rotation was of 90º clockwise.

Then, the function had the base at the same position, however it moved left, hence the second transformation was a translation left.

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The congruent figures are given as follows:

Congruent figures are figures whose outer side lengths have the same measures. They may have different orientations, but the outer side lengths have to be the same.

Hence the congruent figures in this problem are given as follows:

They have different orientations(rotated), but same side lengths.

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Answer:

$12.5xy

Step-by-step explanation:

y = how much the jobs pays

x = hours of work

25/2

= 12.5xy

The statement [tex]log_{2} 4 + log_{2} 8 = 5[/tex] is true.

We have been given two logarithm terms that is the first term is [tex]log_{2} 4[/tex] and second term is [tex]log_{2} 8[/tex].

The properties of logarithm that we are going to use are

          [tex]log a^{m} = m *log a[/tex]  and [tex]log_{a} a = 1[/tex]

First we will find the value of the two terms by operating the above mentioned properties of logarithm to obtained the values of the logarithm.

Thus,

                          [tex]log_{2} 4 = log_{2} 2^{2} \\ = 2* log_{2} 2\\ = 2*1\\ = 2[/tex]

Similarly,    

                            [tex]log_{2} 8 = log_{2} 2^{3} \\ = 3* log_{2} 2\\ = 3*1\\ = 3[/tex]        

Now adding both the terms by substituting its respective values which we have calculated above, we get

                   [tex]log_{2} 4 + log_{2} 8 = 2+3 = 5[/tex]  

Thus,  we have proved that    R.H.S = L.H.S  

Hence the statement is  [tex]log_{2} 4 + log_{2} 8 = 5[/tex] is true.

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Step-by-step explanation:

parallel means it has the same slope.

the slope is always the factor of x : -3/2

I guess the needed equation is in slope-intercept form :

y = ax + b

"a" being the slope, "b" being the y intercept (the y value when x = 0).

but since we have a point on the line and its slope, we can start with the point-slope form

y - y1 = a(x - x1)

"a"is again the slope, (x1, y1) is the given point.

and then we transform this into the slope-intercept form.

in our case we have

y - -1 = -3/2 × (x - 6)

y + 1 = -3x/2 + 18/2 = -3x/2 + 9

y = -3x/2 + 8

or

y = -3/2 x + 8

or

y = -1/2 × (3x - 16)

The value of x is 2 and the value of y is -6.

The substitution method is one of the methods used to solve simultaneous equations. It entails making one of the variables the subject of the equation in one of the equations.

Then the variable is substituted for in the first equation:

3x-y=12

Second equation :

1Y=4x-14

Substitute for y in equation 1 using equation 2 :

3x - (4x - 14) = 12 3x -4x + 14 = 12

Combine similar terms:

14 - 12 = 4x -3x

Add similar terms;

2 = x

Substitute for x in equation:

2y = 4(2) - 14 y = 8 - 14 y = -6

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The value of x is 2 and the value of y is -6.

The substitution method is one of the methods that is used to solve for simultaneous equations. It entails making either of the variables the subject of the formula and then replacing for the variable in the other equation.

Other methods that can be used to solve simultaneous equations are the graph method and the elimination method.

3x - y = 12 equation 1

Y= 4x - 14 equation 2

y is the subject of the formula in equation 2

Substitute for y in equation 1

3x - (4x - 14) = 12

3x -4x + 14 = 12

Combine similar terms together:

14 - 12 = 4x -3x

Add similar terms together

2 = x

In order to determine the value of y, take the following steps

Substitute for x in equation 2

y = 4(2) - 14

8 - 14

y = -6

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After simplifying and rationalizing the expression 1 - √ 3 x / √ 6 x, we get the result as - (√ 2 / 2) + (√6 / 6) x .

We are given the expression:

1 - √ 3 x / √ 6 x

We need to simplify each expression by rationalizing the denominator.

Multiply √ 6 in both numerator and denominator, we get that:

(1 - √ 3 x)  / √ 6 x    ×    ( √ 6 / √ 6)

We get that:

= (√ 6 - 3 √ 2 x) / 6 x

= - (√ 2 / 2) + (√6 / 6) x

Therefore, after simplifying and rationalizing the expression 1 - √ 3 x / √ 6 x, we get the result as - (√ 2 / 2) + (√6 / 6) x .

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It should be noted that the value of angle B in thee complementary angle is 60°.

It should be noted that the total angles on a complementary angle is illustrated as 90°.

Therefore, based on the information given, it should be noted that we will add the equation and equate them to 90°.

This will be:

5x + 8 + 6x + 4 = 90°

11x + 12 = 90°

11x = 90° + 12°

11x = 102°

Divide

x = 102° / 11

x = 9.27

Therefore the value of angle B will be:

= 6x + 4

= 6(9.27) + 4

= 55.6 + 4

= 59.6°

= 60° approximately

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We need to know about inverse of a function to solve this problem. The inverse of the given function is (x+1)/4.

The inverse of a function is a function for whom the range of the function becomes it's domain. The domain of a function is the set of values that the function can take as input. The range of a function is the set of values that the function can have as possible output. The inverse of a function is a function that finds the pre-image of it's function. If the function is in terms of x, then the inverse of the function will be in terms of y. The inverse of a function can be found by making y the independant variable and expressing x in terms of y.

f(x)=4x-1

write this function in terms of y and wquating to x

x=4y-1

x+1=4y

y=(x+1)/4

[tex]f^{-1} (x)[/tex]=(x+1)/4

Therefore we found the inverse of the function to be (x+1)/4.

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The measure of each angle is 159° and 21°.

So, supplementary angles = 180

Then,

Therefore, the measure of each angle is 159° and 21°.

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Based on the amount that the trader bought the goods for, when he sells them, he would make a profit of $287

The amount that the trader will sell the goods for is $1,107

The dollar profit that the trader will make from selling the goods is:
= Cost of the goods x Percentage profit

= 820 x 35%

= 820 x 0.35

= $287

The amount that the trader will sell the goods for is:

= Cost of the goods + Profit on the goods

= 820 + 287

= $1,107

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Answer:

10 x^3 - x^2 - 29 x - 30 = (10 x + 9)(x^2 - x - 2) + -12

Step-by-step explanation:

Compute (10 x^3 - x^2 - 29 x - 30) ÷ (x^2 - x - 2) using polynomial long division:

x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30

To eliminate the leading term of the numerator, 10 x^3, multiply x^2 - x - 2 by 10 x to get 10 x^3 - 10 x^2 - 20 x. Write 10 x on top of the division bracket and subtract 10 x^3 - 10 x^2 - 20 x from 10 x^3 - x^2 - 29 x - 30 to get 9 x^2 - 9 x - 30:

| | | | | 10 x | |

x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30

| -(10 x^3 | - | 10 x^2 | - | 20 x) | |

| | | 9 x^2 | - | 9 x | - | 30

To eliminate the leading term of the remainder of the previous step, 9 x^2, multiply x^2 - x - 2 by 9 to get 9 x^2 - 9 x - 18. Write 9 on top of the division bracket and subtract 9 x^2 - 9 x - 18 from 9 x^2 - 9 x - 30 to get -12:

| | | | | 10 x | + | 9

x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30

| -(10 x^3 | - | 10 x^2 | - | 20 x) | |

| | | 9 x^2 | - | 9 x | - | 30

| | | -(9 x^2 | - | 9 x | - | 18)

| | | | | | | -12

The quotient of (10 x^3 - x^2 - 29 x - 30)/(x^2 - x - 2) is the sum of the terms on top of the division bracket. The remainder is the expression that remains after the final subtraction step.

| | | | | 10 x | + | 9 | (quotient)

x^2 - x - 2 | 10 x^3 | - | x^2 | - | 29 x | - | 30 |

| -(10 x^3 | - | 10 x^2 | - | 20 x) | | |

| | | 9 x^2 | - | 9 x | - | 30 |

| | | -(9 x^2 | - | 9 x | - | 18) |

| | | | | | | -12 | (remainder) invisible comma

(10 x^3 - x^2 - 29 x - 30)/(x^2 - x - 2) = (10 x + 9) - 12/(x^2 - x - 2)

Write the result in quotient and remainder form:

Answer: 10 x^3 - x^2 - 29 x - 30 = (10 x + 9)(x^2 - x - 2) + -12

Note: 1.5 = 3/2

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

Explanation:

The two points shown on the graph are located at (-3, -2) and (1, 5)

Let's focus on the x coordinates for now.

To find the midpoint of -3 and 1, we do two things in the order shown

Therefore, -1 is the midpoint of -3 and 1 on the number line.

It is also the x coordinate of the midpoint.

------------

Repeat these steps for the y coordinates of the given points.

This is the y coordinate of the midpoint.

-------------

The midpoint overall is located at (-1, 1.5)

I used GeoGebra to confirm the answer as correct.

Step-by-step explanation:

12x - 15 - 2x + 6 = 7

10x - 9 = 7

10x = 16

x = 16/10

x = 8/5

Answer:12.5 Km/L

Step-by-step explanation:[tex]\frac{100km}{8L}[/tex]

=12.5Km/L

Answer: 12.5

100 / 8  = 12.5

CHECK

12.5 x 8 = 100

Hope this helps 0v0

Answer: ab = 3a + 2b + c subtract 3a from both sides. ab - 3a = 2b + c factor the left side. a (b - 3) = 2b + c divide both sides by ( b - 3).

sorry but only one for then second screenshot :/

Hope this helps! :)

After direct variation y = 15 when x = 3.

So,

The initial statement is y = kx

Then to find y when x = 3.

When x = 3:

Therefore, after direct variation y =15 when x = 3.

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