Solve the equation for x. For each step, identify the property used to convert the equation. 18=6(2x – 8)

Problem 5

There are 2 answers and they are choice B and choice C

We can tell by looking at the factors. For something like choice B, the factor (x+6) shows up twice, so that means x = -6 is a double root. Something like choice A has roots x = -6 and x = 6 which aren't the same.

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Problem 6

Ted is correct. He set each factor equal to 0 and solved each equation that resulted from doing so.

Note how 3x-2 = 0 turns into 3x = 2 after adding 2 to both sides. Then he divided both sides by 3 to get x = 2/3. That's the first solution. The second solution x = -5 results from solving x+5 = 0. You subtract 5 from both sides.

To fix Maggie's mistake, you just need to correct her steps to mirror Ted's steps.

Answer:

90 degrees

Step-by-step explanation:

the answer is 90 degrees because when the triangle is a right triangle, the two smaller angles equal 90 degrees.

Step-by-step explanation:

Write 0.1 as

0.1

1

Multiply both numerator and denominator by 10 for every number after the decimal point

0.1 × 10

1 × 10

=

1

10

Reducing the fraction gives

1

10

In fraction form the number 0.1 can be written as 1/10.

Use the concept of fraction defined as:

A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p/q.

The given number is: 0.1

Since the given number is a decimal  number,

And it has only in digit after decimal.

Therefore,

Divide and multiply by 10 with this number,

[tex]0.1 \times \dfrac{10}{10} = \dfrac{1}{10}[/tex]

Hence,

The fraction from of  the number 0.1 is 1/10

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Answer:

Negative

Step-by-step explanation:

If both are negative, they can't grow when you add them. If I owe someone 3 dollars, then I owe them 3 more, I don't owe them 0, I owe them 6. The equation would be My amount of money-3-3

Answer:

[tex]21x^4+3y-35x^2+41[/tex] must be subtracted

As you can see, we added -x+2 to this polynomial to obtain a first degree polynomial. (Though really anything with an x would do. For example, 3x, 2221x, or -224x would all work)

Step-by-step explanation:

We have the following polynomial

[tex]21x^4+3y-6x^2+34[/tex]

And need to find a polynomial to subtract from it to get

[tex]29x^2-7[/tex]

This means that if we subtract these two polynomials, we will get our desired polynomial

[tex]21x^4+3y-6x^2+34-(29x^2-7)\\\\21x^4+3y-6x^2+34-29x^2+7\\\\21x^4+3y-35x^2+41[/tex]

Just to be sure, we can then check our work by finding the difference of the first polynomial and the one that we just found

[tex]21x^4+3y-6x^2+34-(21x^4+3y-35x^2+41)\\\\21x^4+3y-6x^2+34-21x^4-3y+35x^2-41\\\\-6x^2+34+35x^2-41\\\\29x^2-7[/tex]

As we got the desired result, we know that this answer is correct.

And now for the second part of the problem. What polynomial must be added to it to obtain a first degree polynomial?

Recall that a first degree polynomial is one that has the total sum of 1. For example the polynomial x+5 is a first degree polynomial, but x+y+5 has a degree of 2.

This means that our desired polynomial needs to only have some amount of x's and constants.

We can do the same thing as the first time and simply subtract our desired result from the first polynomial. For simplicity, let us use the simple polynomial x+2

[tex]21x^4+3y-6x^2+34-(x-2)\\\\21x^4+3y-6x^2+34-x+2\\\\21x^4+3y-6x^2-x+36[/tex]

As you can see, we added -x+2 to this polynomial to obtain a first degree polynomial. (Though really anything with an x would do. For example, 3x, 2221x, or -224x would all work)

Answer:

13.36

Step-by-step explanation:

18.60 - 5.24

=>13.36

Step-by-step explanation:

Pumping rate my be defined as the the rate ta which a liquid is pumped through a system. It is measured as the flow of the liquid at a unit time. It may be referred to as the capacity of the pump which defines how much liquid is being passed through the pump in a certain given time.

The pumping rate in mL/s refers to the amount of liquid passed in one second of time.

Answer:

63 sandwiches

Step-by-step explanation:

Pete and his friend Danny volunteered to bring sandwiches for lunch at a homeless shelter

They brought 7 loaves of bread

Each loaves have 18 slices

They used 2 slices each to make the sandwich

The first step is to calculate the total number of slices

Sinces 7 loaves of bread are used and each of them contain 18 slices then, the total number of slices can be calculated as follows

= 7 ×18

= 126 slices

Therefore since 2 slices of bread is used to make one sandwich then, the number of sandwiches that was made can be calculated as follows

= 126/2

= 63

Hence 63 sandwiches were made for the shelter

90

Plug in 7 for x and solve.

[tex]{y}^{2} + 5y + 6[/tex]

[tex]{(7)}^{2} + 5(7) + 6[/tex]

[tex]49 + 35 + 6[/tex]

[tex]90[/tex]

Answer:

8 (3/4)

Step-by-step explanation:

convert everything into improper frantions

-3 1/2 = -7/2

-12 1/4 = -49/4

common denominators

-7/2 = -14/4

solve

-(14/4)-(-49/9)

two negative cancel out to make a positive

-(14/4)+(49/9)

35/4

35 divided by 4 = 8.75 = 8 3/4

Answer:

it would be 2 to the 9th over 2 to the 7th

Step-by-step explanation:

Answer:

it would be 2 to the 9th over 2 to the 7th

Step-by-step explanation:

Answer:x=5

Step-by-step explanation:

First we do the parenthesis

-4(7+2x)=-7x-33

To get

-28+-8x=7x+-33

and

-8x-28=-7x-33

Then we Add 7x to both sides.

-8x-28+7x=-7-33+7x

-x-28=-33

Then we Add 28 to both sides.

-x-28+28=-33+28

-x=-5

Lastly Divide both sides by -1.

-x/-1=-5/-1

X=5

Answer:

Race and Ethnicity are considered to be social constructs that enable humans to be grouped or categorized. They are sometimes used interchangeably but most argue that they are different and give them different definitions.

Race is generally used to refer to people that have the same physical characteristics such as skin color or the same texture of hair for instance Black and White/Caucasian.

Ethnicity on the other hand relates to people sharing a common culture, language, nation, and/ or tribal heritage for instance, the English, the Irish and the Igbo.

Answer:

The terms race and ethnicity are often used interchangeably throughout society. However, there is a distinct difference between the two. Race refers to a classification system based on inherited physical or biological traits, such as eye, hair, or skin color. In contrast, ethnicity refers to a group of people that can be linked together by common characteristics such as shared experiences, history, culture, or beliefs. Examples of ethnic groups include Native Americans, French Canadians, and Kongos.

Step-by-step explanation:

(edg2020)

Answer:98.03060747

Step-by-step explanation:

Square root 9610

Answer:

[tex]g(x) = 2x^2 - 3x - 1[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 2x^2 + 3x - 1[/tex]

Required

Determine g(x), if f(x) is reflected across the y axis

When a function (x,y) is reflected across the y axis, the new function becomes (−x,y).

In other words,

[tex]g(x) = f(-x)[/tex]

Calculating f(-x)

[tex]f(-x) = 2(-x)^2 + 3(-x) - 1[/tex]

[tex]f(-x) = 2x^2 - 3x - 1[/tex]

Substitute g(x) for f(-x)

[tex]g(x) = 2x^2 - 3x - 1[/tex]

Hence;

[tex]g(x) = 2x^2 - 3x - 1[/tex]

Answer

Median

Step-by-step explanation:

It should be noted that medians are resistant to outliers.

Outliers simply means the data records which are different from every other record. It escapes normality. The outlier affects mean, inter-quartile range, mode and the range.

It should be noted that the median isn't affected by outliers. The reason for this is that the median depends on the arrangement and the order of the data. For example, when one changes the lowest score in a given set of numbers, the order won't be affected.

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Answer:

[tex]-5p^2-9pq+17q^2[/tex]

Step-by-step explanation:

[tex](p-4q) (3p+q) - (2p+3q) (4p-7q)\\\\\mathrm{Expand}\:\left(p-4q\right)\left(3p+q\right):\quad 3p^2-11pq-4q^2\\=3p^2-11pq-4q^2-\left(2p+3q\right)\left(4p-7q\right)\\\\\mathrm{Expand}\:-\left(2p+3q\right)\left(4p-7q\right):\quad -8p^2+2pq+21q^2\\=3p^2-11pq-4q^2-8p^2+2pq+21q^2\\\\\mathrm{Simplify}\:3p^2-11pq-4q^2-8p^2+2pq+21q^2:\\\quad -5p^2-9pq+17q^2[/tex]

Answer:

-5p² -9pq +17q²

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

Step-by-step explanation:

y - 2 = 3(x - 1)

y - 2 = 3x - 3

y = 3x - 1

Answer: bus makes a stop at 2:30, letting off 15 people and letting on 9

-15 + 9 = -6

The bus makes another stop ten mins later to let off 4 more people  

-4

Happy to Help! (Now i must go back to my planet ^^)

Answer:

Largest possible number of sweets in each tray[tex]=4[/tex]

Step-by-step explanation:

Given:

Number of orange-flavored sweets = 36

Number of grape-flavored sweets = 44

To find: largest possible number of sweets in each tray

Solution:

HCF(highest common factor) of two or more numbers refers to the greatest number which can divide the given numbers

To find largest possible number of sweets in each tray, find the HCF(highest common factor) of 36 and 44.

[tex]36=2^{2}\times 3^{2}\\44=2^{2}\times 11[/tex]

So,

[tex]HCF(36,44)=2^{2}=4[/tex]

So,

Largest possible number of sweets in each tray[tex]=4[/tex]

The largest possible number of sweets in each tray is 4.

In order to determine the largest possible sweets in each tray, the highest common factor of the number of sweets have to determined. The highest common factor is the highest factor that is common to two or more numbers.

Factors of 36 =  1, 2, 3, 4, 6, 9, 12, 18, and 36.

Factors of 44 = 1, 2, 4, 11, 22, 44.

Common factors = 1, 2, 4

Highest common factor - 4  

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Answer:

124 degrees

Step-by-step explanation:

Look at the equation from the information they gave you. Supplementary angles always add up to 180 degrees, so make up the equation of 8x + 12 +  2x + 28 = 180. Simplify to get 10x + 40 = 180. Subtract 40 from both sides to get 10x = 140. Divide both sides by 10, and you will get x=14. Substitute the value of 10 into the variable x in the angle ZWYK to get 8(14) + 12. This will simplify into 112 + 12, which will eventually get you 124 degrees.

Answer:

Step-by-step explanation:

Since angles ZWYX and ZZYX are supplementary it means that the sum of their angles sum up to 180°

To find mZWYX we must first find x

To find x add ZWYX and ZZYX and equate them to 180 to find x

That's

ZWYX + ZZYX = 180

8x + 12 + 2x + 28 = 180

10x + 40 = 180

10x = 180 - 40

10x = 140

Divide both sides by 10

x = 14°

From the question

mZWYX = 8x + 12

Substitute the value of x into the expression

We have

mZWYX = 8(14) + 12

= 112 + 12

We have the final answer as

Hope this helps you

Answer:

1. Profit =  Revenue - Cost

2.  For the Alcone Company Revenue = $45 × x

For the Besame Beauty Revenue = $55 × x

3.  Alcone Company; Cost = $1,500 + $36×x

Besame Beauty; Cost = $2,200 + $44×x

4)  For Alcone Company, we have;

Profit = $9 × x - $1,500

For  Besame Beauty, we have;

Profit = $11 × x - $2,200

5) For Alcone Company;

Profit= $525

For Besame Beauty;

Profit = $275

6) For Alcone Company;

Profit = -$150

For Besame Beauty;

Profit  -$550

7) Order of operations is used to ensure that the revenue is first calculated before the cost is subtracted to find the costs

8) In order to find the number of tubes that the company would need to manufacture in order to have a profit of greater than 0, we equate the expression using the inequality of greater than 0 to find the value of x that must be surpassed to have a profit greater than 0

9) For Alcone Company;

The profit will be > 0 at x = 167 tubes

For Besame Beauty;

The profit will be > 0 at x = 201 tubes

Step-by-step explanation:

The given parameters are;

The Alcone Company

The price at which the shade of lip color is sold = $45 per tube

The cost incurred to make  the lip color = $36 per tube

The monthly manufacturing cost of manufacturing the lip color = $1,500

For Besame Beauty

The price at which the shade of lip color is sold = $55 per tube

The cost incurred to make  the lip color = $44 per tube

The monthly manufacturing cost of manufacturing the lip color = $2,200

1. The formula for finding the profit is given as follows;

Profit =  Revenue - Cost

Revenue = Sale price × Number of tubes sold

Cost = The monthly manufacturing cost + The cost incurred to make the lip color × Number of tubes

2. The expression for revenue for the Alcone Company is given as follows;

Revenue = $45 × x

The expression for revenue for the Besame Beauty is given as follows;

Revenue = $55 × x

3. The expression for the cost for the manufacture of the lip color by the Alcone Company per month is given as follows;

Cost = $1,500 + $36×x

The expression for the cost for the manufacture of the lip color by the Besame Beauty per month is given as follows;

Cost = $2,200 + $44×x

4)  For Alcone Company, we have;

Revenue = $45 × x

Cost = $1,500 + $36×x

By transitive property and distributive property, we have

Profit =  Revenue - Cost = $45 × x - ($1,500 + $36×x) = $9 × x - $1,500

Profit = $9 × x - $1,500

For  Besame Beauty, we have;

Revenue = $55 × x

Cost = $2,200 + $44×x

By transitive property and distributive property, we have;

Profit =  Revenue - Cost = $55 × x - ($2,200 + $44×x) = $11 × x - $2,200

Profit = $11 × x - $2,200

5) With the number of tubes produced = 225 tubes, we have;

For Alcone Company;

Profit = $9 × x - $1,500 = $9 × 225 - $1,500 = $525

ForBesame Beauty;

Profit = $11 × x - $1,500 = $11 × 225 - $2,200 = $275

6) With the number of tubes produced = 150 tubes, we have;

For Alcone Company;

Profit = $9 × x - $1,500 = $9 × 150 - $1,500 = -$150

For Besame Beauty;

Profit = $11 × x - $2,200 = $11 × 150 - $2,200 = -$550

7) Order of operations is used to ensure that the revenue is first calculated before the cost is subtracted to find the costs

8) In order to find the number of tubes that the company would need to manufacture in order to have a profit of greater than 0, we equate the expression using the inequality of greater than 0 to find the value of x that must be surpassed to have a profit greater than 0

9) For Alcone Company;

Profit = $9 × x - $1,500 >0

$9 × x  >0 + $1,500

$9 × x  > $1,500

x > $1,500/$9

x > 500/3

x > [tex]166\frac{2}{3}[/tex]

Therefore, the profit will be > 0 at x = 167 tubes

For Besame Beauty;

Profit = $11 × x - $2,200 > 0

$11 × x  > 0 + $2,200

$11 × x  > $2,200

x > $2,200/$11

x > 200

Therefore, the profit will be > 0 at x = 201 tubes

Answer:

Step-by-step explanation:

g(x) = x^2 + 6

f(x^2 + 6) = 2(x^2 + 6) + 1 = 2x^2 + 12 + 1 = 2x^2 + 13

Hi There!!

B = 1/2A + 30

C = 3/2A + 20

B = C

1/2A + 30 = 3/2A + 20

30 - 20 = 3/2A - 1/2A

10 = A

B = 1/2A + 30

B = 1/2(10) + 30

B = 5 + 30

B = 35

C = 3/2A + 20

C = 3/2(10) + 20

C = 15 + 20

C = 35

type A cabinets produced was 10

type B and type C cabinets produced were both 35

Good Luck!!

[tex]Itsbrazts[/tex]

Answer:

If the company made the same number of type B and type C cabinets last week, then the number of type A cabinets produced was 10. The total number of cabinets produced last week was 80.

Step-by-step explanation:

I took the test.

Answer:

m = -1

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out equation

-13 = 5(1 + 4m) - 2m

Step 2: Parenthesis (distribute)

-13 = 5 + 20m - 2m

Step 3: Combine like terms (m)

-13 = 5 + 18m

Step 4: Subtract 5 on both sides

-18 = 18m

Step 5: Divide both sides by 18

-1 = m

Step 6: Rewrite

m = -1

Answer:

m = -1

Step-by-step explanation:

-13 = 5(1 + 4m) - 2m

Step 1 : Distributive Property

-13 = 5 + 20m - 2m

Add like terms

-13 = 5 + 18m

Subtract 5 on both sides

-18 = 18m

Divide

[tex]\frac{-18}{18}[/tex] = [tex]\frac{18m}{18}[/tex]

m = -1

Answer:

0.68

Step-by-step explanation:

We can use long division to find the decimal equivalent of [tex]\frac{13}{19}[/tex] since a fraction is just another way of writing a division statement.

[tex]19\overline{\smash{)}#13}\\\\0.\\19\overline{\smash{)}#130}\\\\0.6\\19\overline{\smash{)}#130-114=16}\\\\0.6\\19\overline{\smash{)}#160}\\\\0.68\\19\overline{\smash{)}#160-152 = 8}\\\\0.68\\19\overline{\smash{)}#80}\\\\0.684\\19\overline{\smash{)}#80}[/tex]

0.684 to the nearest hundredth is 0.68.

Hope this helped!

Answer:

$5400 USD

Step-by-step explanation:

Investment=3,000

Interest=8% = .08

Time=10 years

([3000 x .08 x 10] + 3,000

[240 x 10] + 3,000

2,400 + 3,000= 5,400

Answer:

a

Step-by-step explanation:

Answer:

[tex]x[/tex]  = -6

[tex]x[/tex] = 3

Step-by-step explain

[tex]x^{2}[/tex] = 3[tex]x[/tex] - 18 =0

[tex]x^{2}[/tex] =6[tex]x[/tex]  - 3[tex]x[/tex]  - 18 = 0

[tex]x[/tex] x ([tex]x[/tex] + 6) -3[tex]x[/tex]  - 18 = 0

[tex]x[/tex] x ([tex]x[/tex] + 6) - 3([tex]x[/tex]  = 6)=0

([tex]x[/tex]  = 6) x ([tex]x[/tex] 3) = 0

[tex]x[/tex] +6 = 0

[tex]x[/tex] - 3 = 0

[tex]x[/tex]  = -6

[tex]x[/tex] = 3