A farmer has 30 boxes of eggs.
6 There are 6 eggs in each box.
Write, as a ratio, the number of eggs in three boxes to the total number of eggs.
Give your answer in its simplest form

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

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: 1.29

Step-by-step explanation: 2/5 = 0.4.

1/9 = 0.1111...

So, 3-2 = 1.

0.4-0.1111 = .28888889 (its repeating so you are going to have a rounded number)

3-2= 1 --- .4 - .1111 = 2.8888889

= 1.288889 (The 8's are not exact as they keep repeating)

Round up to 1.29 and it will be correct.

Hope this helped:)

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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Step-by-step explanation:

when you use 3 por multiply the answer is 5×

(5×)+3

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.

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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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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Answer:

option 4 and option 3

Step-by-step explanation:

(3)

using the rule of exponents

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , then

[tex](x^{\frac{3}{2}) } ^{6}[/tex]

= [tex]x^{\frac{3}{2}(6) }[/tex]

= [tex]x^{9}[/tex]

(4)

using the rule of exponents/ radicals

[tex]x^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{x^m}[/tex] , then

7[tex]x^{\frac{2}{3} }[/tex]

= 7 × [tex]\sqrt[3]{x^2}[/tex]

= 7 [tex]\sqrt[3]{x^2}[/tex]

The total amount earned when he waits 18 tables is $143

The total amount earned when he waits t tables is $35 + $6t

The equation that can be used to determine the total amount Carson earns is a linear equation. A linear equation is an equation that when drawn on a graph yields a straight line.

A linear equation increases by a constant amount. The highest power of a variable in a linear equation is 1.

The form of a linear equation is y = a + bx

Where:

Total amount earned = guaranteed wage + (tip per table x total number of tables he waits)

Total amount earned when he waits 18 tables: $35 + ($6 x 18)

$35 + $108 = $143

Total amount earned when he waits t tables: $35 + ($6 x t)

$35 + $6t

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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

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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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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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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Answer:

$12.5xy

Step-by-step explanation:

y = how much the jobs pays

x = hours of work

25/2

= 12.5xy

Answer: 1. 0.937

2. 20.786

3. 35.001

Step-by-step explanation:

1. 0.9+0.03+0.007=

0.900+0.030+0.007=0.937

2. 20 +0.7 + 0.08 + 0.006=

20.000 +0.700 + 0.080 + 0.006=20.786

3. 35 + 0.01 - 0.009=

35.000 + 0.010 - 0.009=

35.010 - 0.009=35.001

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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she needs to make 12 visits to the movie theatre to earn the rest of the 145 points and get a free movie ticket.

We are given that:

Jocelyn received 25 reward points just for signing up.

She earns 12.5 points for each visit that she makes to the movie theatre.

The free movie ticket is available when she has 170 points with her.

Points to be collected more for a free movie ticket will be:

Points = 170 points - 25 points = 145 points.

So, the number of visits she has to make to the movie theatre will be calculated with the help of division.

Number of visits = 145 points / 12.5 points

Number of visits = 11.6 visits that is 12 visits.

Therefore, she needs to make 12 visits to the movie theatre to earn the rest of the 145 points and get a free movie ticket.

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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

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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The equation that best fits all the points on the graph is y = -2x + 3.

The line of best fit is a line that can be drawn to connect most of the points on the graph. In other words, it best fits the points.

Using a linear regression tool, input the coordinates that are on the graph including:

(-4, 10) (-2, 8) (-1, 5) (1, 3) (2, 0) (2, -3)

The formula you get for line of best fit would be:

y = -2.08564x + 3.01259

Rounding up gives:

y = -2x + 3

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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! :)

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

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

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

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

Answer:

[tex]x = 1 + \frac{y}{2} \\ \\ x = 4 - y \\ y = 4 - x[/tex]

Step-by-step explanation:

[tex]1. \: y + 2 = 2x \\ 2. \: \frac{y + 2}{2} = x \\ 3. \: 1 + \frac{y}{2} = x \\ 4. \: x = 1 + \frac{y}{2} \\ \\ \\ 1. \: x = 4 - y \: or \: y = 4 - x[/tex]

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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Answer:

m + n + p = a

Step-by-step explanation:

m - a = n- p

M = a - n - p

M + n = a - p

M + n + p = a