Does this have, one solution, no solutions, or infinite solutions?

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:

person above lol

Step-by-step explanation:

9514 1404 393

Answer:

  x = -2 because that is the value that makes the equation true

Step-by-step explanation:

Minus signs are everywhere. They can all be eliminated by multiplying both sides of the equation by -1.

  -1(-x -6 -x) = -1(-2)

  (-1)(-x) +(-1)(-6) +(-1)(-x) = 2 . . . . . distribute the -1

  x + 6 + x = 2 . . . . . . . . simplify

  x + x + 6 = 2 . . . . . . . . rearrange

  (1 +1)x +6 = 2 . . . . . . . . factor, using the distributive property

  2x +6 = 2 . . . . . . . . . . . simplify

  2x +6 -6 = 2 -6 . . . . . . subtract 6 from both sides

  2x = -4 . . . . . . . . . . . . . simplify

  (2x)/2 = (-4)/2 . . . . . . . divide both sides by 2

  x = -2 . . . . . . . . . . . . . . simplify

x is -2 because that is the value we get when we apply the properties of equality to the equation. We can check to see if it works in the original equation.

Check

-x -6 -x = -2

-(-2) -6 -(-2) = -2 . . . . put -2 where x is

2 -6 +2 = -2 . . . . . . . . simplify the signs

-4 +2 = -2 . . . . . . . . . . add the first two terms (could do all at once)

-2 = -2 . . . . . . . . yes, the value of x=-2 makes the equation true

_____

Additional comment

The properties of equality we're concerned with here are the multiplication property of equality, the addition property of equality and the division property of equality. Respectively, these tell us that multiplying, adding, or dividing both sides of the equation by the same number doesn't change the value of the variable.

These properties are essential to understanding how algebra works.

Answer:

The answer is 20π

Step-by-step explanation:

C = dπ

C = 20π

Answer:

c, 40 feet

Step-by-step explanation:

if half the area of a circle is 20, the other half is also 20, so 20 plus 20 is 40

Answer:

you can place a point on any number to the left of -1 on the number line, just don't place one on it because that would be equal to.

Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

volume of sphere = 4πr³/3 = 972π in³

r³ = 729 in³

r = 9 in

The value of its radius is,

⇒ r = 6.14 inches

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The volume of this sphere is 972 pi cubic inches.

Now, We know that;

Volume of sphere is,

⇒ V = 4/3πr³

⇒ 972 = 4/3 × 3.14 × r³

⇒ 972 × 3 = 12.56 × r³

⇒ r³ = 232.16

⇒ r = ∛232.16

⇒ r = 6.14 inches

Thus, The value of its radius is,

⇒ r = 6.14 inches

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Answer:198 Girls were there

Step-by-step explanation:

Total number of people tthat attended the study = 392

Number of adults = 105

Number of boys = 89

Number of Girls= Total number of people attended the study - ( Number of adults + Number of boys)

392- ( 105+89)

392- 194

=198 Girls

Answer:

Should be 4 divided by 5

Answer:

0.16

Step-by-step explanation:

1st term: 500

Divide 500 by 5 to get the 2nd term: 100

Divide 100 by 5 to get the 3rd term: 20

Divide 20 by 5 to get the 4th term: 4

Divide 4 by 5 to get the 5th term: 0.8

Divide 0.8 by 5 to get the 6th term: 0.16

I hope this helped! :)

Answer:it is most lickley.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

24 1/8 teaspoons are equ to 4 3/4 teaspoons

Answer:

Step-by-step explanation:

See the drawing attached

Answer:

1.33 or 1 1/3 pounds

Step-by-step explanation:

12 ÷ 9 = 1.33

Answer:

95 Degrees Celsius

Answer: 500%

Step-by-step explanation:

125 / 25 = 5 = 500%

We can check this answer by doing 5×25 = 125 so our answer is correct.

I am not a professional, I am simply using prior knowledge!

Note- It would mean the world to me if you could mark me brainliest!

Answer:

Because elena must have went higher above ground

Step-by-step explanation:

Answer:3.0%

Step-by-step explanation:

Answer:

3%

Step-by-step explanation:

Answer:

The number must be greater than 6.7. Thus, the sum will be negative.

For example, the number could be 7.

6.7 - 7 = -0.3

The number can be in the range -  x ∈ (- ∞ , - 6.7)

We have - the sum of 6.7 and a number is negative.

We have to determine the possible value of that number.

For f(x) to be negative -

f(x) < 0

2x + 10 < 0

2x < - 10

x < - 5

x ∈ (- ∞ , - 5)

According to the question, we have - the sum of 6.7 and a number is negative.

Now -

6.7 + x < 0

x < 6.7

x ∈ (- ∞ , - 6.7)

Hence, the number can be in the range -  x ∈ (- ∞ , - 6.7).

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Answer:

20%/100 = 8 peeps / 40 items in the basket

(40 total items)

Step-by-step explanation:

Let x be the total number of items in the basket. The ratio of peeps to the total item is 1/5. Therefore,

1/5 = 8/x

x = 40

40 total items

Answer:

A

Step-by-step explanation:

it only makes sense, hope this helped

Answer:

2x-3y=-8?

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

they need the same angle measures and side lengths to be congruent. also you need to line up the angles of the same measure in each triangle in the name

Answer: D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use the formula:

Substitute the values and find P:

Correct choice is A

Answer:

given length [l]=30

width[w]=75

perimeter= 2 (l + w )=2(30+75)=210

so

answer is A.210

Answer:

1. false

2. true

3. false

4. false

Step-by-step explanation:

1. 128 is not equal to 125

2. 119.7 = 119.7

3. 13.2 is not equal to 1.32

4. 5.88 is not equal to 12

Answer:-2

Step-by-step explanation:

The rate of change for the interval between -6 and -3 on the x-axis is -2. Therefore, option A is the correct answer.

From the given graph, we have the coordinates (-6, 6) and (-3, 0).

Here, rate of change = (y₂-y₁)/(x₂-x₁)

Now, (0-6)/(-3+6)

= -6/3

= -2

Therefore, option A is the correct answer.

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Answer:

Good morning all friend

Answer:

angles 1 and 6

Step-by-step explanation:

Vertical angles because they share the same Vertex.

One pair of vertical angles in the figure from the options is ∠1 and ∠6.

Vertical angles are angles that are opposite each other at the intersection of two lines. They are also called vertically opposite angles or non-adjacent angles with the same vertex. They have the same angle measurement or size.

Given is a figure, we need to determine the vertical angles in that,

The vertical angles are -

∠2 and ∠5

∠3 and ∠8

∠7 and ∠4

Hence, one pair of vertical angles in the figure from the options is ∠1 and ∠6.

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400, cus 40*10=400. Brainiest if possible, and tysm!

Answer:

40 * 10 = 400

Step-by-step explanation:

You have to multiply to get the answer :)

Hope yall have a awesome and wonderful day