Given f(x) = 2x^2+ kx – 9, and the remainder when f(x) is divided by x + 6 is
57, then what is the value of k?

Answers

Answer 1

Given:

The function is

[tex]f(x)=2x^2+kx-9[/tex]

The remainder when f(x) is divided by x+6 is 57.

To find:

The value of k.

Solution:

According to the remainder theorem, if a polynomial function f(x) is divided by (x-a), then f(a) is the remainder.

The remainder when f(x) is divided by x+6 is 57.

Using remainder theorem, we get f(-6)=57.

Putting x=-6 in the given function.

[tex]f(-6)=2(-6)^2+k(-6)-9[/tex]

[tex]57=2(36)-6k-9[/tex]

[tex]57=72-6k-9[/tex]

[tex]57=63-6k[/tex]

On further simplification, we get

[tex]6k=63-57[/tex]

[tex]6k=6[/tex]

[tex]k=\dfrac{6}{6}[/tex]

[tex]k=1[/tex]

Therefore, the value of k is 1.

Answer 2

Answer:

person above lol

Step-by-step explanation:


Related Questions

Solve: 2x + 3y = 1
y = -23 +11

Answers

Answer:

x = 18.5

y = -12

Step-by-step explanation:

First, solve y:

y = -23 + 11

y = -12

Then, solve the main problem:

2x + 3y = 1

(Substitute y)

2x + -36 = 1

2x - 36 = 1

2x = 1 + 36 = 37

x = 37 / 2

x = 18.5

Forty students went on a trip on Wednesday. On Thursday, 15% less students went on a similar trip. How many students went on the trip on Thursday?

Answers

Answer:

34

Step-by-step explanation:

40 * .15= 6

40-6 = 34

okkk so you do 40 * .15 because you just put a decimal point before all percentages to convert it into number

40*.15= 6

then subtract 6 to the original amount

40-6=34

34 students went on the trip on thursday cause 6 students got killed by bears in the last trip.

I NEED HELP ASAP!!!!!!!

Answers

Answer:

9/25 = 36%

Step-by-step explanation:

First add up all of the students (150)

Then divide 54 by 150, 0.36

0.36 = 36% = 9/25

What is the exact area of a circle having diameter 3 in.?

Answers

Answer:

2.25π square inches

Step-by-step explanation:

Area = π[tex]r^{2}[/tex]

Diameter = 2r

So in this case, radius = 1.5 inches

Plugging that into the area formula produces the answer

Answer these three question for a brainlist, 5 stars and a thanks for extra

Answers

A)
One solution
x = 1
y = 1
B)
One solution
x = 2
y = -1/2
C)
Infinite solutions

12 (3 + 4) =

36 + 48
0.84
123 + 124
15 + 16

Answers

36+48 is the only right answer here
12(3+4)= 84
36+48=84
123+124=247
15+16=21

The equation that passes through (3,6) and is perpendicular to 3x - 4y = - 2

a
y = - 4/3x + 3 1/3
b
y = - 3/4x + 10
c
y = - 4/3x + 10
d
y = 3/4x + 10

Answers

Answer:

C

Step-by-step explanation:

We want the equation of the line that passes through (3, 6) and is perpendicular to:

[tex]3x-4y=-2[/tex]

First, convert the second equation into slope-intercept form:

[tex]-4y=-3x-2\Rightarrow \displaystyle y=\frac{3}{4}x+\frac{1}{2}[/tex]

So, we can see that the slope of the line is 3/4.

The slopes of perpendicular lines are negative reciprocals of each other.

Therefore, the slope of the new line is -4/3.

It passes through the point (3, 6).

We can use the point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

Substitute:

[tex]\displaystyle y-(6)=-\frac{4}{3}(x-3)[/tex]

Distribute:

[tex]\displaystyle y-6=-\frac{4}{3}x+4[/tex]

Therefore:

[tex]\displaystyle y=-\frac{4}{3}x+10[/tex]

The answer is C.

In a class, the ratio of girls : boys is 5:3.

What fraction of the class are boys?

please answer urgent , high points up for grabs , please give good explanation

Answers

you add the 5+3 to get the overall amount of 8 parts, 3 of them parts are boys so the answer is 3/8

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

uh

Step-by-step explanation:

Answer:

wtffffffffffffffffffff

if f(x)=x²-18x+91, solve for x when f(x)=10​

Answers

Answer:

x = 9

Step-by-step explanation:

x²-18x+91 = 10

x²-18x+81 = 0

(x-9)(x-9)= 0

x = 9

check:

9² - 18 (9) + 91

81-162+91 = 10

Why thank you for helping me and I will mark brainliest if you’re right :)

Answers

Answer:

Choice #1)  4.7 cm

Step-by-step explanation:

circumference of full circle = 2(r)(3.14)

a full circle would be = 2(3)(3.14) = 18.84 cm

It is 1/4 circle so 18.84/4=4.7 cm

Answer:

10.7

Step-by-step explanation:

1. I first grabbed a ruler to measure the other straight side of the figure.

2. Both of the straight sides were 3 cm so I knew that the answer had to be greater than 6 cm.

3. I then estimated that the other side was longer than the 3 cm.

4. I then had to my logic to figure out the answer and I very quickly realized that 4.7 cm would not make since because that is less than 6 cm. I know 7.7 cm would not make since because I knew the curved side was longer than 3 cm not shorter. 18.8 cm did not make since because that answer has WAY to much cm. Using the process of elimination, 10.7 cm was the only answer that made since.

Which set of ordered pairs would define a line with a negative slope?

A.
(5, 5) and (0, 1)

B.
(3, 6) and (5, 1)

C.
(2, 3) and (7, 6)

D.
(2, 3) and (-4, -1)

Answers

Answer:

I believe it is B

Step-by-step explanation:

Im not good at explaing, but if you move forward three units and up 6, then draw a point, then go forward to 5 units and down to one unit and connect those dots, the line would be going down to the right

The function y=f(x) is graphed below. What is the average rate of change of the function f(x) on the interval -8 ≤ x ≤ -1?

Answers

Answer:

The average rate of change of the function is: 0

Step-by-step explanation:

The function y = f(x) is graphed below.

From the graph it is clear that:

at x = -8, the value of f(-8) = -10

at x = -1, the value of f(-1) = -10

We have to determine the average rate of change of the function f(x) on the interval -8 ≤ x ≤ -1.

so

at x₁ = -8, f(x₁) = f(-8) = -10

at x₂ = -1, f(x₂) = f(-1) = -10

Using the formula to determine the average rate of change of the function f(x) on the interval -8 ≤ x ≤ -1.

Average rate = [f(x₂) - f(x₁)] / [ x₂ - x₁]  

                      = [f(-1) - f(-8) ] / [-1-(-8)]

                      = [-10 - (-10)] / [-1+8]

                      = [-10 + 10] / 7

                      = 0 / 7

                      = 0

Therefore, the average rate of change of the function is: 0

A CD is circular and has a diameter of 6 centimeters. Which is closest to the area of the CD? Use 3.14 for π

Answers

Answer:

28.26 cm²

Step-by-step explanation:

Area of a circle = πr²

         r = diameter/2

         r = 6/2 = 3

A = (3.14)(3)²

A = 28.26 cm²

Which is equivalent to (125)*?
125
125 3x
1253
125/5

Answers

Answer:

A

Step-by-step explanation:

it only makes sense, hope this helped

A is the only one that makes sense

PLEASE HELP the rise of the ramp is 8 ft tall and the run of the ramp is 16 ft long what is the slope of the ramp ​

Answers

Answer:

1/2 because it is...........

Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.

Answers

Answer:

AB = 4.62    m∠A =  22°   m∠B = 68°

Step-by-step explanation:

Tan A = 1.7/4.3 = .39534...

m∠A = arctan .39534... ≅ 22°

m∠B = 90 - 22 = 68°

AB = [tex]\sqrt{1.7^{2} + 4.3^{2} } = \sqrt{2.89 + 18.49} = \sqrt{21.38} = 4.62[/tex]

     

how can I solve this problem ​

Answers

Answer:

50

Step-by-step explanation:

the angle that they want you to find is complementary to the angle that equals 40. Complementary means they will add up to equal 90. 90-40=50 so ADB = 50

PLEASE ANSWER QUICKLY! THIS IS FOR A STUFY GUIDE DUE IN 5 MINUTES!!!!!
6CO2 + 6H2O ———» C6H12O6 + 6O2

Is the equation above balanced or unbalanced? ___________

a- need to add coefficients
b- I don't know
c- Unbalanced
d- Balanced

Answers

Answer:

It's Balanced

Step-by-step explanation:

A simple word equation that can be used to describe the process of photosynthesis is carbon dioxide + water —> glucose + oxygen + water.  So it's a balanced chemical equation for the process can be written as 6CO2 + 6H2O —> C6H12O6 + 6O2

Hope this helps!

Helpeoepeoeoeo show work

Answers

IMPORTANT THIGNS TO REMEMBER:

Has 20 lb. dog food!Gives dog 1 3/5 everyday!Find how much eaten after 2 days!Find how much is left!

ANSWER:

Dog has eaten 3 1/5 after 2 days!

There is 16 4/5 left in bag!

EXPLANATION:

Since she gives 1 3/5 to her dog everyday and their asking for 2 days you would multiply 1 3/5 × 2 OR add 1 3/5 + 1 3/5

Which would give you 3 1/5

So, the dog has eaten 3 1/5 lb. of dog food in 2 days.

However then, you would subtract 20 lb. - 3 1/5 lb. because there is 20 lb. dog food in all and the dog has eaten 3 1/5 of it. This would give you 16 4/5 lb.

Meaning there is 16 4/5 lb. left in the bag of dog food!

. How many dozen must be sold to make a profit of $90? Make a Selection: A. 45 B. 25 C. 30 D. 8

Answers

Answer: A. 45 must be sold to make a profit of $90

solve for u 5u + 9 - 4u = 17 (also don't have the answer be a fraction)

Answers

Answer:

=8

Step-by-step explanation:

Answer:

u=8

hope this helps

Step-by-step explanation:

solve this plz????? thx

Answers

Answer:

AOD i think

Step-by-step explanation:

Answer:

angle aob

Step-by-step explanation:

Write the equation of the line in slope-intercept form: y=mx+b
Given: Point (1,3) Slope: 2

Answers

Answer:

y=2x+1

Step-by-step explanation:

y-y1=m(x-x1)

y-3=2(x-1)

y-3=2x-2

y=2x-2+3

y=2x+1

Recipe B uses 9 ounces of flour to make 12 servings of dough. How many flour is in per serving?

Answers

Answer:

Step-by-step explanation:

9/12 ounce = 3/4 = .75 ounce flour

Select the solution(s) to the following equation: (3x−2)(x+5)=0 SELECT ALL THAT APPLY
x=3/2
x=5
x=-5
x=2/3
x=-2/3
x=-3/2

Answers

Answer:

Step-by-step explanation:

Check by direct substitution.  If we begin by checking x = 3/2, we substitute 3/2 for x in (3x - 2)(x + 5), obtaining (9/2 - 2)(3/2 + 5), which is NOT zero.  Therefore x = 3/2 is not a solution.

(3*5−2)(5+5)=0  False.  x = 5 is not a solution.

(3*[-5]−2)([-5+5)=0  True.  x = -5 is a solution

x = 2/3:  (3*2/3 - 2)( ) = 0.  True  x = 2/3 is a solution

x = -2/3:  ( )( ) = -17 1/3;  so x = -2/3 is not a solution

x = -3/2:  ( ) ( ) = -22 3/4; so x = -3/2 is not a soution

PLEASE HELP ME ?!?!?!

Answers

Answer:

19

Step-by-step explanation:

6x-10=3x+50
3x=60
x=20

hope this helps !

Which of the following sets of measures
cannot be the lengths of the sides of a right
triangle?
A
5 cm, 12 cm, and 13 cm
B
9 cm, 12 cm, and 17 cm
C
1 cm, 2.4 cm, and 2.6 cm
D
2.5 cm, 6 cm, and 6.5 cm​

Answers

you can use the formula of pythagoras theorem to know what of them is wrong

in the first case

-5^2 + 12^2 =169

 13^2=169         ( it's a right equation so it can be lengths of right angle tri )

in the second case

_9^2 + 12^2 =225

  17^2 not equal 225

so these are the lengths that can't be a right angle triangle

A number divided by 3 and then 4 is added to the quotient.the result is 8.find the number

Answers

Answer:

12

Step-by-step explanation:

8-4= 4 So, 4 is the quotient.

4x3= 12 So 12 is the original number  

12/3 + 4= 8

i need help i will mark u brainlest

Answers

the answer is C,
step-by-step: i had the same test lolll

Answer:

3rd one

Step-by-step explanation:

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