Factor the polynomial: b^3 - 5b^2 - 4b + 20

Answers

Answer 1

b^3 - 5b^2 - 4b + 20

b^2(b - 5) - 4(b - 5)

(b - 2)(b + 2)(b - 5)





Related Questions

Solve the system of equations: 12x + 6y = 60 and 3y = -6x + 30

a) (10,0)
b) (0,10)
c) Infinite Solutions
d) No solutions

Answers

Hello there!

12x + 6y = 60
3y = -6x + 30

Ok so we need to solve 12x + 6y = 60 for x

Let's start by adding -6y to both sides

12x + 6y - 6y = 60 - 6y

12x = -6y + 60

Since we are looking for x, we need to divide both sides by 12

12x/12 = (-6y + 60)/12

x = -1/2 y + 5

We are not done yet, now we need to substitute -1/2 y + 5 for x in 3y = -6x + 30

3y= -6x + 30

3y = -6(-1/2 y + 5)+ 30

3y = 3y

Finally subtracting 3y from both sides

3y - 3y = 3y - 3y

0 = 0

Thus, Infinite Solutions

A scuba diver's vertical position in relation to the surface of the water changes by -90 ft in 3 min. What is the average change in the diver's vertical position each minute?

Answers

-90 / 3 = -30 ft per minute <==
I believe the answer to this -30 ft a min. if you take -90 and divide it by 3 you get -30. I hope this helps you out.:)

Read the proposition and the implication shown below. "If the lights are off, there is no one inside." Which statement is a contrapositive to the proposition and logically equivalent to it?

Answers

The contrapositive switches the hypothesis and the conclusion and negates both in this form:
Statement: If A, then B
Contrapositive: If not B, then not A. 

In this case, the statement is: 
 "If the lights are off, there is no one inside."
Contrapositive:
If there is someone inside, the lights are on. 
Final answer:

The contrapositive of the proposition 'If the lights are off, then there is no one inside' is 'If there is someone inside, then the lights are not off'. Contrapositives are formed by negating and interchanging the hypothesis and conclusion of a conditional statement, and is a key concept in mathematics.

Explanation:

In logic, the contrapositive of a conditional statement is formed by negating both the hypothesis and the conclusion, and then interchanging the resulting negations. So, the contrapositive of the given proposition 'If the lights are off, then there is no one inside' would be 'If there is someone inside, then the lights are not off'.

This implies that, in the context of this statement, if we know that there is someone inside, we can deduce that the lights must not be off as per the contrapositive. Thus, contrapositives are a helpful way to understand conditional statements from another perspective, and are an integral concept in logic and mathematics.

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If 4/5 of a population of a certain town is considered to be middle class and the population of the town is 2000 how many people are considered middle class

Answers

First, you would need to create an equation for this problem.
[tex] \frac{4}{5} [/tex] = [tex] \frac{x}{2,000} [/tex]

Next, you would cross multiply. 
5x = 8,000

Now, all you would have to do is isolate the x. To do this, you would divide both sides by 5. 
x = 1,600

1,600 people are considered middle class. 

I hope this helps!

5. At a local store you find the following prices listed: Tape 2 rolls for $1.28 Notepads 3 pads for .87 Highlighters 1 for 1.59 Pens 2 for 1.98 How much would you pay for one roll of tape, two note pads, two highlighters, and two pens? A. $5.72 B. $6.38 C. $4.50 D. $8.07

Answers

To find the cost of one roll of tape, we divide the given price by 2 because the given price is for twice the number of rolls that we want.
$1.28/2 = $0.64
----------------
To find the cost of two note pads, we first divide the given price by 3 because we want to know how much one note pad costs.
$0.87/3 = $0.29
Each note pad is 29 cents. Since we want to note pads, we double this amount.
$0.29*2 = $0.58
----------------

One highlighter costs $1.59. We want two of them, so we double this amount.
$1.59*2 = $3.18
----------------
We want two boxes of ink catridges, and we are told that two boxes cost $1.98.
----------------
Let's total the amounts:
$0.64 + $0.58 + $3.18 + $1.98 = $6.38
We would pay $6.38 for these seven items.
the answer to the question above is $6.38

Which of the angles are congruent, select all that apply

Answers

The first and last one

PLEASE HELP. Which is the best interpretation of the solution set for the compound inequality? 3/2x-1<2x + 4 or 3(2/3x + 1) < 11 A. no solution B. x > -10 C. x<4 D. all real numbers.

Answers

(3/2)x-1<2x+4
3x-2<4x+8
-2<x+8
-10<x
x>-10

3((2/3)x + 1) < 11
(3*2/3)x+1*3<11
2x +3<11
2x<8
x<4

so the compound equality is the set of all numbers which are >-10 or <4, which are D) all real numbers

Answer:

D

Step-by-step explanation:

Just did it

Can someone help me pls ?

Answers

8: 25/5=5 5x10=50 100-50=50
10: 3x5=15 2x5=10 15-10=5
12: 56/7=8 42/7=6 8x6=48



Remember: PEMDAS

Parentheses (please)
Exponets (excuse)
Multiply (my)
Divide (dear)
Add (aunt)
Subtract (sally)

From left to right as if reading a book

i am a fraction in the simplest form. i am greater than 4/5. the sum of my terms is 25. what fraction am i?

Answers

The fraction is 12/13. It is written in simplest form and the sums of the terms are equal to 25.

A ticket agency charges 9.5% fee on all tickets sold .if a ticket cost 40$ what is the fee

Answers

$3.80 

you have to multiply the 9.5% fee by $40 and you will get how much the fee will be 
Find 9.5% of $40 and then add the result to 40
0.095x40=3.8
40+3.8=43.8
So it costs $43.80

Pizza World has a specialty cheese pizza that can be cut into 10 slices, and they have a specialty pepperoni pizza that can be cut into 16 slices. If Pizza World serves combos of one slice of cheese and one slice of pepperoni pizza with no slices left over, what is the smallest number of combos that Pizza World can prepare?

Answers

16/10=1.6 so the smallest number of combos would be 1.

The smallest number of combos that Pizza World can prepare with one slice of cheese and one slice of pepperoni pizza with no slices left over is 80.

The student is asking how many combos of one slice of cheese and one slice of pepperoni pizza Pizza World can prepare with no slices left over given that a cheese pizza has 10 slices and a pepperoni pizza 16 slices. This question is looking for the least common multiple (LCM) of two numbers, which is the smallest number that is a multiple of both numbers. To find the LCM of 10 and 16, we list the multiples of each number until we find a common multiple. The multiples of 10 are 10, 20, 30, 40, 50, 60, ... and the multiples of 16 are 16, 32, 48, 64, 80, .... The smallest common multiple of 10 and 16 is 80. Therefore, we can prepare 80 combos using 8 cheese pizzas (because 8 x 10 = 80) and 5 pepperoni pizzas (because 5 x 16 = 80).

the music for Alyssa's dance routine last exactly 4 min. when she dances her routine, she starts with her music and finishes 12 seconds before the music ends. what percent of the time the music is playing is Alyssa dancing.

Answers

If her music lasts 4 minutes, her music is 60*4=240 seconds since there are 60 seconds in a minute. Next, since her dance is 12 seconds less than the music, her dance is 240-12=228 seconds long. To finish this up, we have 228/240. I challenge you to figure out the percentage on your own!

As an example, we have 123/463, which is around 0.266. Multiplying that by 100, we end up with around 26.6 percent as the percent 123 is of 463

joe's cell phone costs him $21 per month plus $3 for every 1GB of data downloaded. What is the limit to the number of GBs he can download to stay within his monthly budget of $30.

Answers

3GB’s you just add 21 to 3 and keep adding 3 until you reach 30

21+3=24 24+3=27 27+3=30

joe can only use 3gb of data . bill is 21

21+9+30

1gb=3

3*9=9

3(3)+21=30

-4 1/2, -5.6, -2 3/8, 2.35 from least to greatest

Answers

Hello!

-2 3/8, -5.6, -4 1/2, 2.35.

Those are ordered from least to greatest!

I really hope you found this helpful! c:

1.2 divided by .3 in the model

Answers

Final answer:

The solution for the division of 1.2 by .3 is 4. This can be visualized by considering how many times .3 fits into 1.2, or by dividing equivalent decimals.

Explanation:

To solve the problem 1.2 divided by .3, simply divide the numbers as you would normally. For this problem, 1.2 divided by .3 equals 4. This is because the fundamental basis of division is how many times one number fits into another. In this case, .3 'fits' into 1.2, four times.

Alternatively, you can think of this process in three steps: First, convert 1.2 to an equivalent decimal of 12 tenths. Then, divide that by .3 (or 3 tenths). The result is 4 because 3 tenths 'fits' into 12 tenths, four times.

Another way to cross-verify your result is by multiplying the divisor (.3) by the quotient (4). The product should be equal to the dividend (1.2). Here, .3 multiplied by 4 equals 1.2, hence confirming the correctness of the answer.

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Final answer:

To divide 1.2 by 0.3 in a model, first convert the decimal numbers to fractions. Then, divide the numerator by the denominator to get the answer, which is 4.

Explanation:

To divide 1.2 by 0.3 in a model, we can use a similar approach to the example given. Let's first convert the decimal numbers into fractions by using the place value of the decimal places. 1.2 is equivalent to 12/10 and 0.3 is equivalent to 3/10.

Next, we can set up a division problem where the numerator is 12 and the denominator is 3, giving us 12 ÷ 3. This can be simplified to 4, so 1.2 divided by 0.3 in the model is equal to 4.

Therefore, the answer to 1.2 divided by 0.3 in the model is 4.

-6 + (-5) + 7
what do I need to do first?

Answers

Add the negative numbers.

-6 + (-5) +7

just add from left to right:

 1st step:

-6 + (-5) = -11

 2nd step:

-11 +7 = -4

Please solve this equation 2/5h +g =d for h

Answers

2/5h+g=d
(2)         (2)
2times 2 cancels out 
5h+g=2d
     -g  -g
g cancels out 
5h=2d-g
/5     /5
5 cancels out 
h=(2d-g)/5

163water bottles in 9 cases=

Answers

you would do 163 ÷ 9 and you will get your answer

A students work to solve 2 6/7 / 2/7 is shown below.
Which of the following statements do you agree with.

2 6/7 / 2/7 =
19/7 / 2/7 =
7/19 x 2/7 =
1/19 x 2/1 = 2/19

A. The only mistake is changing the mixed number to an improper fraction.
B. There's a mistake with the multiplicative inverse 2/7 .
C. The problem looks correct.
D. There's a problem with changing the mixed number to an improper fraction, as well as changing the division problem to multiplication.

Answers

A) the only mistake is changing the mixed number to an improper fraction . 

Answer:

D. There's a problem with changing the mixed number to an improper fraction, as well as changing the division problem to multiplication.

Step-by-step explanation:

We have shown work of a student to solve a division of fractions. We are asked to check student's work.

Let us check

[tex]2\frac{6}{7}\div\frac{2}{7}[/tex]

Convert mixed fraction into improper fraction:

[tex]2\frac{6}{7}\Rightarrow \frac{2\times 7+6}{7}=\frac{14+6}{7}=\frac{20}{7}[/tex]

[tex]\frac{20}{7}\div\frac{2}{7}[/tex]

Convert division problem to multiplication problem by flipping the 2nd fraction:

[tex]\frac{20}{7}\times\frac{7}{2}[/tex]

[tex]\frac{20}{1}\times\frac{1}{2}[/tex]

[tex]\frac{20}{2}[/tex]

[tex]10[/tex]

Therefore, the student made two mistakes and option D is the correct choice.

Amber has a 4/5 pound bag of colored sand, she uses 1/2 of the bag for an art protect. How much sand does she uses for the protect?

Answers

Okay. So, Amber used 1/2 of the 4/5 bag for the art project. Let’s do 4/5 / 2. 4/5 * 1/2 is 4/10 or 2/5 in simplest form. Amber uses 2/5 of a pound of sand for her art project.

In solving the inequality -3x < 9, you would divide both sides of the inequality by -3 and flip over the inequality symbol. true or false

Answers

True.

Dividing by a negative number flips the inequality symbol while if you divided by a positive number, the inequality would remain facing the same way.

Answer: true.

Step-by-step explanation: do you really want an explanation?

what is the area of a rectangle with a length of 6 2/5 feet and width of 4 1/6 feet

Answers

6.4 Ft. *  4.2 feet equals  26.88 square feet

Solve (−3) ⋅ 2.
−6
−5
5
6

Answers

The answer is -6 because a negative times a positive is a negative 
To solve (-3) • 2

You can simply multiply -3 by 2 by thinking of adding adding -3 to itself twice

-3 + -3

-6 is your answer

Hope this helps!

is it true that Kilogram is a unit of volume.

Answers

This is false. Kilograms are units of Mass.

A candle is 6 inches tall and burns at a rate of one half an inch per hour. Write an equation to represent the situation.

Answers

Answer: [tex]y=6-0.5x[/tex]

Step-by-step explanation:

Given  : The initial height of candle = 6 inches

Amount of candle burn each hour = one half an inch per hour.

[tex]=\dfrac{1}{2}\text{ inch per hour}[/tex]

Now , the height of candle = ( initial height ) -( Rate of burning) (Numb er of hours)

Let y be the height of the candle after x hours.

Then, the equation to represent the situation will be :

[tex]y=6-\dfrac{1}{2}x\\\\\Rightarrow\ y=6-0.5x[/tex]

The equation to represent the situation will be, [tex]y=6-\frac{1}{2} \times x[/tex].

Given A candle is 6 inches tall.

The candle burns at a rate of one half an inch per hour.

Let [tex]x[/tex] be the number of hours candle burn and [tex]y[/tex] be the height of the candle after [tex]x[/tex] hours.

Now , the height of candle = ( initial height ) -( Rate of burning) (Number of hours)

So, the equation to represent the situation will be, [tex]y=6-\frac{1}{2} \times x[/tex].

For more details on equation forming follow the link:

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(1-x)y"-4xy'+5y=cosx

Answers

y"(1-x) - 4ry' + 5y - cos(x)= 0

passes through (-1,4) and m=4

Answers

point-slope formula;

y - y1 = m(x - x1)        given point(-1, 4) and slope(m) is 4.

y - 4 = 4(x - (-1)

y - 4 = 4x + 4

y = 4x + 4 + 4

y = 4x + 8               << the equation.

hope this helped, God bless!
Final answer:

To find the equation of the line passing through the point (-1, 4) with slope 4, we use the point-slope form. Substituting the values into the formula, we find the equation to be y = 4x + 8.

Explanation:

In the given question, we have a line that passes through the point (-1, 4) and has a slope of 4.

To find the equation of this line, we can use the point-slope form, which is given by y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Substituting the values into the formula, we get y - 4 = 4(x - (-1)). Simplifying further, we have y - 4 = 4x + 4. Rearranging the equation, we find the equation of the line to be y = 4x + 8.

If triangle JKL s congruent to triangle RST which congruences are true by CPCTC

Answers

the true statements by CPCTC are options A, B, and C. [tex]\( \overline{KL} \cong \overline{ST} \)[/tex] ,[tex]\( \overline{JK} \cong \overline{RS} \)[/tex], [tex]\( \angle K \cong \angle S \)[/tex].

CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." It means that if two triangles are congruent, then their corresponding parts are also congruent.

Given that △ JKL ≌ △ RST, let's examine each option:

A. [tex]\( \overline{KL} \cong \overline{ST} \)[/tex] - True by CPCTC, corresponding sides of congruent triangles are congruent.

B. [tex]\( \overline{JK} \cong \overline{RS} \)[/tex] - True by CPCTC, corresponding sides of congruent triangles are congruent.

C. [tex]\( \angle K \cong \angle S \)[/tex] - True by CPCTC, corresponding angles of congruent triangles are congruent.

D. [tex]\( \angle L \cong \angle R \)[/tex] - This statement cannot be determined solely from the fact that △ JKL ≌ △ RST. The corresponding angles may or may not be congruent, depending on the specific congruent triangles.

E. [tex]\( \overline{JL} \cong \overline{RS} \)[/tex] - This statement cannot be determined solely from the fact that △ JKL ≌ △ RST. The corresponding sides may or may not be congruent, depending on the specific congruent triangles.

F. [tex]\( \angle J \cong \angle S \)[/tex] - This statement cannot be determined solely from the fact that △ JKL ≌ △ RST. The corresponding angles may or may not be congruent, depending on the specific congruent triangles.

Therefore, the true statements by CPCTC are options A, B, and C.

The complete question is:

If △ JKL≌ △ RST, which congruences are true by CPCTC? Check all that apply.

A. [tex]\( \overline{KL} \cong \overline{ST} \)[/tex]

B. [tex]\( \overline{JK} \cong \overline{RS} \)[/tex]

C. ∠ K≌ ∠ S

D. ∠ L≌ ∠ R

E. [tex]\( \overline{JL} \cong \overline{RS} \)[/tex]

F. ∠ J≌ ∠ S

Factor out the coefficient of the variable.
The expression 38d+34 factored is

Answers

Final answer:

The highest common factor of 38 and 34 is 2. Dividing both coefficients by 2 gives us 19d and 17. Therefore, the factored expression of 38d + 34 is 2(19d + 17).

Explanation:

Factoring out the coefficient of a variable in the expression 38d + 34 involves finding a number that divides both coefficients exactly. The highest common factor (HCF) of 38 and 34 is 2. So, we divide 38 and 34 by 2 to get 19d and 17 respectively.

Therefore, the expression, when factored out, becomes 2(19d + 17). This means that the expression 38d + 34 can thus be factored into 2 times the expression (19d + 17).

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My number has 2 hundreds. The tens digit is 9 more than the ones digit

Answers

The number is 290. What is in the ones place

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