Mathematics Middle School

Factor: 4b^3 - 12b^2 - 9b + 27

Answers

Answer 1

Answer:

(2b - 3)(2b + 3)(b - 3)

Step-by-step explanation:

4b³ - 9b - 12b² + 27

b(4b² - 9) - 3(4b² - 9)

(4b² - 9)(b - 3)

(2b - 3)(2b + 3)(b - 3)

Answer 2

Answer:

[tex](4b^{2}-9)(b-3)[/tex]

Step-by-step explanation:

In order to factor this expression you need to factor by grouping.

First focus on factoring the first two terms them factor the last two terms

1. Lets focus on the first 2 terms:

[tex]4b^{3} -12b^{2}[/tex] (You can factor out [tex]4b^{2}[/tex])

[tex]4b^{2} (b-3)[/tex] (this is what you're left with

2. Lets focus on the last 2 terms:

[tex]-9b+27[/tex] (You can factor our a -9)

[tex]-9(b-3)[/tex] (this is what you're left with

3. Now lets put both of the factored parts together:

[tex]4b^{2} (b-3)-9(b-3)[/tex] (Since both equations have the factor (b-3) in common that is one of our answers) (pull out that factor)

[tex](b-3)[/tex]

Now whatever is left create the second factor:

[tex](4b^{2} -9)[/tex]

So, [tex](4b^{2} -9)(b-3)[/tex] are the factors that make this expression.

You can double check that these are the right factors by using the FOIL method.

If you use the FOIL method it forms the original expression [tex]4b^{3} -12b^{2} -9b+27[/tex]

so we know for sure these are the right factors.

I will upload an image of how to use the FOIL method.

FOIL stand for Front, Outer, Inner, Last

Factor: 4b^3 - 12b^2 - 9b + 27

Related Questions

The martins car traveled 468 miles on 18 gallons of gas. Their car averaged how many miles per gallon.

Answers

Answer: 26

Step-by-step explanation: you divide 468 and 18 and you get 26.

Find
1. 7.75 ÷ 0.25
2. 25.5 ÷ 3

Answers

Answer:

31,

8.5

Step-by-step explanation:

1) 7.75/0.25 = (7.75×100)/(0.25×100)

= 775 ÷ 25

= 31

2) 25.5/3 = (25.5×10)/ (3×10) = 255÷30

= 8.5

I hope this was helpful, please mark as brainliest

4.5(32÷8)+12
please help me steps por favor

Answers

Answer:

30

Step-by-step explanation:

4.5(32÷8)+12

32/4 = 4

4.5 x 4 = 18

18 + 12 = 30

Answer:

30

Step-by-step explanation:

PEMDAS

32/8 =4

4.5*4=18

18+12=30

Which factor makes capitalism such a successful economic system?


Business owners have the right to take private property from citizens if it benefits the overall economy.


Banking regulators work to limit the possibility of economic problems.


Individual citizens have the freedom to take risks and improve their lives.


Public corporations make jobs available to those who want them.

Answers

Answer:

C. Individual citizens have the freedom to take risks and improve their lives.

Step-by-step explanation:

Need help ASAP!!!!!!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

[tex]\frac{x^{4}+6x^{3}+5x^{2} -15x-2} {x+3}[/tex]

Answer:

Option 4

Step-by-step explanation:

x + 3 x = -3

(-3)⁴ + 6(-3)³ + 5(-3)² - 15(-3) - 2

= 7

Remainder is 7, so not a factor

one serving of punch is 250 milliliters. Will ten servings fit in a 2 liter bowl ?

Answers

Answer:

yes

Step-by-step explanation:

To find the product of 42.12 and 10³, move the decimal point in 42.12 __ places to the right because 10³ has __ zeros.

Answers

To find the product of 42.12 and 10^3,  move the decimal point in 42.12 3 places to the right because 10^3 has 3 zeros

Solution:

Given that,

[tex]\text{ product of } 42.12 \text{ and } 10^3[/tex]

Which means,

[tex]42.12 \times 10^3[/tex]

Here, the exponent of 10 is positive ( which is 3)

When the exponent is positive, we have to move the decimal point to right

When you multiply a number by a power of 10, ( 10!, 10^2, and so on ) move the decimal point of the number to the right the same number of places as the number of zeros in the power of 10

Here, exponent is 3 , therefore move the decimal point right 3 places in 42.12

Therefore,

[tex]42.12 \times 10^3 = 42120[/tex]

Use substitution to it
7) 4x – 2y=-22
-x+y=3​

Answers

Rearrange -x+y = 3 to y = x+3
Then substitute into the first equation.
4x - 2(x+3)= -22
4x - 2x - 6 = -22
2x -6 = -22
2x = -16
x = -8
Then I put this into y = x+3
y = -8 + 3
y = -5

4- x2 =-32
The equation above is true for what value of x, where
x>0?

Answers

Answer:

x= -6

Step-by-step explanation:

first you want to get rid of the 4 so on both sides you subtract 4

4-x²=-32

-4      -4  that will then make the problem

-x²= -36 to get rid of the square you must do the opposite, square root ([tex]\sqrt{36}[/tex]) so it will get rid of the ²

-x= 6 then you have to get rid of the neggative on x so you will add a negative to 6

x=-6

If both the integers are negative, then their sum is _____​

Answers

Answer:

they are always positive

Step-by-step explanation:

they are always positive because two negatives equal a positive.

If both the integers are negative, then their sum is always negative.

We need to find if both the integers are negative, then what is their sum.

What are integers rules?

Adding integers is the process of finding the sum of two or more integers. It may result in an increase or a decrease in value, depending on whether the integers are positive or negative or a mixture. The addition of integers is an arithmetic operation performed on integers with the same sign or with different signs to find the sum.

Adding two positive integers always results in a positive value that is greater than both the integers.Adding two negative integers always results in a negative number that is smaller than the given numbers.

Therefore, if both the integers are negative, then their sum is always negative.

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1. 9x + 16 = 4x - 19

Answers

Answer:

x=-7

Step-by-step explanation:

9x + 16 = 4x - 19

Subtract 4x from each side

9x-4x + 16 = 4x-4x - 19

5x+16 = -19

Subtract 16 from each side

5x+16 -16 = -19-16

5x = -35

Divide each side by 5

5x/5 = -35/5

x = -7

Answer:

x = -7

Step-by-step explanation:

solve

in order to solve this , make x the subject of formula:

9x + 16 = 4x - 19

9x + 16 - 4x = -16

5x = -19 - 16

5x =-35

x = -35 / 5

x = -7

target sells 25 bottles of water for 3 dollars, and 36 bottles for 4 dollars. Which is a better buy and by how much? PLEASE REPLY ILL GIVE BRAINLIEST

Answers

Answer:

36 bottles for 4 is a slightly better deal per bottle.

Step-by-step explanation:

3÷25=0.124÷36=0.11111111

The cost per bottle is 0.1111111$ per bottle in the 36 pack.

Answer:

36 bottles for $4

Step-by-step explanation:

First you need to calculate the price for one bottle, the lower the cost, the better buy. Do this by dividing the price by the amount of bottles:

= $3 ÷ 24

= 0.125 cents

= $4 ÷ 36

= 0.111 cents

The cheaper option and the better buy is the 36 bottles for $4.

What is 1/6÷7/8 as a fraction in lowest terms

Answers

Answer:

the answer is 5 1/4

Step-by-step explanation:

because u flip it then multiply then u get ur answer

Final answer:

To divide 1/6 and 7/8, we first find the reciprocal of 7/8 which is 8/7, then multiply 1/6 by 8/7 to get 8/42. We simplify this fraction to lowest terms by dividing both the numerator and denominator by their GCD, which is 2, to get the final result, 4/21.

Explanation:

This mathematics question is asking you to divide two fractions, which is 1/6 and 7/8. To do this, you would multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is achieved by switching the numerator and the denominator.

In this case, the reciprocal of 7/8 is 8/7. So, the equation becomes 1/6 * 8/7, which simplifies to 8/42. But this is not in lowest terms. To find the fraction in lowest terms, you would find the Greatest Common Divisor (GCD) of the numerator and the denominator. In this case, the GCD of 8 and 42 is 2.

Dividing both the numerator and denominator by 2, we get 4/21, which is the fraction in lowest terms.

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Which number is irrational?


49√


17√


0.06¯¯¯


1/6


The 0.06 is repeating

Answers

This is the answer but it wasn’t letting me send it

Answer: the square root of 17 is irrational.

Step-by-step explanation:

17 can not be divided evenly therefor it is irrational

Consider the transformation shown in the coordinate plane, which statement is NOT TRUE for similarity transformations? A ) A similarity transformation is a composition of a finite number of dilations or rigid motions B) Two figures are similar if there exists a similarity transformation that maps one figure onto the other in a similarity transformation all corresponding pairs ) angles are congruent and all corresponding pairs of sides are congruent a similarity transformation alt corresponding pairs D of angles are congruent and all corresponding pairs of sides are proportional

Answers

Answer:

C) angles are congruent and all corresponding pairs of sides are congruent a similarity transformation alt corresponding pairs

Final answer:

The correct statement for similarity transformations is D) In a similarity transformation, all corresponding pairs of angles are congruent and all corresponding pairs of sides are proportional.

Explanation:

A similarity transformation is a type of transformation that preserves the shape of a figure but can change its size and orientation. It is characterized by the property that all corresponding pairs of angles are congruent and all corresponding pairs of sides are proportional.

The statement that is NOT TRUE for similarity transformations is A) A similarity transformation is a composition of a finite number of dilations or rigid motions.

A similarity transformation is a type of transformation that preserves the shape of a figure but can change its size and orientation.

The correct statement for similarity transformations is D) In a similarity transformation, all corresponding pairs of angles are congruent and all corresponding pairs of sides are proportional.

This means that the angles in the original figure and the transformed figure are equal, and the ratio between corresponding side lengths remains the same.

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If x=2 and 3x+y=5, what is the value of y

Answers

Answer:

-1

Step-by-step explanation:

X = 2

Lets substitute the equation:

3*2 + y = 5

6 + y = 5

Using equation rules.

y = 5-6

Therefore y = -1

Answer:

y=-1

Step-by-step explanation:

3x+y=5

When x=2

Substitute the value of x in the above equation

3(2)+y=5

6+y=5

Collect like terms

y=5-6

y=-1

otis paints the interior of a home for $45 per hour plus $75 for supplies. Shireen paints the interior of a home for $55 per hour plus $30 for supplies. The equations give the total cost for x hours of work for each painter. For how many hours of work are Otis's and Shireen's costs equal? what is the cost for this number of hours?

Y= 45x + 75 - Otis
Y= 55x + 30 - Shireen​

Answers

Answer:

For 4.5 hours of work Otis's and Shireen's costs are equal

The cost for this number of hours is $277.5

Step-by-step explanation:

Let

x ----> the number of hours

y ----> the total cost

we have

Otis

[tex]y=45x+75[/tex] ----> equation A

Shireen

[tex]y=55x+30[/tex] -----> equation B

Solve the system of equations by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (4.5,277.5)

see the attached figure

therefore

For 4.5 hours of work Otis's and Shireen's costs are equal

The cost for this number of hours is $277.5

HALP PLZ! WILL GIVE BRAINLIEST TO FIRST ANSWER! A health inspector conducts air quality tests on a randomly selected group of 10 classrooms at a high school. Identify the population and sample for this situation. A) The population is all classrooms in the district; the sample is the 10 classrooms selected. B) The population is all classrooms in the high school; the sample is the 10 classrooms selected. C) The population is all students in the district; the sample is the students in the 10 classrooms selected. Eliminate D) The population is all students in the high school; the sample is the students in the 10 classrooms selected.

Answers

Answer:B

Step-by-step explanation:On  usa test prep

The identification of the population and the sample for the given situation is option B. The population is all classrooms in the high school; the sample is the 10 classrooms selected.

Information regarding the population:Since on a random basis, the 10 classrooms are selected.Si here the population represent the all classrooms is in the high school And the sample should be 10 classrooms selected.

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plzzzzzzzzzzzz help asap

Answers

Answer:

The equation in slope-intercept form of a line with slope [tex]m\:=-\:\frac{4}{3}[/tex]  and y - intercept = -2  will be:

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

Step-by-step explanation:

As the slope intercept form is given by

[tex]y=mx+b[/tex]

here

m = slopeb = y-intercept        

As the given slope is

[tex]m\:=-\:\frac{4}{3}[/tex]

y - intercept = b = -2

so substituting the values in the slope intercept form

[tex]y=mx+b[/tex]

[tex]y=\left(-\:\frac{4}{3}\right)x+\left(-2\right)[/tex]

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

Therefore, the equation in slope-intercept form of a line with slope [tex]m\:=-\:\frac{4}{3}[/tex]  and y - intercept = -2  will be:

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


A prism whose base is a 9-sided polygon is intersected by a plane. In which case could the cross section be a 10-sided polygon?​

Answers

The cross-section will be a 10-sided polygon only when the plane makes a narrow angle with the base, i.e. it will cut one base and 8 edges of the prism, resulting in there being 10 points of intersection, leaving a 10-sided polygon as the cross-section.

Answer:

D

Step-by-step explanation:

I took it rate this one

The sum of two numbers is 10. The larger number is 4 times the smaller number. What are the two numbers?
Let x = the smaller number.
Let y = the larger number.
Which two equations represent the system for this word problem?

Answers

Answer:

Equation 1: x + y = 10

Equation 2: y = 4x

Step-by-step explanation:

its right kekkek

Therefore, the equation is of the form

[tex]x+y=10[/tex]

[tex]y=4x[/tex]

What is the simplification?

Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Here given that,

The sum of two numbers is [tex]10[/tex]. The larger number is [tex]4[/tex] times the smaller number.

Let the smaller number is [tex]x[/tex]

Let the larger number is [tex]y[/tex]

The first equation is [tex]x+y=10[/tex] nad the second equation is [tex]y=4x[/tex].

Hence, the equation is of the form

[tex]x+y=10[/tex]

[tex]y=4x[/tex]

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PLS HELP 50 POINTS
I feel like i answered wrong
Question below

Answers

Answer:

Hi there!

The correct answer is: Counterclockwise rotation about the origin by 90 degrees then followed by reflection about the x axis

Answer:

Option 1

Counterclockwise rotation about the origin by 90° followed by a reflection about the x-axis

Find the volume of the three-dimensional figure in terms of x.

Answers

Answer:

That is a cylinder and cylinder volume = PI * radius^2 * height

radius = x + 5

height = x

volume = PI * (x + 5)^2 * x

volume = PI * (x^2 + 10x + 25) * x

volume = PI * x^3 + 10x^2 + 25x

Step-by-step explanation:

Today a father's age is five times his son's age. Exactly three years ago, the sum of their ages was 30. How old is the son today?

Answers

Today the age of sun is 6 years.

What is algebra?

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

Given that,

Father's present age is five times of his son's age.

Let son's age is x years,

Then father's age will be 5x.

Also, three years  ago the sum of their ages was 30.

Three years ago the age of son and father will be x - 3 and 5x - 3.

Since, the sum = 30

x - 3 + 5x - 3 = 30

6x - 6 = 30

6x = 36

x = 6

The age of son is 6 years.

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A square pyramid has a height of 18 cm. A side length of the base of 11 cm. What is
the volume of the pyramid?

Answers

Answer: 66cm^3

Step-by-step explanation:AB=a2

V=a2h

3

Solving forV

V=ABh

3=11·18

3=66cm³

Find the surface area for number 3, will give Brainliest

Answers

Answer:

984 cm^2

Step-by-step explanation:

Base: 10 × 24 = 240

Rectangular faces: 13 × 24 = 312 (×2 = 624)

Triangular faces: 12 × 10 = 120

Add: 240 + 624 + 120 = 984

can you pls help me out? i would sincerely appreciate it!!

Answers

Step-by-step explanation:

Step 1: Given

BD bisects ∠ADC

Step 2: Given

BD ⊥ AC

Step 3: Corresponding Parts of Congruence Triangles are Congruent

∠1 ≅ ∠2

Step 4: By definition of perpendicular

∠ABD = ∠CBD = 90° (BD ⊥ AC )

∠3 and ∠4 are right angles.

Step 5: By CPCTC,

∠3 ≅ ∠4

Step 6: Reflexive postulate

Any side or angle is reflexive to itself.

DB ≅ DB

Step 7: ASA postulate

∠1 ≅ ∠2 (A),   DB ≅ DB (S)   and   ∠3 ≅ ∠4 (A),

∴ ΔABD ≅ ΔCBD (by ASA)

Step 8: By Corresponding Parts of Congruence Triangles are Congruent

DA ≅ DC

Step 9: Opposite sides of a triangle are equal.

ΔACD is isosceles.

Hence proved.

Solve this equation -8-x=x-4x

Answers

Answer:

x=4

Step-by-step explanation:

-8-x=x-4x

Combine like terms

-8 -x =-3x

Add x to each side

-8 -x+x = -3x+x

-8 = -2x

Divide each side by -2

-8/-2 = -2x/-2

4 = x

(6x-3y - 12
- (2x+2y=10

Answers

Answer:

8x - 5y - 13

Step-by-step explanation:

(6x - 3y - 12) - (2x +2y - 10)

(6x - 3y - 12) - 2x - 2y + 10

6x - 3y - 23 - 2x - 2y + 10

8x - 5y - 13

Answer:

4x+y=22

Step-by-step explanation:

6x+3y-12-(2x+2y)=10

Based on BODMAS we will have to deal with the bracket first

6x+3y-12-2x-2y=10

To continue with the solution we will have to collect like terms

That is,

6x-2x+3y-2y=10+12

4x+y=22

This can't be solved further because we don't really know the value of x and y...it can only be solved further by knowing the value of either x or y but we are not given...so we will have to leave our final answer to be

4x+y=22

The probability of drawing a yellow or green marble out of a bag containing 3 blue, 2 green , 8 yellow , 4 red , and 3 orange marbles.

Answers

Final answer:

The probability of drawing a yellow or green marble from a bag with various colored marbles is calculated by adding the individual probabilities of drawing a yellow marble and a green marble. Since there are 8 yellow and 2 green marbles out of a total of 20, the combined probability is 0.5 or 50%.

Explanation:

The question relates to the probability of drawing a yellow or green marble from a bag containing marbles of various colors. To find this probability, we must consider the total number of marbles and the number of yellow and green marbles specifically. If a bag contains 3 blue, 2 green, 8 yellow, 4 red, and 3 orange marbles, the total count of marbles is 20.

The probability of drawing a yellow marble (P(Yellow)) is the number of yellow marbles divided by the total number of marbles, which is 8/20 or 0.4. The probability of drawing a green marble (P(Green)) is the number of green marbles divided by the total number of marbles, which is 2/20 or 0.1.

The combined probability of drawing either a yellow or a green marble is found by adding the individual probabilities because these two events are mutually exclusive (they cannot both happen at the same time). So, the probability of drawing a yellow or green marble (P(Yellow or Green)) is P(Yellow) + P(Green) = 0.4 + 0.1 = 0.5.

Therefore, the probability of drawing a yellow or green marble is 0.5 or 50%.

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After 2 days, however, the cost of the delay is $400 plus $50 per day (prorated) for each additional day. That is, if the waiting time is 3.5 days, the cost of the delay is $400 $50(1.5)Find the expected value of the builders cost due to waiting for supplies. Given that Z = X m W = 4x + 20 and m Y = x + 26 find the value of x for which WXYZ must be a parallelogram A city pool sells full-day and half-day passes during the summer. The goal is to make $1000 each day from pool pass sales. The graph shows the number of full-day and half-day passes they need to sell to make $1000. What is the maximum number of half-day passes the pool can sell and make exactly $1000? Which of the following statements can be added to support the idea that when the government gets involved, people conserve more? A. By conserving water, it benefits people who live in communities that rely on one water source. B. Glass is a resource many people never consider recycling because of its weight. C. 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