22. What is the value of k such that x - 6 is a factor of
f(x) = 3x³ - 17x² - kx + 18? Justify your answer.

Answers

Answer 1

Answer:

k = 9

Step-by-step explanation:

According to the Factor theorem, if (x - a) is a factor of f(x) then f(a) = 0

given (x - 6) is a factor of f(x) then f(6) = 0 , that is

3(6)³ - 17(6)² - 6k + 18 = 0

3(216) - 17(36) - 6k + 18 = 0

648 - 612 - 6k + 18 = 0

36 - 6k + 18 = 0

54 - 6k = 0 ( subtract 54 from both sides )

- 6k = - 54 ( divide both sides by - 6 )

k = 9


Related Questions

SOMEONE HELP ME PLEASE
What is the least common multiple of 4, 9, and 12?

Answers

Answer:

36 I think

Step-by-step explanation:

jxjejjirirjxjd

Answer:

36

Step-by-step explanation:

4 x 9 = 36

9 x 4 = 36

12 x 3 = 36

K Rick's dad used a ladder to hang up their Christmas lights on the roof. When he leaned the ladder against the house, it created a triangle. If the height of the wall measures 12 feet, the ladder measures 15 feet, and Rick's dad put the base of the ladder 9 feet from the wall, what is the area of the triangle that is created? A 36 feet2 B) 54 feet 67.5 feet? D 90 feet​

Answers

Answer:

A) 36 pies

Step-by-step explanation:

Which of the following is the graph of f(x)=2(x−4)2−1?

Answers

Answer:

there is no graph but it's a positive graph and a few of the points would be (3,-5) (4,-1) (5,3) (6,7)

Step-by-step explanation:

The question is the picture

Answers

Answer:

Step-by-step explanation:

Hope this helps u!!

note :if u change divide sign to multiplication sign then do the reciprocal

for eg:

3/4÷3/100

then write,

3/4*100/3

what is (-5q-8) - (q+3)

Answers

The answer would be −6q−11

Answer:

-6q-11

Step-by-step explanation:

11
Which improper fraction is equivalent to 5 ?
40

Answers

Answer:

211/40, B

Step-by-step explanation:

Make it an improper fraction:

5 x 40 = 200, 200 + 11 = 211

211/40, B

A vending machine has twice as many quarters in it as dollar bills if the quarters and dollar bills have a combined value of $96. 00 how many quarters are in the machine

Answers

According to question, we can say that there are 128 quarters in the machine.

What is fraction?

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

N  = the  number of dollars  2N  the  number of  quaters.....so  we  have

25(2N)  + 1N   =   96

1.50N  =  96

so, by fraction we have -

N  =  96  / 1,50   =  64   dollars

2(64)   =    128  quarters

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Is the function f/x )= x x − 4 − − − − √ is continuous on the interval 4 [infinity]?

Answers

No, the function f(x) = x - √x - 4 is not continuous on the interval [4, infinity].

Here's why, A function is considered continuous if the function is defined at every point in its domain and there are no breaks or jumps in the function's graph. In this case, the function f(x) = x - √x - 4 is defined for all x > 4, However, the function includes a square root of x-4, which is defined only for non-negative real numbers, thus for x < 4, the function is undefined. Therefore, the function is not continuous on the interval [4, infinity].

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can anyone solve this?

Answers

Answer:

the yo u thichi cutis lo u you

Answer:

its the same thing look at the coordinates

Step-by-step explanation:

Write the given expression as the sine of an angle
sin(105°) cos(35°) + sin(35°) cos(105°)
Will give brainiest.

Answers

Answer:

sin140°

Step-by-step explanation:

Using the addition formula for sine

sin(A + B) = sinAcosB + cosAsinB

Given

sin105°cos35° + sin35°cos105°

= sin105°cos35° + cos105°sin35° ← right side of expansion above

= sin(105 + 35)°

= sin140°

Evaluate the expression 5+2n^2 when n=3

Answers

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

23

»»————- ★ ————-««  

Here’s why:  

[tex]\boxed{\text{Evaluating the expression given:}}\\\\5+2n^2 \text{ when } n=3.\\-----------\\\rightarrow5+2(3)^2\\\\\rightarrow5+2*9\\\\\rightarrow 5 + 18\\\\\rightarrow\boxed{23}[/tex]

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

The value of the expression  5 + 2n² at n = 3 is 23.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given an expression  5 + 2n².

Now at n = 3, we'll simply replace n with 3, So 5 + 2n² is

= 5 + 2(3)².

= 5 + 2(9).

= 5 + 18.

= 23.

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4. Determine the type of triangle with the given set of side lengths. Show your work. A. a = 8, b = 15, c = 17 B. a = 6, b= 15, c = 18 C. a = 7, b = 10, c = 12​

Answers

So A is a triangle, and B is a triangle, and C is a right triangle (or a right-angled triangle)

Define Pythagoras Theorem.

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs.

What is right angle triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

A. a = 8, b = 15, c = 17

We can use the Pythagorean theorem to determine the type of triangle:

c² = a² + b²

17² = 8² + 15²

289 = 64 + 225

289 ≠ 289

Therefore, this is not a right triangle.

B. a = 6, b= 15, c = 18

We can use the Pythagorean theorem to determine the type of triangle:

c² = a² + b²

18² = 6² + 15²

324 = 36 + 225

324 ≠ 324

Therefore, this is not a right triangle.

C. a = 7, b = 10, c = 12

We can use the Pythagorean theorem to determine the type of triangle:

c² = a² + b²

12² = 7² + 10²

144 = 49 + 100

144 = 144

Therefore, this is a right triangle.

So A is a triangle, and B is a triangle, and C is a right triangle (or a right-angled triangle)

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The tables show the prices for ordering team jerseys from two different companies. You can use the information to write ratios showing the relationship between the cost and the corresponding number of jerseys. 1/5=5 25/5=5 50/10=5 75/15=5. 5/1=5 20/5=4 40/10=4 69/15=4. These ratios are all equivalent. These ratios are not all equivalent. This relationship is proportional. This relationship is not proportional. Explain how you can tell whether a group of ratios represents a proportional relationship.

Answers

Even though this relationship is proportional, not all of these ratios are equal.

What is the solution to the 3 to 5 ratio?

Verify that the ratios provided are equal. The ratios of 3:5 and 15:25 are both equal. Because the first ratio 3: 5 can be derived by multiplying the ratio 15: 25 by 5 on both the numerator and denominator. The initial ratio of 3: 5 can be multiplied by 5 to get the ratio 15: 25, and vice versa.

What is an illustration of a 4:1 ratio?

This indicates that you would require an 8 fl oz can (a quarter of a quart) of Part B if you were ordering a quart of Part A. You will have 1.25 after combining Parts A and B.

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GIVING BRAINLIST
GIVING BRAINLIST

PLS HELP

Answers

Answer:It could be 10, 2, 3

Step-by-step explanation:

basically as long as the lengthxwidthxheight=60, then it should be fine

Answer:

Their are multiple ways you could do this but you can use 10 as the length, 3 as the width, and 2 as the height

Step-by-step explanation:

The formula for the volume of a rectangular prism is v=l*w*h  so plugging in our values would give us 10*3*2 which is equal to 60.

Points D, B, and E are collinear. Find the value of a so that points A, B, and C
are collinear.

Answers

Answer:

Since A, O and B are collinear,

i.e.,

A

O

B

=

180

or,

A

O

D

+

D

O

C

+

B

O

C

=

180

(

x

10

)

+

(

4

x

25

)

+

(

x

+

5

)

=

180

Or,

x

+

4

x

+

x

10

25

+

5

=

180

Or,

6

x

30

=

180

Or,

6

x

=

180

+

30

=

210

Or,

x

=

210

6

=

35

B

O

C

=

x

+

5

=

35

+

5

=

40

help me please? its algerbra

Answers

Answer:

Option 1

Step-by-step explanation:

option 1=243

option 2=125

Find the area of the following composite figures ​

Answers

I think the answer is 592 c2

What is the radius of a circle with a diameter of 24 m?

Answers

12 m

Step-by-step explanation:

24/2 = 12

I hope this helps you, have a good day!

Answer:

answer: 12

Step-by-step explanation:

The radius is just half of the diameter since the diameter is 24 we just have to divide that by 2 to get the answer so 24 ÷ 2 = 12 so 12 is the radius Hope that helps!

write an explicit formula for an,the nth term of the sequence 72,12,2​

Answers

Answer:

[tex]a_n = 432 \cdot \left(\frac{1}{6}\right)^n[/tex] OR [tex]a_n = 72 \cdot \left(\frac{1}{6}\right)^{n-1}[/tex]

Step-by-step explanation:

The first term is 72, and each term is equal to the previous term multiplied by 1/6. This yields the expression [tex]a_n = 72 \cdot \left(\frac{1}{6}\right)^{n-1}[/tex], which is equivalent to [tex]a_n = 432 \cdot \left(\frac{1}{6}\right)^n[/tex].

Answer:

[tex]n _{th} = n _{1} {r}^{n - 1} \\ n _{th} = 72 \times 12 {}^{(n - 1)} \\ n _{th} = 72 \times ( {12}^{n} .12^(-1)) \\ n _{th} = 6 × {12}^{n} [/tex]

heyy! i’ll give brainliest help asap pls

Answers

Answer:

I think the best answer is Marble

hope this helps

have a good day :)

Step-by-step explanation:

Answer: I would go with B:

Step-by-step explanation: if not then its gott to be A

The length of the rectangle is X units more than its
width. The width of the rectangle is 11 units and the
length of the wire that is used to make this rectangle
is a maximum of 57 units. Represent this situation
using an inequality.

Answers

Answer:   [tex]2x+44 \le 57\\\\[/tex]

Explanation:

W = width

W = 11

L = length

L = width+x

L = 11+x

P = perimeter of the rectangle

P = 2L+2W

P = 2*(11+x)+2*11

P = 22+2x+22

P = 2x+44

The perimeter is at max 57 units because it is the length of wire used. Think of it like fencing around a piece of land. Be sure not to mix up the length of the wire with the rectangle length; those are two different things.

Anyways, because the perimeter maxes out at 57, this means either P = 57 or P < 57.

This leads to:

[tex]P \le 57\\\\2x+44 \le 57\\\\[/tex]

sydney is selling is comic book selection on the internet the scatter plot

Answers

What is the question please?

Mr.Coy receives a 80 bill for his meal. He leaves 14.30 as a tip. What percent did he leave​

Answers

Answer:

around 18%

Step-by-step explanation:

14.30/80=0.17875

0.17875*100=17.875

18%

Answer:

Step-by-step explanation:

the answer is [tex]\frac{14.30}{80}[/tex]=17.875%

Use the data set to answer the question.
{22, 26, 28, 35, 45, 63, 91}
What is the mean of the data set?
Enter your answer as a number rounded to the nearest tenth,

Answers

Answer:

Yes

Step-by-step explanation:

because if you add that and then you subtract that you get that answer

41.43 is the answer I got, exact answer being 41.4285714286

PLEASE HELP!!!!!! Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim. Choose the correct option based on the problem information.

Use a significance level of α = 0.01 to test the claim that μ > 2.85. The sample data consist of 9 scores for which = 3.1 and s = 0.6. Identify the correct null and alternative hypotheses.


A. H0: μ = 2.85. H1: μ > 2.85.


B. H0: μ ≥ 2.85. H1: μ < 2.85.


C. H0: μ > 2.85. H1: μ ≤ 2.85.


D. H0: μ ≠ 2.85. H1: μ = 2.85.

Answers

Answer:

C. H0: μ > 2.85. H1: μ ≤ 2.85.

Step-by-step explanation:

hope it helps

What is the value of the expression 5x(3+6)-8

Answers

Answer:

45x - 8

Step-by-step explanation:

Answer:

Nodijsikmjkf

Step-by-step explanation:

45x-8

0.5- 2 2/5 = 1/2y +2.4 Please help! Find the value of y! Thanks!

Answers

The value of y, given the equation, can be found to be - 8 .6

How to find the value of y ?

To find the value of y, first convert the mixed fraction to a decimal for easier calculation :

2 ² / ₅ = 2 + 2 / 5

= 2 + 0. 4

= 2. 4

The equation then becomes :

0. 5 - 2.4 = 1 / 2 y + 2. 4

This can be rewritten as :

0. 5 - 2.4 = 1 / 2 y + 2. 4

0. 5 - 2 . 4 - 2. 4 = 1 / 2 y

1 / 2 y = - 4. 3

y = - 4. 3 / 1 / 2

y = - 8 .6

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Help me with this ASAP!!

Answers

Okay with what and I’d like to help but with what?

topic:(derivatives)

paki sagutan po please asap huhuhu

1. find y' of y=x+1 / x-1
2. find y'' of y = x(x+2)
3. find y'' of y = (3x+1)(x-2)
4. find y'' of y = (3x+4)squared
5. find y' of y = 3x-2

with solutions narin po if kaya pls, nagmamakaawa po ako huhu​​

Answers

2. find y'' of y = x(x+2)

y=x²+2x

y'=2x+2

3. find y'' of y = (3x+1)(x-2)

y=3x²+x-6x-2

y=3x²-5x-2

y'=6x-5

4. find y'' of y = (3x+4)squared

y=(3x+4)²

y'=2(3x+4)(3)=6(3x+4)=18x+24

5. find y' of y = 3x-2

y'=3

In Duck Creek, a bicycle license plate consists of one letter followed by one digit; for example, $Q7$ or $J1$. How many different license plates are possible

Answers

On solving the provided question, we can say that by permutation 26 possible letters  x  10 possible digits  = 260 possible plates

what is permutation?

The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order. like in the case of

26 possible letters  x  10 possible digits  =

26 x 10   =

260 possible plates

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