Use the remainder theorem to determine whether x - 2 is a factor of

f(x) = x3 + 3x2 - x - 18


A)

Yes, x - 2 is a factor of f(x) because f(2) = 0



B)

No, x - 2 is not a factor of f(x) because f(2) = 0



C)

Yes, x - 2 is a factor of f(x) because f(-2) = -12



D)

No, x - 2 is not a factor of f(x) because f(-2) = -12

Answer: The answer is 8.06.

Step-by-step explanation:

First, write the Pythagorean Theorem. c^2 = a^2 + b^2

Next, determine the values of (a,b,c) for the Pythagorean Theorem.

Step-1 : Multiply the coefficient of the first term by the constant   3 • -20 = -60  

Step-2 : Find two factors of  -60  whose sum equals the coefficient of the middle term, which is   -11 .

     -60    +    1    =    -59  

     -30    +    2    =    -28  

     -20    +    3    =    -17  

-15    +    4    =    -11  

                           That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -15  and  4  

                    3x2 - 15x + 4x - 20

Step-4 : Add up the first 2 terms, pulling out like factors :

                   3x • (x-5)

             Add up the last 2 terms, pulling out common factors :

                   4 • (x-5)

Step-5 : Add up the four terms of step 4 :

                   (3x+4)  •  (x-5)

            Which is the desired factorization

Answer:

c, after you move the 5x to the left side to make the equation (-4x-5x+10>55), you subtract the +10 to erase it, and also subtract the 55 to be 45.

Answer:

When cooper was 15 years old, he scored an 85 on an iq test. he took the test again when he was 35 years old and scored an 85 again. this indicates that the iq test is highly: __________

Reliable

Because his scores were so close together the test would be considered as Reliable.

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#2 is x = 16

[Given]

20 + x = 4 + 2x

[Subtract x from both sides]

20 = 4 + x

[Subtract 4 from both sides]

16 = x

#3 is x = 4

[Given]

12x - 16 = 8 + 6x

[Add 16 to both sides]

12x = 24 + 6x

[Subtract 6x from both sides]

6x = 24

[Divide both sides by 6]

x = 4

Note

With the of "add 16" or "subtract x" you can flip the order. If you have multiply variables on each side you can pick the steps you take. I usually, when possible, like to make it so I end up with all negative or all positive numbers because it is easier for me!

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

3) 12x - 16 = 8 + 6x

Step 1: Collect like terms
12x - 6x = 6x

-16 - 8 = -24

Step 2: Divide by the coefficent with the variable

-24/6 = - 4
6x/6 = 1x

x = 4

Answer:

Step-by-step explanation:

The statements that are true regarding the diagram given are:

The triangle sum theorem states that all the three interior angles in a triangle have a sum of 180 degrees all together.

Thus, in the diagram given, the statements that are all true are:

m∠3 + m∠4 = 180° (angles on a straight line)

m∠4 = m∠1 + m∠2 (external angle theorem)

m∠1 + m∠2 + m∠3 = 180° (triangle sum theorem).

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Answer:

A, D, E

Step-by-step explanation:

I got it right.

Answer:

y = -2

Step-by-step explanation:

You substitute 2 as x, y = 6 - 4 * 2, which is y = 6 - 8 = -2.

A hypothesis can be differentiated from a theory because it is a specific prediction arising from the theory. The statement that is true is, a hypothesis can be differentiated from a theory because it is a specific prediction arising from the theory. A hypothesis is a suggested explanation of a phenomenon or observed data that is testable.

Hypotheses are more detailed, and are written to explain precisely what you think is going to occur in your research and the reason for that prediction. A hypothesis will be rejected if it does not fit the data, whereas a theory will be modified to fit the data.

A hypothesis is more like a forecast, and a theory is more like a law that explains how certain events operate. Thus, we can conclude that a hypothesis is a specific prediction arising from the theory.

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a. y/x = 40/1, 76/2, 112/3, 148/4 does not represent a proportional relationship. . y/x = 48/2, 96/3, 144/4, 192/5 does not represent a proportional relationship. c. y/x = 18/1, 54/3, 90/5, 126/7  represents a proportional relationship.

A proportional relationship means that the ratio of y to x is constant throughout the table. Let's check each table:

a. y/x = 40/1, 76/2, 112/3, 148/4

If we simplify the fractions, we get y/x = 40, 38, 37.33, 37. This is not a constant ratio, so this table does not represent a proportional relationship.

b. y/x = 48/2, 96/3, 144/4, 192/5

If we simplify the fractions, we get y/x = 24, 32, 36, 38.4. This is not a constant ratio, so this table does not represent a proportional relationship.

c. y/x = 18/1, 54/3, 90/5, 126/7

If we simplify the fractions, we get y/x = 18, 18, 18, 18. This is a constant ratio, so this table represents a proportional relationship.

d. y/x = 24/1, 21/2, 18/3, 15/4

If we simplify the fractions, we get y/x = 24, 10.5, 6, 3.75. This is not a constant ratio, so this table does not represent a proportional relationship.

Therefore, the table that represents a proportional relationship is c. y/x = 18/1, 54/3, 90/5, 126/7.

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Answer: Just use MathPapa.

Step-by-step explanation:

Answer:

See below both methods.

Step-by-step explanation:

9x + 6y = 18

-6x - 6y = -24

Elimination:

9x + 6y = 18

-6x - 6y = -24

Since 6y and -6y add to zero, add the equations to eliminate y and solve for x.

      9x + 6y = 18

(+)   -6x - 6y = -24

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

       3x        = -6

x = -2

Now we need to eliminate y and solve for x. Divide both sides of the second equation by 6 and multiply both sides of the second equation by 9 to get this new equation.

-9x - 9y = -36

Add this new equation to the first original equation to eliminate x.

      9x + 6y = 18

(+)  -9x - 9y = -36

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

            -3y = -18

y = 6

Solution: x = -2; y = 6

Substitution:

9x + 6y = 18

-6x - 6y = -24

Divide both sides of the first equation by 3. Divide both sides of the second equation by -6.

3x + 2y = 6    (Equation 1)

x + y = 4     (Equation 2)

Solve the second equation for x.

x = 4 - y

Substitute 4 - y for x in Equation 1 and solve for y.

3(4 - y) + 2y = 6

12 - 3y + 2y = 6

-y + 12 = 6

-y = -6

y = 6

Now substitute 6 for y in equation 2 and solve for x.

x + 6 = 4

x = -2

Solution: x = -2, y = 6

The given coins [1, 2, 5] and the value 11, the minimum number of coins needed is 2.

Here are the steps to find the minimum number of coins:

1. First, we create an array of size equal to the given value, initialized with a very large number. This array will store the minimum number of coins needed to make each value from 0 to the given value.

2. We set the first element of the array to 0, as it doesn't require any coins to make a value of 0.

3. Next, we iterate through all the coins available and for each coin, we iterate through all the values from the coin value to the given value.

4. For each value, we calculate the minimum number of coins needed by taking the minimum of the current minimum and the value obtained by subtracting the coin value from the current value and adding 1 to it.

5. Finally, we return the value stored in the last element of the array, which represents the minimum number of coins needed to make the given value.

Let's consider an example to better understand the process:

Given coins: [1, 2, 5]
Given value: 11

1. Initialize the array with [INF, INF, INF, INF, INF, INF, INF, INF, INF, INF, INF, INF] (INF represents infinity).

2. Set the first element of the array to 0, so it becomes [0, INF, INF, INF, INF, INF, INF, INF, INF, INF, INF, INF].

3. For the first coin (1), iterate through the array from index 1 to 11.

  - For index 1, the minimum number of coins needed is 0 + 1 = 1.
  - For index 2, the minimum number of coins needed is 0 + 1 = 1.
  - For index 3, the minimum number of coins needed is 0 + 1 = 1.
  - ...
  - For index 11, the minimum number of coins needed is 0 + 1 = 1.

  The array becomes [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

4. For the second coin (2), iterate through the array from index 2 to 11.

  - For index 2, the minimum number of coins needed is 1 (minimum of 1 and 0 + 1 = 1).
  - For index 3, the minimum number of coins needed is 1 (minimum of 1 and 0 + 1 = 1).
  - For index 4, the minimum number of coins needed is 1 (minimum of 1 and 1 + 1 = 2).
  - ...
  - For index 11, the minimum number of coins needed is 1 (minimum of 1 and 1 + 1 = 2).

  The array becomes [0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2].

5. For the third coin (5), iterate through the array from index 5 to 11.

  - For index 5, the minimum number of coins needed is 2 (minimum of 2 and 0 + 1 = 1).
  - For index 6, the minimum number of coins needed is 2 (minimum of 2 and 1 + 1 = 2).
  - ...
  - For index 11, the minimum number of coins needed is 2 (minimum of 2 and 2 + 1 = 3).

  The array becomes [0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2].

6. The minimum number of coins needed to make the given value (11) is 2.

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Answer:

5ft

Step-by-step explanation:

15÷3=5

As a result, the answer to the following question, As a result, the length triangle of side JS is 18.

A triangle is a polygon because it contains four or more parts. It features a simple rectangular shape. A triangle ABC is a rectangle with the edges A, B, and C. When the sides are not collinear, Euclidean geometry produces a single plane and cube. If a triangle contains three components and three angles, it is a polygon. The corners are the points where the three edges of a triangle meet. The sides of a triangle sum up to 180 degrees.  

We must apply the Pythagorean theorem to answer question 19. We know that JN is the hypotenuse of a right triangle with legs of 6 and 8 lengths. As a result, we may apply the formula:

\(JN^2 = 6^2 + 8^2\\JN^2 = 36 + 64\\JN^2 = 100\\JN = square root (100)\\JN = 10\\\)

As a result, the length of side JN is 10.

JS/NS = JM/JN

When we substitute the provided values, we get:

12/10 = JS/NS

When we simplify the left side, we get:

6/5 = JS/NS

When we multiply both sides by NS, we get:

JS = (6/5)NS

We also know that NS is 15, therefore we may substitute that number for:

\(JS = (6/5) * 15\sJS = 18\)

As a result, the length of side JS is 18.

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The value of 'x' is 5/2  

An exponent is a number that is written in superscript (above and to the right of another number) and indicates how many times that number should be multiplied by itself.    

Exponents are used in many areas of mathematics and science, including algebra, calculus, physics, and chemistry.  

Here we have

\(3^{x+1} - 3^{x-1} = 24\sqrt{3}\)      

Can be solved as follows

=>  \(3^{x} \times 3^{1} - 3^{x} \times 3^{-1} = 24\sqrt{3}\)  

=>  \(3^{x} [ 3^{1} - 3^{-1}] = 24\sqrt{3}\)  

=>  \(3^{x} [ 3 - \frac{1}{3} ] = 24\sqrt{3}\)  

=>   \(3^{x} [ \frac{9- 1}{3} ] = 24\sqrt{3}\)  

=>  \(3^{x} [ 8 ] = 3 \times 24\sqrt{3}\)  

=>  \(3^{x} = 3 \times 3\sqrt{3}\)  

=>  \(3^{x} = 3^{2} \sqrt{3}\)    

=>  \(3^{x} = 3^{2 + \frac{1}{2} }\)    

=> x = 5/2

Therefore,

The value of 'x' is 5/2  

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Answer:

-2

Step-by-step explanation:

slope= \(\frac{y_{1}-y_{2} }{x_{1}-x_{2} }\)

Let's use points (-3,6) and (3,6).

\(\frac{6-(-6)}{-3-3}= \frac{12}{-6} = -2\)

Answer:

in five years.

Step-by-step explanation:

I'm not good at explaining this but you can keep adding years to your equation until you get the answer to be 3. For example your starting equation is 85/25 which = 3.4 years, you can keep going like 86/26 = 3.3 years, 87/27 =3.2 years until you get to 3. When the terracotta bust is 90 years old and the marble bust is 30, it will be three times as old. (90/30 is simplified to 9/3 then to 3.)

the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute, is approximately 0.081 or 8.1%.

How to solve?

To solve this problem, we can use the Poisson distribution, which models the probability of a certain number of events occurring in a fixed interval of time or space, given the expected rate of occurrence.

Let lambda be the expected rate of customer arrivals per minute. If exactly two customers arrive in the first minute, then the expected number of customers to arrive in three minutes is lambda ×3. We can use this expected value to calculate the probability of at least seven customers arriving in three minutes:

P(X ≥ 7 | X ~ ∝(λ×3))

= 1 - P(X ≤ 6 | X ~ ∝(λ×3))

= 1 - ∑[k=0 to 6] (e²(-λ3) ×(lλ3)²k / k!)

where e is the mathematical constant approximately equal to 2.71828, and k! denotes the factorial of k.

To find lambda, we can use the fact that exactly two customers arrive in the first minute. The Poisson distribution assumes that the number of events in a fixed interval of time or space follows a Poisson distribution with parameter lambda, which represents the expected rate of occurrence. Therefore, lambda is equal to the number of customers arriving per minute, which is 2.

Substituting lambda = 2 into the formula, we get:

P(X ≥ 7 | X ~ ∝(2×3))

= 1 - P(X ≤ 6 | X ~ ∝(6))

= 1 - ∑[k=0 to 6] (e²(-6) ×6²k / k!)

Using a calculator or computer software, we can evaluate this expression to get:

P(X ≥ 7 | X ~ ∝(6)) ≈ 0.081

Therefore, the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute, is approximately 0.081 or 8.1%.

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Based on the information provided in the question, it is not clear what correlation is being referred to. To accurately conclude the clarity of the water from 1950 to 1980 based on a correlation, we would need more specific information about the correlation itself.

However, if we assume that the correlation being referred to is between a particular factor and the clarity of the water, we can make some general statements about how the clarity of the water might be affected during that time period.

1. If the correlation indicates a positive relationship between the factor and the clarity of the water, we might conclude that the water became clearer from 1950 to 1980. This could suggest that measures were taken to improve water quality, such as implementing stricter pollution control regulations or enhancing water treatment processes.

2. On the other hand, if the correlation indicates a negative relationship between the factor and the clarity of the water, we might conclude that the water became less clear from 1950 to 1980. This could suggest that factors such as increased pollution, deforestation, or other human activities negatively impacted water quality during that time period.

3. If the correlation is weak or close to zero, it would be difficult to draw any conclusive statements about the clarity of the water from 1950 to 1980 based solely on this correlation. Other factors or variables not considered in the correlation may have had a significant impact on water clarity during that time.

In summary, without specific information about the correlation being referenced, it is not possible to provide a definitive conclusion about the clarity of the water from 1950 to 1980.

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The numbers that do not form a fact family are solved

Given data ,

A fact family consists of a set of related addition and subtraction facts that use the same numbers. For example, the numbers 3, 5, and 8 form a fact family because:

3 + 5 = 8

5 + 3 = 8

8 - 5 = 3

8 - 3 = 5

Numbers that do not form a fact family are any set of numbers that do not follow this pattern. For example, the numbers 2, 4, and 7 do not form a fact family because no combination of addition and subtraction using these numbers produces the other two numbers.

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First, we want to note two things:

We can describe this with an inequality:  x ≥ -10
Be sure you use ≥ and not >, since -10 is included.

We can describe this with interval notation: [ -10, infty )
Be sure you use [ and not ( on -10, since -10 is included.

You can also use set-builder notation: { x | x ≥ -10 }

In question 27, the price elasticity of supply for shampoo is given as 20, and the price of shampoo increases by 0.7%. The expected change in the quantity of shampoo supplied can be determined using the concept of price elasticity of supply. However, the specific percentage change in quantity supplied is not provided, so a precise answer cannot be given based on the given information.

In question 20, an inferior good in which the income effect dominates the substitution effect is referred to as a Giffen good. It is not classified as a normal good, luxury good, mass-produced good, or favored good.

In question 30, the cross elasticity of demand measures the responsiveness of the quantity demanded of a particular good to changes in the prices of its substitutes and complements. The correct answer is that the cross elasticity of demand measures the responsiveness to changes in both substitutes and complements.

In question 27, without the specific percentage change in quantity supplied, we cannot determine the exact outcome based on the given information. The price elasticity of supply of 20 suggests that the quantity supplied is highly responsive to changes in price, but the specific percentage change in quantity supplied cannot be calculated without additional data.

In question 28, the relationship between pasta being a Giffen good and other characteristics is not specified. While pasta being a Giffen good indicates that the quantity demanded increases as the price increases, it does not imply whether pasta is a normal good, luxury good, or how price changes affect quantity demanded.

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Answer:

well, the value of x is unknown

a monster can eat 48 cookies in 12 minutes me thinks

Answer: A monster can eat 48 cookies in 12 minutes

Step-by-step explanation:

The expression which is equivalent to; six to the negative power of two as given in the task content is; 1 / 36.

It follows from the task content that the expression which is equivalent to six to the negative power of two is to be determined.

Since the given word phrase can be expressed as; 6^-²; it follows from the laws of indices that we have;

= (1 / 6)²

= 1² / 6²

= 1/36.

Ultimately, the equivalent expression is; 1 / 36.

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Answer: 10

Step-by-step explanation:

6-5 = 1

-2 x 1 = -2

-2 x -5 = 10

The variance of the number of free-throws that Sam will score before her first miss is 3/4.

To find the expected value and variance, we need to use the concept of geometric distribution. The geometric distribution models the number of trials needed to achieve the first success in a series of independent Bernoulli trials, where each trial has the same probability of success.

In this case, Sam has a 2/3 chance of scoring each time she shoots from the free-throw line. So the probability of success (scoring) in each trial is p = 2/3, and the probability of failure (missing) is q = 1 - p = 1/3.

The expected value of a geometric distribution is given by E(X) = 1/p, and the variance is given by Var(X) = q / p^2.

Calculating the expected value:

E(X) = 1/p = 1 / (2/3) = 3/2 = 1.5

So the expected value of the number of free-throws that Sam will score before her first miss is 1.5.

Calculating the variance:

Var(X) = q / p² = (1/3) / (2/3)² = (1/3) / (4/9) = 3/4

So the variance of the number of free-throws that Sam will score before her first miss is 3/4.

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The perimeter of the shape is approximately 20.57 inches.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

The shape consists of two shapes; a square and 2 semi-circles

Perimeter of square = 4L

where L = 2 inches

Perimeter = 4(2)

Perimeter = 8 inches

Perimeter of Semi-circle = \(\pi r}\)

where \(\pi = 3.142\)

r = 2 inches

Perimeter of Semi-circle = 3.142 x 2

Perimeter of Semi-circle = 6.284 inches

Perimeter of shape = Perimeter of square + 2 x Perimeter of Semi-circle

Perimeter of shape = 8 inches + 2 x  6.284 inches

Perimeter of shape = 8 inches + 12.568 inches

Perimeter of shape = 20.568 inches

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a) The accumulated sales for the first 9 days is approximately $9,359.49.

b) The sales from the 2nd day through the 5th day is approximately $6,022.25.

To find the accumulated sales for the first 9 days, we need to integrate the given rate of change of sales with respect to time:

S'(t) = \(23e^t\)

Integrating both sides with respect to t, we get:

S(t) = ∫S'(t) dt = ∫\(23e^t\)dt = \(23e^t\) + C

where C is the constant of integration.

To find the value of C, we use the initial condition that the sales at day 0 (i.e., the starting point) is $0:

S(0) = 0 = 23e^0 + C

Therefore, C = -23.

Substituting this value of C, we get:

S(t) = \(23e^t\) - 23

a) To find the accumulated sales for the first 9 days, we need to evaluate S(9) - S(0):

\(S(9) - S(0) = (23e^9 - 23) - (23e^0 - 23) = 23(e^9 - 1) ≈ $9,359.49\)

Therefore, the accumulated sales for the first 9 days is approximately $9,359.49.

b) To find the sales from the 2nd day through the 5th day, we need to evaluate S(5) - S(2):

\(S(5) - S(2) = (23e^5 - 23) - (23e^2 - 23) = 23(e^5 - e^2) ≈ $6,022.25\)

Therefore, the sales from the 2nd day through the 5th day is approximately $6,022.25.

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