Mathematics College

I WILL GIVE BRAINLIEST IF YOU CAN ANSWER THESE TWO QUESTIONS!!!!

2. Darwin believes that x + b is a factor of (x + b)3 + (x + c)2 – (b - c), while Eunju
believes it is not. Who is correct? Justify your response.

3. How can you prove that x2 + 5x + 6 is a factor of x* + 5x3 + 2x2 – 20x – 24, without
using long or synthetic division?

Answers

Answer 1

Answer:

2. Eunju is right

3. [tex]x^2+5x+6[/tex] is a factor of [tex]x^4+5x^3+2x^2-20x-24[/tex].

Step-by-step explanation:

Polynomial Remainder Theorem

The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-a) is equal to f(a).

As a consequence, if a polynomial is divisible by x-a, f(a)=0.

Part 1:

Let's make:

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

To find out if x+b is a factor of f(x), we find f(-b):

[tex]f(-b)=(-b+b)^3+(-b+c)^2-(b-c)[/tex]

Operating:

[tex]f(-b)=(-b+c)^2-(b-c)[/tex]

The value of f(-b) is not zero. This means Eunju is right, x+b is not a factor of f(x).

Part 2:

We must find out if [tex]x^2+5x+6[/tex] is a factor of [tex]x^4+5x^3+2x^2-20x-24[/tex] without using long division or synthetic division.

We can use the polynomial remainder theorem again, but since the factor is not in the form (x-a), we can factor it as follows:

[tex]x^2+5x+6 =(x+2)(x+3)[/tex]

Now we just apply the theorem twice. If both remainders are zero, then the assumption is true.

Let's make:

[tex]f(x)=x^4+5x^3+2x^2-20x-24[/tex]

Find f(-2):

[tex]f(-2)=(-2)^4+5(-2)^3+2(-2)^2-20(-2)-24[/tex]

[tex]f(-2)=16-5*8+2*4+40-24 =16-40+8+40-24=0[/tex]

Find f(-3):

[tex]f(-3)=(-3)^4+5(-3)^3+2(-3)^2-20(-3)-24[/tex]

[tex]f(-3)=81-5*27+2*9+60-24[/tex]

[tex]f(-3)=81-135+18+60-24 =0[/tex]

Since both f(-2) and f(-3) are zero, [tex]x^2+5x+6[/tex] is a factor of [tex]x^4+5x^3+2x^2-20x-24[/tex].

Related Questions

Henry is using a total of 16 ft. of lumber to make a bookcase. The left and right sides of the bookcase are each
4 ft. high. The top, bottom, and two shelves are all the same length, labeled S. How long is each shelf?

Answers

Answer: Each shelf is 2ft

Step-by-step explanation:

16 = (2 x 4) + 4s

16 = 8 + 4s

8 = 4s (subtract 8 from both sides)

8/4 = 4s/4 (divide both sides by 4)

2 = s

Solve the equation

(- 5 + 7)5x+ 4=16

The solutions are:

Answers

Answer:

x=2

Step-by-step explanation:

Answer:

x=1.2

Step-by-step explanation:

Please help me in struggling!!!!!!!!!!!!!

Answers

Answer:

Here’s the answer

Step-by-step explanation:

Steve's bedroom measures 12 feet by 13 feet. Ricardo's bedroom measures 8 feet by 14
feet. Assuming that both bedrooms are rectangular, whose room has the greater area?

Answers

Answer: Steve's bedroom has the greater area.

Step-by-step explanation: The formula for area is Area = Length x Width.

So all you have to do to figure this out is multiply the Width of the rooms by the length.

So Steve's room is 12ft X 13ft = 156ft

Ricardo's room is 8ft X 14ft = 112ft

156ft > 112ft

Steve's room has a greater area.

Can anyone help me out solving this?

Answers

Answer: 25

Step-by-step explanation: When you divide exponents with the same base, you can subtract the exponents. It becomes 5^4-2, which is 5^2, which is 25

Yeah 5^4 is 625 and 5^2 is 25 so 625/25 is 25 the answer is 25

what is Evaluate 2. to the 2 power

Answers

Answer:

2^2 = 4

Step-by-step explanation:

2*2 = 4

2 to the 2 power is 2^2 = 2 x 2 = 4

how much change did she receive?

Answers

Umm I’m not good at showing my work but the answer is -1.21

Bob wants to make a profit of $1.25 on each fish. How much should he sell each fish for to make this profit? Show your calculation.

note that each fish costs 2.14

Answers

Bob would have to sell each fish at $3.39 in order to make a profit of $1.25 on each fish sold

What is the selling price per fish?

The selling price per fish can be determined as the sum of the cost price of $2.14 and the profit per fish which is $1.25, in essence, the selling price in this case is the sum of the cost and profit or alternatively, we can model the profit as the selling price minus the cost price as shown below:

profit per fish=selling price-cost price

profit per fish=$1.25

selling price=unknown

cost price=$2.14

By making the selling price the subject of the formula, we can determine the selling price using the formula above

$1.25=selling price-$2.14

selling price=$2.14+$1.25

selling price=$3.39

Find out more about profit on:https://brainly.com/question/17041968

#SPJ1

Angela is planting flowers in her flowerbed. She wants the ratio of tulips to roses to be 5 to 2. If a total of 63 flowers are planted, how many tulips should there be?

Answers

Answer:

45 Tulips

Step-by-step explanation:

63/7=9

Tulips: Roses=5:2

Tulips=9x5=45

Roses=9x2=18

1. The temperature was very cold. Then the temperature doubled. Then the temperature dropped by 10 degrees. Then the temperature increased by 40 degrees. The temperature is now 16 degrees. What was the starting temperature?

Answers

Answer:

10,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

PLEASEEEE HELPP !
A company sells bottles of vitamin capsules. The graph and table show the linear relationship between the cost per capsule in cents and the number of bottles ordered. What is the slope of the line that models this situation?

Answers

Answer:

[tex] slope (m) = -5 [/tex]

Step-by-step explanation:

The slope can be calculated using two points, (2, 60) and (4, 50) as shown below:

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} [/tex], where,

[tex] (2, 60) = (x_1, y_1) [/tex]

[tex] (4, 50) = (x_2, y_2) [/tex]

Plug in the values into the equation

[tex] slope (m) = \frac{50 - 60}{4 - 2} [/tex]

[tex] slope (m) = \frac{-10}{2} [/tex]

[tex] slope (m) = -5 [/tex]

Answer:

x=6

Step-by-step explanation:

How many blueberries on the on cake roof

Answers

Answer:

say what

Step-by-step explanation:

Find the slope of the line graphed below.

Answers

Answer:

-3/5

Step-by-step explanation:

So first, you have to find out the two points :

(-1,-1), and (4,-4)

Next, you have to put into this formula:

y1-y2/x1-x2

The y values in our points are -4 and -1, and our x values are 4 and -1. Lets now substitute:

-4-(-1)/4-(-1)

Now simplify: -4+1/4+1, and solve and you will get -3/5 as the slope

If you liked it, please give me a good rating and please mark me as the brainliest... Thanks!

Hope you do well on your assignment!

Please help i was crying :(
Also there is another one
“Subtract. Write Your answer in simplest form” which is: 6 3/4 - 2 3/20

Answers

4 and 3 fifths i think 4 3/5

Answer:

is it 4 3/5 it might be

Step-by-step explanation:

Which solution would make this equation have infinitely many solutions?

A.-18
B.-9
C.9
D.18

Answers

Answer: -18

Step-by-step explanation:

it’s would be -9 for sure

d=1/2at^2+s, solve for a

Answers

Step-by-step explanation:

Perhaps the equation is d=1/2at2 and you are given the distance (40 m) and acceleration (9.8 m/s2) and asked to find the time. or convert the equation in terms of t and then plug in the numbers to solve.

find m
right anwser gets brainliest

Answers

Answer:

The measure of <FDE is 18°

The sum of three numbers $x$ ,$y$, $z$ is 165. When the smallest number $x$ is multiplied by 7, the result is $n$. The value $n$ is obtained by subtracting 9 from the largest number $y$. This number $n$ also results by adding 9 to the third number $z$. What is the product of the three numbers?

Just take the $ out

Answers

You're given

x + y + z = 165

7x = n

n = y - 9

n = 9 + z

and you want to find xyz.

Solve the last three equations for x, y, and z :

7x = n → x = n/7

n = y - 9 → y = n + 9

n = 9 + z → z = n - 9

Substitute x, y, and z into the first equation and solve for n :

n/7 + (n + 9) + (n - 9) = 165

n/7 + 2n = 165

n + 14n = 1155

15n = 1155

n = 77

Now solve for x, y, and z :

x = 77/7 = 11

y = 77 + 9 = 86

z = 77 - 9 = 68

Then the product is

xyz = 11 • 86 • 68 = 64,328

The product of the three numbers is 8,192,040. The sum of three numbers x, y, z is 165: x + y + z = 165

The problem states:

1. When the smallest number x is multiplied by 7, the result is n: 7x = n

2. The value n is obtained by subtracting 9 from the largest number y: n = y - 9

3. The value n is also obtained by adding 9 to the third number z: n = z + 9

Now, let's proceed to find the values of x, y, z, and n:

From equation (2), we can express x in terms of n:

x = n/7

Now, substitute the value of x in equation (1):

(n/7) + y + z = 165

From equation (3), we can express y in terms of n:

y = n + 9

Now, substitute the value of y in the equation above:

(n/7) + (n + 9) + z = 165

From equation (4), we can express z in terms of n:

z = n - 9

Now, substitute the value of z in the equation above:

(n/7) + (n + 9) + (n - 9) = 165

Combine the terms with n:

3n/7 = 165

To isolate n, multiply both sides by 7/3:

n = 165 * (7/3)

n = 385

Now, we have the value of n, which is 385. To find the values of x, y, and z, substitute n back into the respective equations:

x = n/7 = 385/7

≈ 55

y = n + 9 = 385 + 9

= 394

z = n - 9 = 385 - 9

= 376

Now, we have the values of x, y, z, and n:

x = 55,

y = 394,

z = 376,

n = 385

To find the product of the three numbers, simply multiply them:

Product = x * y * z

= 55 * 394 * 376

≈ 8,192,040

So, the product of the three numbers is 8,192,040.

To know more about three numbers:

https://brainly.com/question/30269736

#SPJ2

solve x 3+3(x+2)=-24

Answers

Answer:

x=-11

Step-by-step explanation:

3+3x=6=-24

3x+9=-24

3x=-33

x=-11

Answer:

x = -11

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

3 + 3(x + 2) = -24

Step 2: Solve for x

Distribute 3: 3 + 3x + 6 = -24Combine like terms: 3x + 9 = -24Isolate x term: 3x = -33Isolate x: x = -11

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x: 3 + 3(-11 + 2) = -24Add: 3 + 3(-9) = -24Multiply: 3 - 27 = -24Subtract: -24 = -24

Here we see that -24 does indeed equal -24.

∴ x = -11 is the solution to the equation.

What is the area of a rectangle with a length of 1/3 yards and width of 3/4 yard?

Answers

Answer:

1/4 yards squared

Step-by-step explanation:

Area of a rectangle equals length times width.

1/3 x 3/4 = 3/12, or 1/4

Answer:

It would be 1/4 and if not try 3/12

Step-by-step explanation:

I hope this helped

Which of the following ratios is not equivalent to the rest: *
6 to 8
54 : 72
36 : 56
3 to 4

Answers

Answer:

36:56

Step-by-step explanation:

Answer: C 34:55

Step-by-step explanation:

start with 6:8 that’s the first one multiply by 9 on each side you get 54:72 so that’s the same and then 6:8 divide by 2 and you get 3:4 but for 36:56 you’d have to multiply by 6 and that would give you 36:48 not 36:56

A typical tip in a restaurant is 15% of the total bill. If the bill is $160, what would the typical tip be?

Answers

Answer:

24$

Step-by-step explanation:

15%=0.15

160*0.15=24

Which polynomial is in standard form?
N
O 26x5 + 12x7-8x3 + 6x
O 3x5 +x-6x2 + 5
11x5-6x2-9x+12
5x2 + 18x3 - 12x4 +4x7

Answers

Answer:

i am pretty sure it is D

Step-by-step explanation:

Answer:

Its C.) 11x^5 - 6x^2 - 9x + 12

Step-by-step explanation:

ejenuwitee

Point k lies at (-3,4). Point k is reflected over the y-axis and then translated 7
units down to produce K'. Which rule could have been used to produce K' from K?
K(x, y) +K'(x,y-7)
K(x,y) →K'(-x, y-7)
K(x,y) →K'(x, -y-7)
K(x,y) → K'(-x-7.-y-7)

Answers

Answer:

Step-by-step explanation:

Answer:B

Step-by-step explanation:

Tina is taking picture of her friends. if she sets a tripod level on the ground, will the bottom of each of the legs of tripod be coplanar

Answers

Answer:

Yes

Step-by-step explanation:

Please help. I will brainliest!!

Answers

Answer:

12. 20 ft

13. 4.5

Step-by-step explanation:

12. (29x29)-(21x21)=400

sq root 400= 20

13. (2x2)+(4x4)= 20

sq root 20= 4.5

What is the first step to solving the division problem below?

Divide 15 into 82 to get 5.
Divide 15 into 82 to get 6.
Multiply 15 by 5 to get 75.
Multiply 15 by 6 to get 80.

Answers

Answer:

divide 15 into 82 to get 5 is the first step

Step-by-step explanation:

Answer:

The answer is A, ¨Divide 15 into 82 to get 5.¨

Step-by-step explanation:

Please make as brainliest! Thanks and i hope it is right!!! Pls say if wrong. Bye

Abbey receives a $40 gift card for downloading music and wants to determine how many songs she can purchase. Each downloaded song costs $2.89 a. Let m represents the number of songs downloaded. Write an inequality that represents this given situation? b. What is the maximum number of songs Abbey can download?

Answers

Answer:

A. $2.89(m)=$40

B. 13 songs

Step-by-step explanation:

$2.89(m)=$40

m=$40/$2.89

m=13.84

She can download a maximum of 13 songs

Check:

$2.89 (13 songs)=$37.57

$40-$37.57=$2.43 left on her gift card

m=13.84, check that 0.84 of the cost of a song is left over 0.84*$2.89=$2.43

Answer:

13 songs

Step-by-step explanation:

40 divided by 2.89 is 13.84. DO NOT ROUND TO 14

So its a maximum of 13 songs, otherwise it will cost 40.46 for 14 songs

Can you help me with this question please

Answers

Answer:

Step-by-step explanation:

Answer:

34 just subtract

Step-by-step explanation:

You earn 90% on a quiz. If you earned 36 points, how many points was the quiz worth?

Answers

40 questions
Reasoning: 36/40=0.9

Answer:

36/90%=40

Step-by-step explanation:

40 points in total

Other Questions

cuales son los cuatro tipos de oraciones Liquid or solid water that falls to the ground is called Which equation, in slope-intercept form, passes through (2, 4) and has a slope of 3? F. y = 3x - 2 G. y = 3x + 10 H. y = 3x - 10 I. y = 3x +2 charles charges $4 an hour to baby-sit. He also adds an extra $10 onto the total for families with more than three children. Write an equation for what Charles charges to baby-sit a family of 4 children.y = 4x - 10y = 4x + 10y = 40xy = 4x + 10x Write the Direct Object pronounUstedes comen los mariscos. Ustedes ___Comen This year, my New Year's resolution was to not buy anymore books until I had read all of the books I already had. But, after getting fifty dollars for my birthday, I couldn't resist stopping by the library's used book sale. Chose the answer that beat corrects the underlined portion of the sentence. If the underlined portion is correct as written, chose "NO CHANGE". The underlined portion is "But," found in the second sentence Line FG goes through the points (4,9) and (1,3). Which equation represents a line that is perpendicular to FG and passes through the point (2,0)? -2x+ y=-4 -2x+y=2X+2y=2X+2y=4 A 65-cm segment of conducting wire carries a current of 0.35 A. The wire is placed in a uniform magnetic field that has a magnitude of 1.24 T. What is the angle between the wire segment and the magnetic field if the force on the wire is 0.26 N?a. 37.b. 43.c. 23.d. 53.e. 67. Brainliest PLZ HELP IM TIMED Based on what you observe in the photos, why do you think many people believed that industrialization was both a blessing and a curse to the cities in which industries were located What was Marie curies citizenship later in life like? amigo brothers felix characterization I need help with french pleaseeee someone help asappppp!!! using the model, what is the mass of the atom pictured?A) 3amuB) 5amuC) 7amuD) 9amu An organism's genotype isA. its physical appearanceB. its combination of allelesC. the mutations it inheritsD. the crossing over that occurs during meiosis PLS I NEED TO FINISH THIS PLS HELP You and your friends want to take a vacation to florida. The 5 of you will split the cost of the trip evenly. Each person has said that they would chip in up to $600 for the trip. What amounts represent possible total costs of the trip? Which of these best explains a difference between a Representative Democracy and Parliamentary Democracy? Pls help im being timed) compare the original DNA I need help ASAP plz