Consider the polynomial function g(x) = 8x5 + ax4 + 5x + 20, where a is an unknown real number. If (x+4) is a factor of g(x), what is the value of a?

Answers

Answer 1

[tex]g(x) =8x^5 + ax^4 +5x +20 \\\\\text{If}~ x +4 ~ \text{is a factor of g(x) then,}~ \\\\g(-4)=0\\\\\implies 8(-4)^5 +a(-4)^4+5(-4) +20 = 0\\\\\implies 256a -8192 = 0\\\\\implies a = \dfrac{8192}{256} = 32[/tex]


Related Questions

Does anyone know all of these? (11th Grade Algebra)

Answers

Answer:

Step-by-step explanation:

17) In parallelogram, adjacent angles are supplementary (add up to 180)

⇒∠A +  ∠D = 180

5x + 30 + x = 180  

5x +x + 30 = 180    {Combine like terms}

     6x + 30 = 180 {Now, subtract 30 from both sides}

6x + 30 - 30 = 180 - 30

             6x  = 150

Now divide both sides by 6

              x = 150/6

              x = 25

∠A = 5x + 30

     = 5*25 + 30

     = 125 + 30

     = 155

In parallelogram, opposite angles are congruent.

∠C = ∠A

∠C = 155°

18)In parallelogram, adjacent angles are supplementary (add up to 180)

⇒∠A +  ∠D = 180

3x + 4 + x = 180  

3x +x + 4 = 180    {Combine like terms}

     4x + 4 = 180 {Now, subtract 4 from both sides}

4x + 4 - 4 = 180 - 4

             4x  = 176

Now divide both sides by 4

              x = 176/4

x =44

19) In parallelogram, adjacent angles are supplementary (add up to 180)

⇒∠GAC +  ∠ACF = 180

125 + ∠ACF  = 180  

       Now, subtract 125 from both sides

∠ACF = 180 - 125

∠ACF = 55

21) In parallelogram, adjacent angles are supplementary (add up to 180)

∠CFG + ∠ACF = 180

2w +30 + w + 15 = 180

2w +w + 30+ 15 = 180

          3w + 45   = 180

                      3w  = 180 - 45

                      3w = 135

                        w = 135/3

w = 45

∠ACF = w + 15

           = 45 + 15

ACF =  60

21) In parallelogram, opposite sides are congruent.

GF = AC

4x - 14 = 2x + 2

       4x = 2x + 2 + 14

       4x = 2x +  16

4x - 2x  = 16

    2x    = 16

          x = 16/2

         x = 8

22) In parallelogram, the diagonals bisect each other.

XC = GX

3y - 3  =2y + 2

       3y = 2y + 2 + 3

       3y = 2y + 5

  3y - 2y= 5

         y = 5

23) The length of the  middle segment of trapezium is half the sum of the two parallel sides.

[tex]\dfrac{b_{1}+b_{2}}{2}=110\\\\\\b_{1}+b_{2}=110*2\\[/tex]

Joe collects toy cars and marbles. Whenever he collects 4 cars, he also collects 12 marbles. How many marbles does he collect after collecting 20 cars? What rule is being used?

Answers

Answer; 60

Step-by-step explanation:

solution:

here,

4 cars = 12 marbles

1 car = 12/4. = 3 marbles

then,

20 cars = 3(20) marbles

= 60 marbles

We can make this into a fraction  4/12 = 20/x

Then, we will solve for x

4x = 240    cross multiply

x = 60

Joe collects 60 marbles after collecting 20 cars.

The Multiplicative Inverse Property is being used.

which of the following is true about the sequence graphed below?

Answers

Answer:

The sequence is arithmetic because the terms have a common difference

Step-by-step explanation:

The difference between each term in the sequence is constant. The sequence shown below, considering the y values of the coordinates, are 9, 7.5, 6, 4.5, 3, 1.5. Each term has a difference of 1.5, thus making all terms have a common difference, and making the sequence arithmetic.

There should be 2 answers

Answers

[tex]|6m-2|=0\\\\\implies 6m-2 =0~~~~~~~~~~~~~;[\text{If}~ |x| = 0 ~\text{then}~ x = 0]\\\\\implies m = \dfrac 26 = \dfrac 13[/tex]

Westford Lake was originally blue because it only had 810 algae plants. Then towns and farms cropped up by the lake. This caused 9,772 more algae plants to grow, which turned the lake green. How many algae plants are now in Westford Lake?

Answers

Answer:

10,582 algae plants

Step-by-step explanation:

10,582 algae plants. You have to add 810 and 9,772 to get 10,582 algae plants.

Pablo had $319 in his savings account. He got $28 for helping a neighbor, and he saved all but $11 of it.

How much is in Pablo's savings account now?

A.
$330

B.
$336

C.
$347

D.
$358

Answers

Answer:

the correct answer is B. $336

Step-by-step explanation:

you first add 319 and 28. Then, you subtract the product with 11.

To be honest I think the answer is B

Help help ASAP math math

Answers

Answer:

-9

Step-by-step explanation:

225 ÷ -25 = -9

A park has a rectangular shape. One side of the park is 175 23 meters long and the
other is 67.5 wide. Find the area of the park. (Round to the nearest hundredth if
necessary)

Answers

Answer:

Step-by-step explanation:

The area of a rectangle is length x width.

Given:

length = 175.23m

width = 67.5m

Area = 175.23m x 67.5m = 11828.025[tex]m^{2}[/tex]

(a) A color page prints 20 pages in 7 minutes. How many pages does it print per minute?

(b) it takes 55 pounds of seed to completely plant a 7- acre field. How many acres can be planted per pound of seed?

If needed round to nearest hundredth.

Answers

Answer:

A. 20 / 7 = 3 (or 2.85)

B. 55 / 7 = 8 (or 7.85)

Brainliest is appreciated!

_ daintysword.mp4

Answer:

A.3

B.8

Step-by-step explanation:

this is the answer

Using the Addition Method, find the value of y in
the system of equations 2x1= 3y – 5 and 5x + 6y =
28

Answers

Answer:

28?

Step-by-step explanation:

Find the measure of the indicated arc

Answers

Step-by-step explanation:

we need the length of the arc ?

the length of the arc fully around the circle (360°) is the circumference of the circle : 2×pi×r

and the arc length for 123° is then

2×pi×r×123/360

but we would need r to calculate that. you did not provide that.

the only other thing that comes to mind is : the arc angle is indeed the angle at the center of the circle and is 123°.

i don't know how else to help you, as i cannot think of anything else you might need there.

Use E to decode the coded message matrix

Answers

Answer:

D because I was doing it for a while and I know it

Paul leaves £4000 in the bank for two years. It earns compound interest of 5% per year. Calculate the total amount Paul's has in the bank at the end of the two year.

Pls give me working out and explanation !!!!

Answers

Answer:

£4400

Step-by-step explanation:

5% of 4000 is 200

200*2=400

4000+400=4400

£4400

A flashlight is projecting a triangle onto a wall

Answers

Answer:

24

Step-by-step explanation:

The the triangles are similar, the lengths of corresponding sides are in proportion.

15/20 = 18/n

3/4 = 18/n

1/4 = 6/n

n = 4 × 6

n = 24

Answer:

n = 24

Step-by-step explanation:

In similar triangles, corresponding sides are in same ratio.

[tex]\dfrac{n}{18}=\dfrac{20}{15}\\\\\\n=\dfrac{20}{15}*18\\\\\\n = 4*6\\\\n = 24[/tex]

The sum or difference of p and q is the of the x-term in the trinomial.​

a. ss. www.
coefficients

Answers

Answer:

coefficient..........

use multiplication to show how many twelfths equal 2/3.

you can get 74 points

Answers

[tex]\\ \rm\rightarrowtail \dfrac{2}{3}[/tex]

We need. the denominator as 12

So

[tex]\\ \rm\rightarrowtail \dfrac{2(4)}{3(4)}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{8}{12}[/tex]

Answer is 4

Answer:

[tex]\sf \dfrac23=\dfrac{2 \times 4}{3 \times 4}=\dfrac{8}{12}[/tex]

Step-by-step explanation:

To get from 3 to 12, we must multiply 3 by 4 since 3 x 4 = 12

Therefore, multiply both the numerator and denominator by 4:

[tex]\sf \dfrac23=\dfrac{2 \times 4}{3 \times 4}=\dfrac{8}{12}[/tex]

Which CANNOT be the third side of a triangle if the two sides measure 10 cm and 32 cm ?

A.
32 cm

B.
33 cm

C.
44 cm

D.
40 cm

Answers

[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer☂}}[/tex]

The Length of the third side of a triangle shouldn't be greater than the some of other two sides,

So, let the side be x

[tex]\qquad \sf  \dashrightarrow \: x < 32 + 10[/tex]

[tex]\qquad \sf  \dashrightarrow \: x < 42[/tex]

And hence, the third side should be less than 42 cm, therefore the only option that doesn't satisfy the condition is option D

Therefore, 44 cm can't be a side of that Triangle.

Probability Practice: Cass is interested in figuring out how many customers have applied for a home mortgage recently.

Review the data and calicut are the probability that if Cass runs into one of the financial institutions customers at random, that person has applied for a home mortgage this year.

What is the total number of customers?

How many customers applied for a home mortgage?

Answers

The data given relating to the probability shows that the total number of customers will be 27300.

How to calculate probability?

The total number of customers will be:

= 24300 + 3000

= 27300

The number of customers that applied for a home mortgage will be:

= 2430 + 150

= 2580

In conclusion, the total number of customers will be 27300.

Learn more about probability on:

https://brainly.com/question/24756209

Which equation represents an exponential function with an initial value of 500? f(x) = 100(5)x f(x) = 100(x)5 f(x) = 500(2)x f(x) = 500(x)2h equatWhich equation represents an exponential function with an initial value of 500? f(x) = 100(5)x f(x) = 100(x)5 f(x) = 500(2)x f(x) = 500(x)2ion represents an exponential function with an initial value of 500? f(x) = 100(5)x f(x) = 100(x)5 f(x) = 500(2)x f(x) = 500(x)2

Answers

Answer:

  (c)  f(x) = 500(5^x)

Step-by-step explanation:

An exponential function is one that has the independent variable (x) in the exponent. The initial value of an exponential function (or any function) is the value when x=0.

__

Examine the Choices

You are looking for a function with x in the exponent, and with an initial value of 500. Eliminate answer choices that don't have x in the exponent. Evaluate the remaining choices for x=0 and see which gives you a value of 500.

  f(x) = 100(5)^x   ⇒   f(0) = 100·1 = 100 ≠ 500

  f(x) = 100(x^5) . . . not an exponential function

  f(x) = 500(5)^x   ⇒   f(0) = 500·1 = 500 . . . . . the function you're seeking

  f(x) = 500(x^2) . . . not an exponential function

Answer:

a

Step-by-step explanation:


A=
B=
C=
? ? ? ? ? ? ? ? ? ? ? ? ? ?

Answers

Answer:

a=5 b=7 c=9

hope I helped :)

Which of the following expressions is equivalent to……

Answers

Answer:

Box 4

Step-by-step explanation:

negative divided by negative is positive so both negatives cancel out and u get (5/6) / (1/3)

the sum of three consecutive natural numbers is 1146, find the numbers.

the three numbers in increasing order are ______ , _____, and ________

Answers

[tex]\text{Let the 3 consecutive numbers be}~ x,~x+1~ \text{and} ~x+2.\\\\\text{According to the condition,}\\\\x+x+1+x+2 = 1146\\\\\implies 3x +3 = 1146\\\\\implies 3(x+1) = 1146\\\\\implies x+1 = \dfrac{1146}3 = 382\\\\\implies x= 382-1 = 381\\\\\text{Now, the numbers are}~ 381,~382~\text{and}~383[/tex]

What is the range of possible sizes for side x?

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

The value of third side should be lesser than the the sum of other two sides ~

[tex]\qquad \sf  \dashrightarrow \:x < 2.8 + 2.8[/tex]

[tex]\qquad \sf  \dashrightarrow \:x < 5.6[/tex]

and, value of third side should also be greater than the difference of other two sides ~

[tex]\qquad \sf  \dashrightarrow \: x> 2.8 - 2.8[/tex]

[tex]\qquad \sf  \dashrightarrow \:x > 0[/tex]

Now, combine the two inequalities, we will get ~

[tex]\qquad \sf  \dashrightarrow \:0 < x < 5.6[/tex]

I hope you got the required Answer ~

CAN SOMEBODY HELP ME SOLVE THIS EQUATION

Answers

Step-by-step explanation:

Slope m=4

Y intercept b=(-5)

formula f(x)=4x-5

If u need how to solve do let me know

The graph of f(x) is shown. For what values of X does f(x)= 0

-1,1,2
-2,-1,1
-3,-1,1
-1,1,3

Answers

Answer:

-3, -1, 1

Step-by-step explanation:

The values of x when f(x) = 0 are the points on the graph when the curve intercepts the x-axis.

From inspection of the graph, the curve intercepts the x-axis at

x = -3,  x = -1  and  x = 1

Liz records the amount of rainfall in her backyard. It rained 3/8 inch for 4 days in a row.

Which shows the amount of rainfall after 4 days?

A : 1 4/8

B : 1 5/8

C : 1 6/8

D : 1 7/8

Answers

A: 1 4/8 because 4x3/8=12/8 which is equivalent to 1 4/8

If log_10(x) = 3 + log_10(y), then find x/y

Answers

Answer:

 1000

Step-by-step explanation:

[tex]log_{10}x = 3 + log_{10}y[/tex][tex]log_{10}x - log_{10}y = 3[/tex][tex]log_{10}(x/y) = 3[/tex][tex]x/y = 10^3[/tex][tex]x/y = 1000[/tex]

Answer:

  x/y = 10^3 = 1000

Step-by-step explanation:

The rules of logarithms tell you ...

  log(x/y) = log(x) -log(y)

__

Here, we have ...

  log(x/y) = log(x) -log(y)

  = (3 +log(y)) -log(y) = 3 . . . . . . . . substittute for log(x)

Taking the antilog, we get ...

  log(x/y) = 3

  x/y = 10^3 = 1000

_____

Additional comment

The expression log(x) is often used to refer to the "common log" of x, which is the logarithm to the base 10. This lets us avoid the cumbersome notation log_10(x).

In more formal mathematics, log(x) may be used to refer to the natural log. The distinction is usually made in high school algebra by referring to the natural log using ln(x).

Adam is purchasing a new television that costs $2,187.96 after tax. He borrowed the money from his parents and must pay back the full amount plus simple interest at the rate of 3.5%. What is the interest he will pay if he takes 2 years to pay his parents back? (Include Decimal with the cents; No Commas)

Answers

Using simple interest, considering the parameters stated in the exercise, it is found that he will pay an interest of $153.16.

Simple Interest

Simple interest is used when there is a single compounding per time period.

The amount of interest after t years in is modeled by:

I = Prt

In which:

P is the initial amount.r is the interest rate, as a decimal.

In this problem, the parameters are given as follows:

P = 2187.96, r = 0.035, t = 2.

Hence, the interest paid will be of:

I = Prt = 2187.96 x 0.035 x 2 = $153.16.

More can be learned about simple interest at https://brainly.com/question/25296782

A 20-ounce bottle of lotion costs $3.95. How much does each ounce cost?\

Answers

Answer:

$0.20

Step-by-step explanation:

3.95/20 = 0.1975

0.1975 would round up to 0.20

Answer:

$0.1975

Step-by-step explanation:

Do $3.95 divided by 20 so you can find the proportion of 1 ounce

How do I do this question folks?

Answers

Answer:

Correct answer: B

Step-by-step explanation:

Syntax: in piecewise functions such as the one attached, the "if:" section shows the domain, or x-axis values which that function pertains to.

In the graph, you can see that the graph is defined for [tex]-3\leq x < 1[/tex] (not-including 1 because there is an open hole there, indicating it is not part of the domain), and [tex]2\leq x\leq 4[/tex].

Now that we know the domain, we can attach it to the graphs that lie on those domains.

We see that the leftmost line appears to have a positive slope and a negative y-intercept, and that the second line should have a positive y-intercept and a negative slope.

At this point, you can just start crossing off answers that don't meet this criteria.

Cheers!!

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