p(x) = 3(x + 10x + 5) - 5(x - k)

In the polynomial p(x) defined above, k is a
constant. If p(x) is divisible by x, what is the value
of k?

Answers

Answer 1

First, you should simplify the function expression.

 

3(x2 + 10x + 5) - 5(x-k) = 3x2 + 30x + 15 - 5x + 5k = 3x2 +15x +15 +5k

 

In order for the polynomial to be divisible by x, all terms need to divide by x with no remainder.  The first two terms clearly divide by x.  However, the last two do not.  In order for this to work out where k is constant, 5k would have to cancel out the  +15 term, leaving nothing to divide by x.

 

So: 15 + 5k = 0

 

5k = -15

k = -3


Related Questions

Which number line correctly shows the graphing of point A,2 1/2 point b -2.75 and point c -0.25

Answers

Answer:

C

Step-by-step explanation:

There are two negative numbers must be before zero and one positive number must be after zero

A = 2 1/2 = 2.5 between 2 and 3

B = -2.75 between -2.5 and -3

C = -0.25 between 0 and -0.5

What is the slope of the line that contains these points?

Answers

Answer:

8

Step-by-step explanation:

Let,

x1 = 0

x2 = 1

y1 = 18

y2 = 26

Formula : -

Slope = ( y2 - y1 ) / ( x2 - x1 )

Slope = ( 26 - 18 ) / ( 1 - 0 )

= 8 / 1

Slope = 8

I am a 4digit numbe the sum of my middle two digit is 6 remove my middle two digit and Iwill become95. The digit inthe hundred place is 9less than the digit in the thousand place What number am I

Answers

Answer:

9065

Step-by-step explanation:

A Four digit Number

sum of A+B=6

Hundreds Place is 9 lesser than thousand Place

2 Middle Number remove = 95

Thousand= 9

Hundreds = 0

Tens=6

Ones=5

Answer:

here you go

Step-by-step explanation:

0+6 = 6

remove two middle numbers i become 95 which means the two outer numbers are 9 and 5

answer is 9065

HELP PLS I NEED THIS DONE BY 1:00 help me

Answers

Monsoon

Speed = distance/time
3/1 = 3
5/2 = 2.5
15/4 = 3.75

Monsoon has the lowest speed going 2.5km per hour.

Caleb wants to rent a kayak. Kayak rentals cost $70.58  for a half hour. If Caleb rents a kayak for 5.0 hours, how much will it cost him?

Answers

Answer:[tex]{ \times 2 + \times - 20} \div { \times - 4[/tex]

Step-by-step explanation:

divide each of the following: using the two methods

When do we use 180 or 360 to solve interior or exterior angles

Answers

Answer:

when it is alternate

Step-by-step explanation:

Answer:

here

Step-by-step explanation:

when it iş alternate

The local newspaper has letters to the editor from 80 people. If this number represents 2​% of all of the​ newspaper's readers, how many readers does the newspaper​ have?

Answers

Answer:

The local newspaper has letters to the editor from 80 people. If this number represents 2% of all of the newspaper's readers, how many readers does the newspaper have?

Step-by-step explanation:

2%ofx=80

or, 2/100 *X = 80

or, 2x =800

or, x = 400

Any helpp? someone....?

Answers

Answer:

I think that the speed is 65mph, because there is the largest number of people on the graph for 65mph.

Step-by-step explanation:

What is the value of k?

2k+9=7−3k


k=−2

k=−0.4

k = 2

k = 3.2

Answers

Answer:

k = -0.4

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify

2k + 9 = 7 - 3k

Step 2: Solve for k

[Addition Property of Equality] Add 3k on both sides:                                  5k + 9 = 7[Subtraction Property of Equality] Subtract 9 on both sides:                        5k = -2[Division Property of Equality] Divide 5 on both sides:                                 k = -0.4

Engineering An overpass intersects two
lanes of a highway. What must the value of x
be to ensure the two lanes are parallel?

Answers

Answer:

they are already paralell

Step-by-step explanation:

ok

Express the fraction 2/3, 3/4,5/6

Answers

Answer:

The required fractions for 2/3, 3/4, and 5/6 with a denominator of 12 are 8/12, 9/12, and 10/12 

Answer:

8/12, 9/12, and 10/12

Step-by-step explanation:

PLEASE HELP

If 87 people attend a concert and tickets for adults cost $3.5 while tickets for children cost $3.25 and

total receipts for the concert was $291.75, how many of each went to the concert?

Answers

Answer: 51 Children and 36 Adults.

Step-by-step explanation: Let's call x the number of children admitted and call z the number of adults admitted.

We know that x+z= 87

We also know that 3.25x+3.5z= 291.75.

We want to find the value of x and z. Then we solve the system of equations:

Multiply the first equation by -3.5 and add it to the second equation:

-3.5x-3.5z= -304.5

3.25x+3.5z= 291.75

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

-0.25x=-12.75

x= -42.75 ÷ -0.25

x=51

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

Now we substitute the value of x in the first equation and solve for the variable z

51+z=87

z=87-51

z= 36

Omg took me like 10 minutes to calculate would appreciate brainliest. Have a wonderful day.

The next model of a sports car will be 12.6% less than the current model. The current model is 32,000. How much will the price decrease? How much will the next model be?

Answers

The next model will cost $27968.

100% - 12.6% = 87.4%

12.6% x 32000 = 4032

32000 - 4032 = 27968


pls mark me as brainliest!

write an expression in factored form for the polynomial of least possible degree graphed below.

i’m confused because when i’m trying to find « a » i end up getting 0 and i feel i’m doing something wrong. thank you!!

Answers

Answer:

- 1/64 (x+4)² (x-3) (x-4) = 0

Step-by-step explanation:

f(x) = a (x+4)²(x-3)(x-4)   ... curve touch (-4,0) and not cross x axis

x=0   f(x) = -3

a (4)² * (-3) * (-4) = -3

a = - 1/64

- 1/64 (x+4)² (x-3) (x-4) = 0

Factor use please help I need this and quick

Answers

[tex]8a^{3} +\sqrt{3^{2}*3 } b^{3}[/tex]

[tex]8a^{3} +(\sqrt{3^{2} } *\sqrt{3})b^{3} \\\\[/tex]

[tex]8a^{3} +(3^{\frac{2}{2} } *\sqrt{3} )b^{3}[/tex]

[tex]8a^{3} +(3*\sqrt{3} )b^{3}[/tex]

[tex]8a^{3} +3*\sqrt3} *b^{3}[/tex]

Find the Area of the figure below, composed of an isosceles trapezoid and one semicircle. Rounded to the nearest tenths place


Answers

Step-by-step explanation:

the area =

[½(8+2)×4] + [½×3.14×1²]

= 20 + 1.57

= 21.57

= 21.6

Gabe's bill at Colton's was $25. If he decided to leave his server a 20% tip, how muc
money did he spend in all?

Answers

Answer:

$31.25

Step-by-step explanation:

If I understood the question correctly, it should be $31.25. 25 x 0.25 (25 percent) = 6.25. 25 + 6.25 = 31.25.

1/2(x+24)=21 (distributive property) thanks

Answers

Answer:

x=18

Step-by-step explanation:

since x+24 is in parenthesis, we need to distribute 1/2 to all the parts inside the parenthesis.

1/2 * x = 1/2x

1/2 * 24= 12

1/2x+12=21

subtract 12 from both sides

1/2x= 9

divide 1/2 from both sides

x=18

so your answer would be x=18

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]\frac{1}{2}(x+24)=21 \rightarrow \frac{1}{2}x + 12 = 21\\\\x = 18[/tex]

»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\frac{1}{2}(x+24) = 21\\\rule{150}{0.5}\\\\\rightarrow \frac{1}{2}*x = \frac{1}{2} \\\\\rightarrow \frac{1}{2} * 24 = 12\\\\\rightarrow \frac{1}{2}x + 12 = 21\\\\\rightarrow \frac{1}{2}x + 12 - 12 = 21 - 12\\\\\rightarrow \frac{1}{2}x = 9\\\\\rightarrow (\frac{1}{2}x)2 = 9 * 2\\\\\rightarrow\boxed{x = 18}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

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

Simplify 5b4×4b3 what is the answer for it ​

Answers

Answer:

[tex]{ \rm{ {5b}^{4} \times {4b}^{3} }}[/tex]

• from laws of indices:

[tex] \hookrightarrow \: { \boxed{ \rm{ {rx}^{n} + {px}^{m} = (r \times p) {x}^{(n + m)} }}} \\ [/tex]

• substitute:

[tex]{ \rm{ {5b}^{4} \times {4b}^{3} = (5 \times 4) {b}^{(4 + 3)} }} \\ \\ = { \boxed{ \boxed{ \rm{ \: 20 {b}^{7} \: \: }}}}[/tex]

The soccer team raises $919.60 for new uniforms. If there are 20 players on the team, how much does each player get for a new uniform?​

Answers

Answer:

10☺☺☺☺☺☺☺☺☺☺10 i think is 10

In Bobby's grade, 679 students are enrolled in health and 21 students are not. What percentage of the students in the school are enrolled in health? Write your answer using a percent sign (%).​

Answers

97.07%

Step-by-step explanation:

total number of students is

696+21=717

696/717×100=97.07

answer is 97.07%

NEDDDD ASAPPPPP!!!!!!!!!

Answers

Answer:

9

Step-by-step explanation:

4y + 6y = 90

10y =90

y = 90÷10

y = 9

Hi, I need help with homework on review for test.

Answers

Answer:

-24+48i

Step-by-step explanation:

yan po ata sagot

try to determine which set of digits ends product three consecutive natural numbers?​

Answers

Answer:

0, 4, 6

Step-by-step explanation:

1 * 2 * 3 = 6

2 * 3 * 4 = 24

3 * 4 * 5 = 60

4 * 5 * 6 = 120

5 * 6 * 7 = 210

6 * 7 * 8 = 336

7 * 8 * 9 = 504

etc.

Answer: 0, 4, 6

What is 32008 rounded to the nearest highest place value

Answers

32008 rounded to the nearest highest place value is 32010
32008 rounded to the nearest highest place value is 32010

Im not sure what method is best used to solve these types of inequalities.

Answers

Answer:

There is no specific method you can solve it as you like

Step-by-step explanation:

you can do it as a normal equation first get rid of the (x-9) by multiplying the whole radical by x-9/x-9, then you will get rid of the x-9 down and you will have (x-9) . (x+6) . (x-1) [tex]\leq[/tex] 0 then multiply them together and solve it normally. Also dont forget to do the check part :)

If you need further help comment down :)

Answer:

I would say solve for the x value

Step-by-step explanation:

Rainwater is collected in a large pool. After a significant rainstorm, the pool contains
3 3/4 gallons of water. The sun came out after the rain ended. Within a couple of hours, 1/6 of the water collected in the pool evaporated. What value represents the change in the amount of water in the pool? Enter your answer as a simplified fraction in the box.

Answers

Answer:

3 1/8

Step-by-step explanation:

3 3/4 and 1/6 percent of the water evaporated

3 3/4 as a inproper fraction 15/4  

15/4  * 1/6= 15/24 = 5/8

so we have to subtract 5/8 from 15/ 4

15/4*2/2= 30/8

30/8-5/8= 25/8

Answer:

3 1/8

Step-by-step explanation:

A family bought a total of 13 tickets to a magic show, some adult and some child. The family paid a total of $85
Adult tickets are $15 each and child tickets are $5 each.
Let x represent adult tickets and y represent child tickets.
Write an equation to model the total amount of money that they spent.

Answers

Answer:

250 $3 tickets and 100 $2 tickets were sold.

Step-by-step explanation:

The cost of tickets for a play is $3.00 for adults and $2.00 for children. 350 tickets were sold and $950 was collected. How many tickets of each type were sold?

Solution:

Step 1: Set up a table with quantity and value.

quantityvaluetotal$3 tickets$2 ticketstogether

Step 2: Fill in the table with information from the question.

The cost of tickets for a play is $3.00 for adults and $2.00 for children. 350 tickets were sold and $950 was collected. How many tickets of each type were sold?

Let x = number of $3 tickets

Let y = number of $2 tickets

Total = quantity × value

quantityvaluetotal$3 ticketsx33x$2 ticketsy22ytogether350950

Step 3: Add down each column to get the equations

x + y = 350                    (equation 1)

3x + 2y = 950                (equation 2)

Use Substitution Method

Isolate variable x in equation 1

x = 350 – y                     (equation 3)

Substitute equation 3 into equation 2

3(350 – y) + 2y = 950

1050 – 3y + 2y = 950

3y – 2y = 1050 – 950

y = 100

Substitute y = 100 into equation 1

x + 100 = 350

x = 250

help dududidihendhhejrjfjf

Answers

Answer:

x = − 8

Step-by-step explanation:

Factor then solve to find the complex solutions.

A glass block window is made of two different-sized glass squares. The window has side lengths of 40 inches. The large glass squares have side lengths of 10 inches. Find the total area of the small glass squares?

Answers

Given,

A glass block window is made of two different-sized glass squares.

The window has side lengths of 40 inches. The large glass squares have side lengths of 10 inches.

40 × 10 = 400

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