complete the steps to solve the polynomial equation x3-21x=-20 according to the rational root theorem, which number is a potential root of the polynomial?

Answers

Answer 1

x^3 - 21x + 20 = 0

potential roots are factors of 20 eg 1, 2 ,4 ,5, 10, 20 and the negative values of these
1 looks like a rots . Try it:-
f(1) = 1 - 21 + 20 = -20+20 = 0

Yes 1 is a solution.

2 is not.

Try 4:-

4^3 - 21*4 + 20 = 64 - 84 + 20 = 0

Try 5 No
Try 10 - N0
20 no.

Try -4 - No
-5:-

Yes

Roots are 1, 4 and -5

Related Questions

Which equivalent expression will be generated by applying the Distributive Property and combining like terms in the expression 11 + 4(x + 2y + 4)?

Answers

11 + 4(x + 2y + 4)
= 11 + 4x + 8y + 16 ..........distributive property
= 4x + 8y + 27 .................combine like terms

How many possible outcomes are there from choosing an outfit from a blue shirt, a red shirt, black shorts, tan shorts, a pair of sneakers, and a pair of sandals?

Answers

2 shirts
2 shorts
2 shoes

2 x 2 x 2 = 8 different ways

PLZ HELP!! 20 points!

Is (3,-2) the solution to this system of equations? show how you determined your answer.

-2x-4y=2
3x+4y=8

Answers

To find if a point is a solution to a system of equations, we need to plug in the x and y values of the point into each equation, and see if the equation is true.

Let's plug it into the first equation first:

-2(3) - 4(-2) might = 2
-6 + 8 = 2

The first equation is true.

Now, we need to check the second equation:

3(3) + 4(-2) might =8
9 - 8 does not = 8

Therefore, even if the point satisfies one equation, it does not satisfy the other. We can conclude that this is not a solution.

Hope this helps!

A cab driver is paid $6 plus $0.45 per mile driven. Which expression shows the amount of money the cab driver earns in m miles?

Answers

No expressions are showing to choose from, but it should look like:

A= amount of money earned
m= # of miles driven

Amount earned equals $6 plus ($0.45 times the # of miles driven.)

EQUATION:
A= $6 + $0.45m

Hope this helps! :)

Answer:

C/ 0.45m + 6

Step-by-step explanation:

i did the quiz

Jose and Sue are playing a board game. If they land on a red or blue square, they lose 1 point. The inequality statement compares the magnitude of their scores at the end of the game. |−2|<|−5| What does the inequality statement show?

Answers

Final answer:

The inequality statement |−2|<|−5| shows that 2 is less than 5.

Explanation:

In mathematics, an inequality compares two expressions or values, indicating their relative size. Symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to) represent inequalities.

The inequality statement |−2|<|−5| compares the magnitude of two numbers, -2 and -5. To find the absolute value of a number, we remove the negative sign. So, |−2| is equal to 2 and |−5| is equal to 5. Therefore, the inequality statement |−2|<|−5| means that 2 is less than 5.

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A city council consists of six democrats and five republicans. If a committee of seven people is selected, find the probability of selecting four Democrats and three republicans.

Answers

Use hypergeometric distribution where there are two categories of identical objects/persons, each with a know size.
d=number of Democrats selected
D=total number of Democrats = 6
r=number of Republicans
R=total number of Republicans =5
Then
[tex]P(d,r)=\frac{C(D,d)C(R,r)}{C(D+R,d+r)}[/tex]
where
[tex]C(n,r)=\frac{n!}{(n!(n-r)!)}[/tex] = combination of r items selected from n,
D+R=total number of members = 6+5 =11
d+r=number of members selected = 7

[tex]P(d,r)=\frac{C(D,d)C(R,r)}{C(D+R,d+r)}[/tex]
[tex]P(4,3)=\frac{C(6,4)C(5,3)}{C(6+5,4+3)}[/tex]
[tex]=\frac{C(6,4)C(5,3)}{C(11,7)}[/tex]
[tex]=\frac{15*10}{330}[/tex]
[tex]=\frac{5}{11}[/tex]

Answer: the probability of selecting 4 Democrats and 3 Republicans is 5/11

Two cones have a radius of 2 cm. The height of one cone is 8 cm. The other cone is 14 that height. Which of these statements is NOT true?

Answers

the correct question is
Two cones have a radius of 2 cm. The height of one cone is 8 cm. The other cone is 1/4 that height. Which of these statements is NOT true?

the statements in the attached figure

we know that
r=2 cm
h1=8 cm
h2=(1/4)*8=2 cm
[Volume of cone 1]=(π*r²*h)/3--------> (π*2²*8)/3= 33.49 cm³
[Volume of cone 2]=(π*r²*h)/3--------> (π*2²*2)/3---------> 8π/3= 8.37 cm³

Statements A)
The volume of the smaller cone is (1/4)(1/3π • 2 • 2 • 8) cm3---------> is true

Statements B)
The volume of the smaller cone is (1/3)(4π • 2) cm3.-----------> is true

Statements C)
The volume of the smaller cone is (8/3)π cm3. -----------> is true

Statements D)
The volume of the smaller cone cannot be determined because its height is unknown-----------> is not true

the answer is the Statements D)
The volume of the smaller cone cannot be determined because its height is unknown-----------> is not true

Select the ratios that are equivalent to 3 boys and 5 girls

Answers

You have given no choices, but here are some.
6/10
9/15
12/20
15/25

kenny wants to buy gifts for all 18 of his co workers. He can buy t shirts for $10 and hats for $12. He plans on spending $200 for all 18 gifts. If Kenny wants to spend all of his money, how many of each type of gift can he buy?

Answers

10 hats, 8 t shirts = 18
10X12=120 8X10=80 12+80=200

Martha is standing on a street corner in a big city, facing south. She walks 5 blocks to the south. Then, she turns right and walks 3 blocks. Then, she turns right as walks 2 blocks. Then, she turns right again and walks 1 block. Finally, she turns left and walks 5 blocks. What direction is she facing when she is done?

Answers

In the north direction, Martha facing if the Martha is standing on a street corner in a big city, facing south.

What is direction?

The four cardinal directions, sometimes known as cardinal points, are the four principal compass directions: north, east, south, and west, which are frequently abbreviated as N, E, S, and W.

We have:

Martha is standing on a street corner in a big city, facing south. She walks 5 blocks to the south.

Then, she turns right and walks 3 blocks. Then, she turns right as walks 2 blocks. Then, she turns right again and walks 1 block.

If we draw a line diagram, we will see:

She will be facing at North.

Thus, in the north direction Martha facing if the Martha is standing on a street corner in a big city, facing south.

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108+621 is the same as 100+ what

Answers

I think the answer you looking for is 629

Hayden is a manager at a landscaping company. He has two workers to landscape an entire park, Cody and Kaitlyn. Cody can complete the project in 8 hours. Kaitlyn can complete the project in 6 hours. Hayden wants to know how long it will take them to complete the project together.

Write an equation and solve for the time it takes Cody and Kaitlyn to complete the project together. Explain each step.

Answers

Answer: 3.4 h

Explanation:

1) The basis to solve this kind of problems is that the speed of working together is equal to the sum of the individual speeds.

This is: speed of doing the project together = speed of Cody working alone + speed of Kaitlyin working alone.

2) Speed of Cody

Cody can complete the project in 8 hours => 1 project / 8 h

3) Speed of Kaitlyn

Kaitlyn can complete the project in 6 houres => 1 project / 6 h

4) Speed working together:

1 / 8 + 1 / 6 = [6 + 8] / (6*8 = 14 / 48 = 7 / 24

7/24 is the velocity or working together meaning that they can complete 7 projects in 24 hours.

Then, the time to complete the entire project is the inverse: 24 hours / 7 projects ≈ 3.4 hours / project.Meaning 3.4 hours to complete the project.

Denote all work that should be done as 1. Then if Cody can complete the project in 8 hours, he can do [tex] \frac{1}{8} [/tex] per hour and if Kaitlyn can complete the project in 6 hours, then she can do [tex] \frac{1}{6} [/tex] per hour. Together they complete [tex] \frac{1}{8}+\frac{1}{6} [/tex] per hour.

Simplify this expression:

[tex] \dfrac{1}{8} +\dfrac{1}{6} =\dfrac{3}{24} +\dfrac{4}{24}=\dfrac{7}{24} [/tex].

Then it will take them to complete the project together [tex] \dfrac{1}{\frac{7}{24}} =\dfrac{24}{7} =3\dfrac{3}{7} [/tex] hours

Answer: It will take them to complete the project together [tex] 3\dfrac{3}{7} [/tex] hours.

HELP SUPER FAST PLS A rectangular cardboard has dimensions as shown. The length of the cardboard can be found by dividing its area by its width. What is the length of the cardboard in inches?

Rectangle with width labeled on the right, width equals 4 and 1 over 2 inches. Below the rectangle, it says, length equals question mark. Inside the rectangle, it says area equals 36 and 3 over 4 square inches

Answers

ok, so area/width=length

then they gave you mixed fractions
they want you to practice converting mixed fractions into improper fractions and dividing them

rmember, improper fractions are a/b where a>b sometimes

and also remember that [tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ad}{bc}[/tex]

okie dokie

width
4 and 1/2=width
4+1/2=width
8/2+1/2=width
9/2=width

area=36 and 3/4
area=36+3/4
area=144/4+3/4
area=147/4

so area/width=length
[tex]\frac{\frac{147}{4}}{\frac{9}{2}}=length[/tex]
[tex]\frac{(147)(2)}{(4)(9)}=length[/tex]
[tex]\frac{294}{36}=length[/tex]
[tex]\frac{49}{6}=length[/tex]
[tex]\frac{48}{6}+\frac{1}{6}=length[/tex]
[tex]8+\frac{1}{6}=length[/tex]

so the length is [tex] 8 \space\ and \space\ \frac{1}{6} \space\ in[/tex]

Answer:

8 1/6

Step-by-step explanation:

hope it helps

What fraction of the circle does the shaded angle represent??

Answers

The fraction of the circle that is not shaded is 3/4
The fraction of the circle that is shaded is 1/4

shaded part is 1/4

non shaded ( not shaded) is 3/4

altogether it would be 4/4 or one whole

What is the circumference of circle p? Express your answer in terms of pi , ab = 14

Answers

C=2πr hope this helps have a great day

Answer:

14 pi in.

Step-by-step explanation:

hop this helps!

which is more, 5,998 millimeters or 6 meters

Answers

6 meters of course is the answer

There is an ice cream and candy shop next-door that is the same size as your bakery. How many 30th of the space does it take up

Answers

Well, this is basically perimeter and Area. So, if there next door, your going to want to find out 50% of the ice cream shop and candy shop. 40% of it is next to each other . So 40 x 2= 80, there’s the answer . Hope this helps!!!

Suppose that g(x) = f(x – 8). Which statement best compares the graph of g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) shifted 8 units to the left.
B. The graph of g(x) is the graph of f(x) shifted 8 units down.
C. The graph of g(x) is the graph of f(x) shifted 8 units up.
D. The graph of g(x) is the graph of f(x) shifted 8 units to the right.

Answers

D. The graph of g(x) is the graph of f(x) shifted 8 units to the right.

The graph of g(x) is the graph of f(x) shifted 8 units to the right.

Option D is correct.

What is shifting of a function?

A shift is a rigid translation in that it does not change the shape or size of the graph of the function. All that a shift will do is change the location of the graph. A vertical shift adds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged.

According to the question

g(x) = f(x – 8)

If the function is shifted to the left it is going to plus(+).

If the function is shifted to the right it is going to minus(-).

Hence, The graph of g(x) is the graph of f(x) shifted 8 units to the right.

Option D is correct.

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Solve using the arrow way
430-230?

Answers

To substract the numbers shown by the method known as the "Arrow way" you must rewrite 430 and substract the hundredths (In this case, it is 200). Then you have to substract the tenths to that result (Result obtained-30). This explanation is shown below:

430 --( -200 )---> 230 --( -30 )---> 200

Therefore, the solution of the mathematical operation 430-230, using the arrow way, is: 200

Please help me with questions 8 and 9

Answers

Problem 8

Answer: Choice A
Coordinates have been multiplied by a scale factor of 0.5

For instance
A = (-3, 4)
Multiply the coordinates by 0.5 to get
-3*0.5 = -1.5
4*0.5 = 2
So the coordinates of A' are (-1.5, 2) which is what matches what we're given above. The same will happen with B and C as well.

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

Problem 9

Answer: choice C) x = 25; larger angle is 107 degrees

Work Shown:
(3x+32)+(x+48) = 180
4x+80 = 180
4x = 100
x = 25
If x = 25, then,
3x+32 = 3*25+32 = 107
x+48 = 25+48 = 73
So the larger angle is 107

Can you please help me out ?

Answers

What you can do for this case is to use the following trigonometric definition.
sine (x) = a / h
Where,
a: side of the triangle.
h: hypotenuse.
Substituting:
sine (x) = 3/6
x = Arcosine (1/2)
x = 30 degrees.
The other angle is:
180-30-90 = 60 degrees
Answer:
W = 30
V = 60
U = 90
option 4

The legs of a right triangle are 12 cm and 16 cm. What is the length of the hypotenuse? 15 cm 17 cm 20 cm 28 cm

Answers

Answer: 20 cm

To solve this, use the Pythagorean Theorem, a² + b² = c², where a and b are the legs of the right triangle, and c is the hypotenuse of the right triangle.
**The Pythagorean Theorem only works for right triangles.**

Substitute in the values.
a² + b² = c²
12² + 16² = c²

Solve for c, the hypotenuse.
12² + 16² = c²
144 + 256 = c²
400 = c²
c = √400
c = 20

Answer:

20cm

Step-by-step explanation:

What is the approximate volume of the cylinder with a height of 5 and a diameter of 4? round to the nearest tenths place

Answers

Formula for volume of cylinder:
V=πr²h
Here height, h= 5 units
Diameter, d= 4 units
So, radius, r= d/2 = 4/2 =2 units
Put values in formula.
V= (3.14)(2)²(5)
V=62.8 Cubic units

Answer: 62.8 cubic units

Alex lives eight tenth of a mile from Sarah. What is eight tenths written as a decimal

Answers

Hello!

Eight tenths = 8/10

To convert a fraction to a decimal, we must divide the numerator by the denominator.

8 ÷ 10 = 0.8

Eight tenths is 0.8 as a decimal.

the answer is 0.8

I hope this helps

How many quarter inches long is 7 3/4

Answers

The number of quarters in 7 is 28 and the number of quarters in 3/4 is 3. Then the total number of quarters is 33.

What is a fraction number?

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.

The quarter is written as one-fourth.

[tex]\rm quarter = \dfrac{1}{4}[/tex]

We have 7 + 3/4

We know that one has 4 quarters then 7 has

→ 7 × 4 = 28

And 3/4 has three quarters.

Then the total quarter will be

[tex]\rm Number\ of \ quarter = 7 \dfrac{3}{4} \times 4 = \dfrac{33}{4} \times 4 = 33[/tex]

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Final answer:

There are 31 quarter inches in 7 3/4 inches. This is determined by converting the mixed number into an improper fraction and then dividing by ¼, which gives us 31/4 or 31 quarter inches.

Explanation:

The question asks how many quarter inches there are in 7 3/4 inches. To find this, we can convert the mixed number into an improper fraction and then divide by the fraction representing a quarter inch (¼ inch).

First, convert 7 ¾ to an improper fraction by multiplying the whole number 7 by the denominator 4 and then adding the numerator 3. This gives us 28 + 3 = 31, so 7 ¾ inches is equivalent to ⅔31/4 or 31 quarter inches. Therefore, 7 3/4 inches is 31 quarter inches long.

James Callahan has available a 10% alcohol solution and a 60% alcohol solution. Find how many liters of each solution he should mix to make 50 liters of a 40% alcohol solution?

Answers

Let
x-------------> liters of 10% alcohol solution
y-------------> liters of 60% alcohol solution

we know that
x+y=50----------------------> x=50-y-----------------> equation 1
0.10x+0.60y=0.40*50----------> 0.10x+0.60y=20---------> equation 2

substitute 1 in 2
0.10*(50-y)+0.60y=20---------> 5-0.10y+0.60y=20
5+0.50y=20------------> 0.50y=15-----------------> y=30
x+y=50----------> x=50-30---------> x=20

the answer is
20 liters of 10% alcohol solution
30 liters of 60% alcohol solution

What does the random variable for a binomial experiment of n trials measure?the random variable measures the number of successes out of n trials.the random variable measures the number of failures out of n trials. the random variable measures the standard deviation of n trials.the random variable measures the mean of n trials?

Answers

My answer is the random variable measures the number of successes out of n trials.

A binomial random variable is defined as the number of successes x in n repeated trials of a binomial experiment. It is more feasible to measure the number of successes than the number of failures because the more successes you have, the nearer you are to your desired goal in a binomial experiment.

Answer:

The random variable measures the number of successes out of n trials.

you lease a car valued at 23,495 for 3 years at $429.95/month with a $500 down payment. If interest is 30% of the payment, how much interest is paid over the 3 years?

Answers

(36 payments)*($429.95)*30% = $4,643.46 . . . . interest paid over 3 years

Solution:

Present Value of car= $ 23,495

Down Payment = $ 500

Total Amount paid monthly for 3 years that is 36 months, if you pay $ 429.95 per month=$ 15478.20

Total amount paid for the car as an agreement which includes Down payment of $ 500 as well as monthly Payment of $ 429.95 for 36 months= $ 15478.20+$ 500=$ 15978.20

As, given Interest is 30% of the payment.

So, total interest = 30% of $ 15978

[tex]=\frac{30}{100}\times 15978.20[/tex]

= $ 4793.40

But if you will calculate interest on payment of $ 429.95 at the rate of 30%, it gives

[tex]=\frac{30}{100}\times 429.95[/tex]

= $128.985

So, total interest for 3 years= $128.985 ×36=$ 4643.46

Also, if you will calculate interest on payment of ($500+$429.95=$929.95) at the rate of 30%

[tex]=\frac{30}{100}\times 929.95[/tex]

=$278.985

Total interest for 3 years= $278.985 ×36=$10,043.46

One positive integer is 6 less than twice another. The sum of their squares is 468. Find the integer

Answers

I think I deserve your points and brainliest :^)

The two integers are 12 and 18.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, one positive integer is 6 less than twice another.

Let positive integer be x and the other positive integer is 2x-6

x²+(2x-6)²=468

x²+4x²-24x+36=468

5x²-24x+36-468=0

5x²-60x+36x-432=0

5x(x-12)+36(x-12)=0

(x-12)(5x+36)=0

(x-12)=0

x=12

So, 2x-6=18

Therefore, the two integers are 12 and 18.

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Find the solution of the differential equation that satisfies the given initial condition. du/dt = (2t+sec^2t)/2u, u(0) = -3

Answers

Consider, pls, this option (see the attachment) of 3 steps.

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