Consider the following. (If an answer does not exist, enter DNE.) f(x) = x3 – 3x2 - 6x + 5 Find the interval(s) on which f is concave up. (Enter your answer using interval notation.) Find the interval(s) on which f is concave down. (Enter your answer using interval notation.) Find the inflection point of f. (x, y)

Answer:

Domain is  [-1, 3]

Range is [1, 2]

================================

Explanation:

The domain is the set of allowed input values. It's the set of all possible x coordinates of the points shown.

The left-most point is when x = -1, while the right-most point is at x = 3.

We can say \(-1 \le \text{x} \le 3\) meaning x is between -1 and 3, including both endpoints.

That compound inequality translates to the interval notation [-1, 3]

Square brackets are used to include the endpoints.

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

The range handles the set of possible y outputs.

The lowest we can go on the graph is y = 1, and the highest is y = 2

Therefore we arrive at \(1 \le \text{y} \le 2\) which translates to [1, 2]

The gcd of the given polynomials in Q[x] is x + a + b.

A more detailed explanation of the answer.

To find the gcd (greatest common divisor) of the two polynomials in Q[x], we can use the Euclidean algorithm. Here are the steps:

1. Start with the two polynomials: f(x) = x + a + b and g(x) = x³ - 3abx + a³ + b³.

2. Divide g(x) by f(x), find the quotient q(x) and the remainder r(x). If r(x) is zero, then f(x) is the gcd.

3. Replace g(x) with f(x) and f(x) with r(x), and repeat step 2 until the remainder is zero.

Let's perform these steps:

Step 1:
f(x) = x + a + b
g(x) = x³ - 3abx + a³ + b³

Step 2:
When we divide g(x) by f(x), we get:

q(x) = x² - (a+b)x + ab
r(x) = -a³ - b³ - 2ab(a+b)

Step 3:
Now, replace g(x) with f(x) and f(x) with r(x):

f(x) = -a³ - b³ - 2ab(a+b)
g(x) = x + a + b

Now, we'll perform long division again. But we can observe that the degree of f(x) is now greater than the degree of g(x). This means that the remainder, r(x), will be g(x) itself, as we can't perform any further division. So, the gcd is g(x) = x + a + b.

Therefore, the gcd of the given polynomials in Q[x] is x + a + b.

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Answer:

3 5/2 i believe

Step-by-step explanation:

Answer: 10

Step-by-step explanation:

parenthesis first 9 - 15 + 8 x 2

multiply 8 x 2

you now have 9 - 15 + 16

subtract first because addition and subrtaction go in the order they're in the equation: 9 - 15 = -6

then add -6 + 16 = 10

Given the expression that models the tip amount for a total bill of $102:

You know that "x" represents the dollar amount of the tax.

You also know that Mr. Jaxon tips $23.50.

Therefore, knowing all that information, you can set up the following equation to represent that situation:

Now you have to solve for "x" in order to find its value:

Hence, the answer is:

Answer:

It means you put full effort into what you're doing, because in math, 100% is perfect, but 110% is more than perfect, so they are saying she put extreme effort into the problem.

Answer:

c is the answers for the question

Step-by-step explanation:

please give me brainlest

Answer:

x =(-2-√-116)/-10=(1+i√ 29 )/5= 0.2000-1.0770i

x =(-2+√-116)/-10=(1-i√ 29 )/5= 0.2000+1.0770i

Step-by-step explanation:

The volume flow rate of the air supply required is 533 CFM and the relative humidity of the air supply should be 60% and the dew point temperature of the air supply should be 55.2°F.

The quantity of air required is calculated using the formula:

CFM = Q/(1.08 x ΔT x 1.1) where,

Q = Sensible Heat Load in Btu/hr

ΔT = Temperature Difference between Room Air and Outdoor Air

CFM = Cubic Feet per Minute of Air Supply 1.08 = Specific Heat of Air at Constant Pressure 1.1 = Density of Standard Air at 70°F and 29.92" Hg Absolute.

According to the problem statement,

Q = 42,000 Btu/hr

ΔT = (86 - 15)°F = 71°F

CFM = 42,000/(1.08 x 71 x 1.1)

= 532.9

~ 533 CFM

Thus, we can say that the volume flow rate of the air supply required is 533 CFM and the relative humidity of the air supply should be 60%, and the dew point temperature of the air supply should be 55.2°F.

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Answer:

Find the mean x of the data 16, 31, 38, 24, 36

16 + 31 + 38 + 24 + 36

= 145

145 ÷ 5

Step-by-step explanation:

You're welcome.

Answer:

2963*100,000 that's the answer for that question

Answer:

sinT = \(\frac{15}{17}\)

Step-by-step explanation:

We require to calculate RT before obtaining sinT

Using Pythagoras' identity in the right triangle

RT² = 30² + 16² = 900 + 256 = 1156 ( take the square root of both sides )

RT  = \(\sqrt{1156}\) = 34 , then

sinT = \(\frac{opposite}{hypotenuse}\) = \(\frac{RS}{RT}\) = \(\frac{30}{34}\) = \(\frac{15}{17}\)

We can add and subtract 4.5 in the left side to complete squares, then we can rewrite the quadratic equation as:

(x + 13)^2 = 4.5

Here we want to rewrite the quadratic equation:

x^2 + 26x + 164.5 = 0

To rewrite it in the desired way, we need to complete squares, remember that the perfect square trinomial is:

(a + b) = a^2 + 2ab + b^2

We can rewrite the given quadratic as:

x^2 + 26x + 164.5 = 0

x^2 + 2*13*x + 164.5 = 0

The missing term to complete squares is 13^2 = 169, so we can add and subtract 4.5 on the left side of that eqation to get:

x^2 + 2*13*x + 164.5 + 4.5 - 4.5 = 0

x^2 + 2*13*x + 169 - 4.5 = 0

(x + 13)^2 = 4.5

That is the equation we wanted to get.

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Answer:

Step-by-step explanation:

12x < 22 + x

11x < 22

x < 2

Option 2 is the answer

Answer:

\( \sf \: b) \: x < 2\)

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The inequation is,

→ 12x < 22 + x

Then the value of x will be,

→ 12x < 22 + x

→ 12x - x < 22

→ 11x < 22

→ x < 22 ÷ 11

→ [ x < 2 ]

Hence, the answer is x < 2.

A(n) b. payoff table is a matrix whose rows correspond to decisions and whose columns correspond to events. therefore, option b. payoff table is correct.

A payoff table is a decision-making tool used to analyze different alternatives or decisions in a given situation. It is a matrix that lists the possible outcomes or payoffs associated with different combinations of decisions and events. The rows correspond to the different decisions that can be made, and the columns correspond to the possible events or scenarios that could occur.

Each cell in the payoff table contains the payoff or outcome associated with a specific combination of decision and event. The payoffs can be expressed in different forms, such as monetary values, utility values, or scores. Payoff tables are commonly used in decision analysis, game theory, and strategic planning to evaluate different options and select the most desirable course of action.

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Answer:

59 cm

Step-by-step explanation:

Given data

we are given the parameter of the circle as

radius= 9.4cm

π = 3.14

We know that

circumference= 2πr

subsitute

C= 2*3.14*9.4

C= 59cm

Hence the circumference is 59 cm

The answers are 27, 70, 32, 64, 33, 4, 12, 65, 21, and 85. The problem can be solved by Venn Diagram method of set theory.

What is Venn diagram?

A Venn diagram, which is a popular diagram type for illustrating the logical relationship between sets.

(1) The number which is common in both Hand ball and swimming is 19 and 8. Hence, the number of students like both Handball and Swimming is 19+8 =27

(2) The number which are common in both Handball and Swimming is 19 and 8. Add these two numbers and subtract from total number of students which is 12+21+19+8+4+10+20+3=98. Now, subtract.

97-(19+8)=70  Hence, total students which do not like both Handball and Swimming is 70.

(3)The number which is neither in Handball nor in Boxing is 20 and 12 students do not linke anything. Hence, total students which do not like both Handball and Boxing is 20+12=32.

(4) The number which are both in Swimming and Boxing are 19, 8, 10, 20, 3 and, 4. Hence, total students are 19+8+10+20+3+4=64.

(5) The number which is neither in Swimming nor in Boxing is 21 and 12 students do not linke anything. Hence, total students which do not like both Swimming and Boxing is 21+12=33.

(6) The numbers which are both in handball and boxing 8 and 4. But the number which is not in swimming from these two numbers is 4. Hence, the answer is 4.

(7) The numbers which are common in both Handball and Boxing are 4 and 8. Hence, total number is 4+8=12.

(8) The numbers which are both in handball and boxing are 21, 19, 8, 4, 3, and 10. Hence, total number is 21+19+8+4+3+10 = 65.

(9) The number of students which are only in Handball and not in any other game is 21. Hence, 21 students likes only Handball.

(10) The number which are common in both Handball and Boxing is 4 and 8. Add these two numbers and subtract from total number of students which is 12+21+19+8+4+10+20+3=98. Now, subtract. 97-(8+4)=85  Hence, total students which do not like both Handball and Boxing is 85.

Hence, the answers are 27, 70, 32, 64, 33, 4, 12, 65, 21, and 85. The problem can be solved by Venn Diagram method of set theory.

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Answer:

B. 5/2

Step-by-step explanation:

150 grams is equal to 5.29 ounces. both are unit of measurement of weight.

The process of unit conversion involves using a conversion factor, which is a ratio that relates the units being converted.

Grams and ounces are units of weight measurement used in different systems of units. To convert grams to ounces, a conversion factor is used to find the equivalent weight in ounces.

The conversion factor is 0.035274, which means that 1 gram is equal to 0.035274 ounces. To convert 150 grams to ounces, the weight in grams is multiplied by the conversion factor: 150 grams * 0.035274 ounces/gram = 5.29 ounces.

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The difference in the account balances at the end of the loan terms is given as follows:

$1,686.87.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

The parameters for the offer 2 are given as follows:

P = 75000, r = 0.035, n = 12, t = 62/12.

Hence the balance of the offer 2 is given as follows:

B = 75000 x (1 + 0.035/12)^(12 x 62/12)

B = $89,842.51.

The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:

91529.38 - 89842.51 = $1,686.87.

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Answer:          

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.

.

2/5

Answer:

\( \frac{2}{5} \)

Step-by-step explanation:

\( - 2\frac{4}{5} \div ( - 7)\)

\( = \frac{2 \times 5 + 4}{5} \)

\( = \frac{10 + 4}{5} \)

\( = \frac{14}{5} \)

\( = - \frac{14}{5} \times 7\)

\( = \frac{14}{5} \div 7\)

\( = \frac{2}{5} \)

Answer:

The actual sculpture is 20 feet.

-

Step-by-step explanation:

\( \frac{2 \: inches}{5 \: feet} = \frac{8 \: inches}{x} \\ \\ \frac{40}{2} = \frac{2x}{2} \\ \\ x = 20\)

The number of emergency kits that Neil packed in total for the 150 bottles is gotten as; k = 50 kits.

We are told that Neil puts 3 water bottles into each emergency kit packed.

Now, let the number of emergency kits be k.

Thus;

3k = 150

Division property of equality, we have;

3k/3 = 150/3

k = 50

Thus, the number of emergency kits that Neil packed is gotten as k = 50 kits.

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Answer:

(5,725)1.045^5

Step-by-step explanation:

(5,725)1.045^5

5,725 is the original amt of $

1.045 is the % of interest

5 is the # of years

Solve this and round the nearest

cent.

Given data:

The width is b=3.

The given height is h= 2.

The length is equal to the unity l=1.

The volume is,

Thus, the volume is 6 cubic-units.

The function f(n) that generates this sequence is 2 + 1/(n+1). This function takes an input of n and outputs the corresponding term in the sequence.

What is an arithmetic sequence?

A progression or sequence of numbers known as an arithmetic sequence maintains a consistent difference between each succeeding term and its predecessor. The common difference in that mathematical progression is the constant difference.

Here, we have

Given: the sequence 2 and one-half comma 2 and one-third comma 2 and one-fourth comma and continues.

Each term in the sequence is 2 plus a fraction where the denominator is one more than the term number. For example:

In the first term, n=1, and the fraction is 1/2

In the second term, n=2, and the fraction is 1/3

In general, the n-th term in the sequence will have the fraction 1/(n+1).

Hence, the function f(n) that generates this sequence is 2 + 1/(n+1). This function takes an input of n and outputs the corresponding term in the sequence.

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