The product of two binomials, u(x) and v(x), is a binomial of degree 8 with a positive leading coefficient. What must be true about the sum of u(x) and v(x)?

Answers

Answer 1

Answer:

From the above conclusion, it can be inferred that  sum of u(x) and v(x) is a binomial of degree 4 with a positive or negative leading coefficient depending on the value of the constant 'a'

Step-by-step explanation:

If the product of two binomials, u(x) and v(x)has a binomial of degree 8, then the individual binomial will have a binomial of degree 4. For example, lets assume u(x) = ax⁴ + bx and v(x) ax⁴+cx. Note that they are both functions of x and contain only two terms since they are binomial.

Taking their product we have;

u(x)*v(x) =  (ax⁴ + bx)*(ax⁴+cx)

u(x)*v(x) = a²x⁸+acx⁵+abx⁵+bcx²

it can be seen that the higest power of x is 8 which gives the degree of the product.

Taking their sum;

u(x)+v(x) =   (ax⁴ + bx)+(ax⁴+cx)

u(x)+v(x) = ax⁴ + ax⁴+ bx +cx

u(x)+v(x)  = 2ax⁴ + bx +cx

It can be seen that the digest power of x is 4 which gives the degree of the sum of the binomial.

From the above conclusion, it can be inferred that  sum of u(x) and v(x) is a binomial of degree 4 with a positive or negative leading coefficient depending on the value of the constant 'a'


Related Questions

3 ft
4 ft
What is the length of the hypotenuse

Answers

The length of the hypotenuse is 5ft
a^2+b^2=c^2
3^2+4^2=c^2
9+16=c^2
c^2=25
sqrt c^2= sqrt 25
c=5
Therefore, the length of the hypotenuse is 5th
:)

Super Strength Inc. has found that the relationship between their sales and their net profit can be described by a polynomial function G(x) in which x is their sales (in thousands of dollars) and G(x) is their net profit (in thousands of dollars). What would be an appropriate domain for this function?

Answers

Answer:

x ≥ 0

Step-by-step explanation:

The domain of the profit function G(x) is the set of all possible values that "x" could assume. In this function, "x"represents the sales in thousand of dollars, therefore the minimum possible value is zero (scenario in which there are no sales). Assuming an hypothetical scenario in which the company has an infinite supply capacity, there is no upper limit for what their sales might be. Thus, the domain for the function is x ≥ 0.

Answer:

x > or equal to 0

Step-by-step explanation:

Find the values of x and y that satisfy the equation.

3x+6i=27+yi
x

Answers

Answer:

x = 9

y = 6

Step-by-step explanation:

3x+6i=27+yi

The real components have to be equal and the imaginary components have to be equal

3x = 27

divide by 3

3x/3 = 27/3

x=9

6i = yi

Divide by i

6 = y

Answer:

x=9, y=6

Step-by-step explanation:

Step-by-step explanation:

we have

3x+6i=27+yi

Equate the Real Numbers

3x=27

solve for x

Divide by 3 both sides

x=27/3=9

Equate the  Imaginary Numbers

6i=yi

Simplify

6=y

Rewrite

y=6

therefore

x=9, y=6

A calculator screen displays 3.294E6. Write this number in standard form.

Answers

Answer:

3.294

Step-by-step explanation:

The standard form of the given number is [tex]3294000[/tex].

Important information:

The calculator screen displays 3.294E6.Standard form:

in a calculator, the numbers on the right side of E are the exponent of 10. So, the scientific notation of the given number is:

[tex]3.294E6=3.294\times 10^6[/tex]

It can be written as:

[tex]3.294E6=3.294\times 1000000[/tex]

[tex]3.294E6=3294000[/tex]

Therefore, the standard form of the given number is [tex]3294000[/tex].

Find out more about 'Standard form' here:

https://brainly.com/question/13139379

PLEASE HELP WILL MARK BRAINLIEST
Keiko plans to watch 2 movies each month. Write an equation to represent the total number of movies n that she will watch in m months.

Answers

Answer:

n=2m

Step-by-step explanation:

If she watches 2 movies a month (2m), plug in any number and it will give you how many movies (n) she will watch in however many months.

Answer:

2n

I hope I helped you! If I am correct, please makr me brainiest. Thanks!

you get in a elevator and go down 8 floors. You exit on the 16th floor. What floor you on the elevator

Answers

Answer:

24th floor

Step-by-step explanation:

To get the number of the floor you were originally on, you add the number of floors you went down to the current floor you are on so 16 + 8 = 24

Answer:

24

Step-by-step explanation:

x-8=16

16+8=24

Write 34.996 to:
i. 2 decimal places​

Answers

Answer:

34.996 to 2 dcp is 35.00

Step-by-step explanation:

6 rounds up 9 goes to 10 add the 1 left over to make the units number equal 5 but as it is decimal place remember to add the 0's

Answer:

35.00

Step-by-step explanation:

just don't leave the zeros.

If 80% of an item is $144.00, what is the original price?

Answers

Answer:

180

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

the original price * 80% = 144

Change to decimal form

the original price * .80 = 144

Divide each side by .80

the original price * .80/.80 = 144/.80

the original price =180

GIVING BRAINLIST TO THE CORRECT ANSWER PLS ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

a = -1/2 & k = 3/7

Step-by-step explanation:

Solve for a over the real numbers:

24 a^3 + 8 a^2 + 6 a + 4 = 0

The left hand side factors into a product with three terms:

2 (2 a + 1) (6 a^2 - a + 2) = 0

Divide both sides by 2:

(2 a + 1) (6 a^2 - a + 2) = 0

Split into two equations:

2 a + 1 = 0 or 6 a^2 - a + 2 = 0

Subtract 1 from both sides:

2 a = -1 or 6 a^2 - a + 2 = 0

Divide both sides by 2:

a = -1/2 or 6 a^2 - a + 2 = 0

Divide both sides by 6:

a = -1/2 or a^2 - a/6 + 1/3 = 0

Subtract 1/3 from both sides:

a = -1/2 or a^2 - a/6 = -1/3

Add 1/144 to both sides:

a = -1/2 or a^2 - a/6 + 1/144 = -47/144

Write the left hand side as a square:

a = -1/2 or (a - 1/12)^2 = -47/144

(a - 1/12)^2 = -47/144 has no solution since for all a on the real line, (a - 1/12)^2 >=0 and -47/144<0:

Answer: a = -1/2

______________________________________

Solve for k over the real numbers:

(7 k - 3) (k^2 - 2 k + 7) = 0

Split into two equations:

7 k - 3 = 0 or k^2 - 2 k + 7 = 0

Add 3 to both sides:

7 k = 3 or k^2 - 2 k + 7 = 0

Divide both sides by 7:

k = 3/7 or k^2 - 2 k + 7 = 0

Subtract 7 from both sides:

k = 3/7 or k^2 - 2 k = -7

Add 1 to both sides:

k = 3/7 or k^2 - 2 k + 1 = -6

Write the left hand side as a square:

k = 3/7 or (k - 1)^2 = -6

(k - 1)^2 = -6 has no solution since for all k on the real line, (k - 1)^2 >=0 and -6<0:

Answer: k = 3/7

Michelle bought 2 soccer balls priced at $24.95 each. She paid for her purchase with three $20 bills. How much change did she receive?

Answers

Answer:

$35.05

Step-by-step explanation:

3 $20 bills turns into $60 and 60-24.95=35.05

5 + x = -2
I need work and answer!!!!

Answers

We need to get x by itself.

We do that by subtracting 5 from both sides.

This leaves us with x = -7.

So x = -7 is the solution.

Answer:

The final answer is [tex]x = -7[/tex] .

Step-by-step explanation:

Solve the equation:

[tex]5 + x = -2[/tex]

Subtract both sides by 5:

[tex]5 - 5 + x = -2 -5[/tex]

[tex]x = -7[/tex]

So, therefore, [tex]x = -7[/tex] is the final answer.

Brainliest question please help please help me now plz

Answers

Answer:

13/b I think

Step-by-step explanation:

Can someone please help me

Answers

Answer:

I think its G, I'm not 100% sure...

I also am pretty sure it’s G

Standard form for y=3×-2

Answers

Answer:

3x-y=2

Step-by-step explanation:

y=3x-2

(y-3x)=-2

-3x+y=-2

change the signs on both sides

3x-y=2

=3x-y=2

Correct answers only!

To the nearest cent, how much will she have in 1 year?

Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

Answers

Answer:

$5150

Step-by-step explanation:

p = 5000

r = 0.03

t = 1

5000 * (1.03) = 5150

A standard deck of 525252 cards contains 444 suits: hearts, clubs, diamonds, and spades. Each suit consists of cards numbered 222 through 101010, a jack, a queen, a king, and an ace. Anthony decides to pick one card at random from a standard deck of 525252 cards. Let AAA be the event that he chooses an ace and HHH be the event that he chooses a heart. What is P(A\text{ or }H)P(A or H)P, left parenthesis, A, start text, space, o, r, space, end text, H, right parenthesis, the probability that the card Anthony chooses is either an ace or a heart?

Answers

The question is not properly written

Correct Question

A standard deck of 52 cards contains 4 suits: hearts, clubs, diamonds, and spades. Each suit consists of cards numbered 2 through 10, a jack, a queen, a king, and an ace.

Anthony decides to pick one card at random from a standard deck of 52 cards. Let A be the events that he chooses an ace and H be the event that he chooses a heart.

What is P ( A or H), the probability that the card Anthony chooses is either an ace or a heart?​

Answer:

2/13

Step-by-step explanation:

From the question, we have in total, 52 cards.

Step 1

We find the probability that Anthony chooses an Ace.

Number of ace cards in each of four suits namely spades, hearts, diamonds and clubs = 1

Therefore, total number of ace cards out of 52 cards = 4

P(A) = 4/52

Step 2

We find the probability that Anthony chooses an Ace.

Probability that Anthony chooses an heart P(H) = 4/52

Step 3

The probability that the card Anthony chooses is either an ace or a heart

P ( A or H) = P(A) + P(H)

= 4/52 + 4/52

= 8/ 52 = 2 /13

I need help with Pythagorean Theorem

Answers

Answer:look at picture

Step-by-step explanation:

Answer:

the sum of the angles pythagorean theorem is a^2+b^2=c^2

Also, the angles of a triangle will add up to 180 degrees

this practice is most commonly found in right triangles

Step-by-step explanation:

The graph shown can be used to convert between kilometres and miles....

Answers

Answer:

where's the picture I can't see it

According to the graph, I can see

42 Miles = 68 Kilometers

32 Miles = 22 Kilometers

The distance between London and Cardiff is 240 Kilometers

Is mile in the metric system?

Mile is under the Imperial System and

Kilometers is under the metric system.

What is metric system?

The metric units used for measuring length, mass, area and capacity. For example, millimeters, centimeters, meters, and kilometers are the metric units of the measurement of length. Grams and kilograms are the units for measuring weight.

Learn more about Measuring System here

https://brainly.com/question/1578673

#SPJ2

solve for a side in right triangles

Answers

Answer:

2.88?

Step-by-step explanation:

What is the x-value in the solution to the system of linear equations?
y = 1/2x + 2
y = -3/2x -2

Answers

Answer: The value of x is  -2.

Step-by-step explanation:

y= 1/2x + 2

y= -3/2x-2

1/2x + 2  = -3/2x -2

         +2               +2

1/2x  + 4 = -3/2x

-1/2x            -1/2x

          4= -2x

   x= -2      

50+50+5050 + 50 + 50 + 50 + 50 + 50 + 50 + 50 + 30 ​

Answers

Answer:

5530

Step-by-step explanation:

Answer:

5530

Step-by-step explanation:

50 times 9 equals 450

then add the 5050 and 30 to get 5080

then add up 5080 and450 and get your answer of 5530

will mark brainliest!! 20 points!! i just need a short paragraph on this....look at attachment

Answers

The tone is negative due to the lion being aggressive and keeping everyone away. The reason the lion does this is due to its damaged paw, “growling at anyone who would get close enough to examine his damaged claw.” This shows the lions aggressive attitude and immediate distrust in others this is why the tone is mostly negative

solve for a side in right triangles

Answers

Answer:

? =8.77

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opposite side/ hypotenuse

sin 20 = 3 / ?

? = 3/ sin 20

? = 8.7714132

To the nearest hundredth

? =8.77

Two step equations. Please help

Answers

Y=7

Step-by-step explanation:

Move all terms not containing y to the right side of the equation.

4y=22+6

Then add 22 and 6.

4y=28

Divide each term in 4y=28 by 4

4y÷4=28÷4

Cancel the common factor of 4 in the first part of the equation so it looks like this...

y=28÷4

Divide 28 by 4.

Therefore y=7

Hope this helps! If you have any more questions or you need further clarification on anything then please comment down below! Good luck!

-1 + n/2 = -11
HELP
THNX

Answers

Answer:

n = -20

Step-by-step explanation:

[tex]-1 +\frac{n}{2} = -11\\[/tex] add 1 on each side

[tex]\frac{n}{2} = -11 + 1\\\\\frac{n}{2} =-10[/tex]multiply by 2

n = -20

Someone please help me this will be a lot of points and I will follow u and Mark u the brainiest​

Answers

Answer:

option D; 20/3 OR 6 2/3

Step-by-step explanation:

CONVERT THE HOURS INTO MINUTES;

3/4 × 60 = 45 mins

1hour = 60 mins

45 mins = 5 miles

60 mins = ??

cross multiply;

60 by 5 ÷ 45 to get 20/3.

Find the quartiles for these data values:

5,7,7,8,10,11,12,15,17

Answers

Answer:

The median {Q2} is 10

Q1 is 7+7/2 which is 7

Q3 is 15+12/2 which is 13.5

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

its coreect

Brainliest for the correct answers!

Answers

Answer:

didn't i answer this on your last post?

Work out the surface area of this solid prism.

Answers

Area of the 3 rectangles that make up the prism:
30 * 25 + 30 * 17 + 30 * 28 = 2100
Area of the two triangles at either end:
Use bh/2
(15 * 28)/2 = 210
There are two so it’s 420
2100 + 420 = 2520cm^2

Answer:

[tex]2( \frac{1}{2} \times 15 \times 28 ) + ( 25 \times 30 ) + ( 17 \times 30) + ( 28 \times 30 ) \\ = 2520 {cm}^{2}[/tex]

Mark is comparing prices of different brands before he goes shopping. Who has the best deal on ice cream​? ​ ​Brand Size & Price​ ​Turkey Hill ​ $4.50 for 30 ounces ​Breyers ​ $15.36 for 128 ounces ​Ben & Jerrys ​ $2.88 for 16 ounces

Answers

Answer:

Breyers is the correct answer

Step-by-step explanation:

$4.50/30 oz = .15

$15.36/128 oz = .12

$2.88/16 oz = .18

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