For the function below, find the local extrema by using the First Derivative Test.
t(x) = 2x ^ 3 + 30x ^ 2 + 144x - 1
Select the correct answer below:
a.There is a local minimum at x = - 4
b.There is a local maximum at x = - 6 and a local maximum at x = - 4
c.There is a local maximum at x = - 4
d.There is a local maximum at x = - 6 and a local minimum at x = - 4
e.There is a local maximum at x = - 6

Answer:

\(72 \: {ft}^{3} \)

Step-by-step explanation:

First, we need to find the area of the base:

a(base) = 6 × 3 = 18 ft^2

Now, since we know that the altitude (h) of the prism is 4 ft, we can find the volume:

\(v = a(base) \times h = 6 \times 3 \times 4 = 72\)

Answer: x = 9, y = 3

Step-by-step explanation:

9 - 2(3) = 3

9 - 6 = 3

2(9) - 3(3) = 9

18 - 9 = 9

Answer:

x=9, y= 3

Step-by-step explanation:

x-2y=3

2x-3y=9

Multiply the first equation by -2

-2x +4y = -6

Add this to the second equation

-2x +4y = -6

2x-3y=9

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

   y = 3

Now find x

x -2y =3

x -2(3) = 3

x-6 = 3

Add 6 to each side

x = 9

Answer:

\(2 \times 9 = 3 \times y \\ y = 18 \div3 = 6 \\ 6 \times 3 = x \times 5 \\ x = 18 \div 5 = 3.6\)

Answer:

The slope is 2 and the y intercept is 6

Step-by-step explanation:

y = 2x+6

This is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope is 2 and the y intercept is 6

Answer:

2

Step-by-step explanation:

slope intercept form is

y = mx + b

m is the slope and b is the y-intercept

y = 2x + 6

m = 2

Slope is 2

Answer:

5

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

The constants that have to multiply to eliminate one variable from the system are 12 and 5.

The equations are

5x+13y = 232

12x + 7y = 218

Elimination Method

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables

Both x term and y terms, choose x terms  and apply the elimination method

The coefficient of x in the first equation is 5 and 12 in the second equation

Coefficient is a number that is being multiplied by the variable. 2x+6x+14. The 2x, 6x, and 14 are terms because they are being added together. 2 and x; 6 and x are factors because they are being multiplied together. 2 from 2x and 6 from 6x are the coefficients because they are being multiplied by the variable.

To make it the same

Prime factorization

Prime factorization is a process of writing all numbers as a product of primes.

5 = 5×1

12 = 2×2×3

LCM (5, 12 ) = 2×2×3×5 = 60

Multiply the first equation by 12 and the second equation by 5

60x + 156y = 2784

60x + 35y = 1090

Subtract equation 2 from equation 1

121y = 1694

Eliminated x term

The constants that we have to multiply to eliminate one variable from the system are 12 and 5

The complete question is:

Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together? 5x + 13y = 232

12x + 7y = 218

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Answer:

A sample is a subset of the population.

Answer:

The answer is 30

I can't explain because the explanation is long

A Japanese music genre that offers great flexibility and can be performed by either a single shamisen or an entire orchestra of twenty musicians is "Gagaku."

Gagaku, a traditional Japanese music genre, encompasses a broad range of compositions and styles that can be adapted to various ensemble size, making it incredibly flexible. Gagaku music originated in ancient Japan and has evolved over centuries, incorporating elements from China and Korea.

It typically combines wind and string instruments, such as the sho (mouth organ), hichiriki (double reed), and biwa (lute), with percussion instruments like the taiko (drum). Gagaku pieces can be performed by a single shamisen player, showcasing the instrument's solo capabilities, or expanded to include a full orchestra with multiple musicians playing different instruments. This adaptability allows Gagaku to be enjoyed in both intimate settings and grand performances.

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The surface area of the first prism is approximately 72.54 square meters. The surface area of the second prism is approximately 299.2 square cm. The surface area of the third prism cannot be calculated due to missing information. The amount of cardboard used to make the box is 856 square inches. Approximately 7.5 cans of paint are needed to paint the lateral surfaces of the prism.

To find the surface area of each prism, we need to calculate the sum of the areas of all its faces. Let's go through each prism one by one:

Now, let's move on to the box:

The dimensions of the box are given as 10 in. wide, 12 in. high, and 14 in. deep. To find the surface area, we need to calculate the sum of the areas of all its faces. Using the formula for a rectangular prism, we get: 2(10)(12) + 2(10)(14) + 2(12)(14) = 240 + 280 + 336 = 856 square inches. Therefore, 856 square inches of cardboard is used to make the box.

Finally, let's calculate the amount of paint needed for the prism:

The prism has regular pentagonal bases. The height of the prism is given as 15 ft, and the length of each side of the pentagon is 3 ft. To find the lateral surface area, we need to calculate the perimeter of the base and multiply it by the height. The perimeter of a regular pentagon is 5 times the length of one side. Plugging in the value, we get: 5(3) = 15 ft. The lateral surface area is then 15 ft multiplied by the height, which is 15 ft. Multiplying, we get: 15(15) = 225 square ft. Since one can of paint can cover 30 square ft, we divide the lateral surface area by the coverage of one can: 225/30 = 7.5 cans. Therefore, approximately 7.5 cans of paint are needed to paint the lateral surfaces of the prism.

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Answer:

1) The image of the line has the same slope as the pre-image but a different y-intercept.

hope this helps ;)

okay only the sy is replaced with xy

hope it helps:)

Answer:

B

Step-by-step explanation:

The probability that all 4 selected coins are genuine is 2/7

There are two cases where the combined weight of the first pair is equal to the combined weight of the second pair

Case 1: Both pairs consist of two genuine coins.

Case 2: One pair consists of two counterfeit coins and the other pair consists of two genuine coins.

Let's calculate the probability of each case separately

Case 1: The probability of selecting two genuine coins from 8 is (8/10) × (7/9) = 28/45 for the first pair, and (6/8) × (5/7) = 15/28 for the second pair (after one genuine coin has been selected from the first pair). Therefore, the probability of selecting two genuine coins for both pairs is (28/45) × (15/28) = 7/15.

Case 2: The probability of selecting two counterfeit coins from 2 and two genuine coins from 8 is (2/10) × (1/9) × (8/8) × (7/7) = 1/45 for the first pair, and (1/8) × (7/7) × (6/6) × (5/5) = 1/8 for the second pair (after one counterfeit coin has been selected from the first pair). There are two ways to select which pair consists of the counterfeit coins, so the total probability for this case is 2 × (1/45) × (1/8) = 1/180.

Therefore, the total probability of selecting two pairs with the same combined weight is (7/15) + (1/180) = 49/90. Since all four selected coins are genuine only in Case 1, the probability that all 4 selected coins are genuine is (7/15) / (49/90) = 14/49 = 2/7.

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The given question is incomplete, the complete question is:

Two counterfeit coins of equal weight are mixed with 8 identical genuine coins. the weight of each of the counterfeit coins is different from the weight of each of the genuine coins. a pair of coins is selected at random without replacement from the 10 coins. a second pair is selected at random without replacement from the remaining 8 coins. the combined weight of the first pair is equal to the combined weight of the second pair. what is the probability that all 4 selected coins are genuine?

In terms of relative growth rate Exponential growth is characterized by a constant relative growth rate.

Exponential growth is the process of increasing quantity over time. Occurs when the instantaneous rate of change of a quantity over time is proportional to the quantity itself. The exponential growth model has the form

y (t) = C eᵏᵗ, where k is the rate constant.

Relative Growth Rate:Relative growth rate (RGR) is the rate of growth relative to size. That is, the rate of growth per unit time relative to the size at that point in time and y'(t)/y(t) is the relative growth rate of a function y at time t.

1/y dy/dt = 1/y d(C eᵏᵗ)/dt

= 1/y(kC eᵏᵗ)

= 1/y ( ky) ( since, y (t) = C eᵏᵗ)

= k

Therefore a constant relative growth rate.

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Complete question:

In terms of relative growth rate, what is the defining property of exponential growth? Choose the correct answer below.

A. The relative growth rate at time t is the slope of the exponential function at time t.

B. dy dt If y represents a population, then the relative growth rate can be represented by dy/dt

C. The relative growth rate is proportional to the size of the population

D. The relative growth rate is constant.

The volume of the rectangular prism is 1435.

To find the volume of the rectangular prism, we need to consider the given information that the sum of its volume, total surface area, and the sum of the lengths of all its edges is equal to 2015. By analyzing the properties of a rectangular prism, we can determine the possible combinations of side lengths that satisfy the given condition.

Let's denote the side lengths of the rectangular prism as a, b, and c. The volume of a rectangular prism is given by V = a * b * c, the total surface area is given by A = 2(ab + ac + bc), and the sum of the lengths of all the edges is given by E = 4(a + b + c).

According to the problem statement, we have the equation V + A + E = 2015. Substituting the formulas for V, A, and E, we get:

a * b * c + 2(ab + ac + bc) + 4(a + b + c) = 2015.

By rearranging the equation, we have:

abc + 2ab + 2ac + 2bc + 4a + 4b + 4c = 2015.

Factoring out common terms, we get:

(a + 2)(b + 2)(c + 2) = 2015 + 8 = 2023.

Now, we need to analyze the factors of 2023 to find the possible combinations of side lengths. The factors of 2023 are 1, 7, 17, and 119. We can write (a + 2), (b + 2), and (c + 2) as these factors.

By examining the factors, we find that the combination (a + 2) = 1, (b + 2) = 7, and (c + 2) = 289 satisfies the condition. Solving these equations, we get a = -1, b = 5, and c = 287.

Since the lengths of a rectangular prism cannot be negative, we discard the solution with a = -1. Thus, the valid solution is a = 1, b = 5, and c = 287.

Finally, we can calculate the volume using the formula V = a * b * c:

V = 1 * 5 * 287 = 1435.

Therefore, the volume of the rectangular prism is 1435.

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Answer:

\(( \sqrt[3 ]{x^{4} } )^{5} = (x^{ \frac{4}{3} } )^{5} = x^{ \frac{4 \times 5}{3} } = {x}^{ \frac{20}{3} } \)

Answer:

option C

Step-by-step explanation:

Here, we want the first best step

looking at the expression, we can see that if we divided both sides by -2, we will have to answer a regular

Thus, by dividing both sides by -2, then we have the answer

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MathLab

MathLab simply refers to an virtual learning platform for mathematics turos to help students who have difficulty in understanding mathematics.

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Answer: 300,000

Step-by-step explanation:

There are two ways to get this answer.

WAY 1

400x800= 320,000 and to get 1 significant figure you round down to 300,000

WAY 2

423x764=323,172 and to get 1 significant figure you round down to

300,000

Answer: N > -4

Step-by-step explanation:

Cuz It's Right

The solution for inequality  is n < -4.

The given inequality is −2(n − 3.5) > 15

An inequality will have the sign < , > , ≥ or ≤ instead of an equality in an equation. That is, an inequality compares two quantities on either sides of the inequality sign.

We are asked to solve the inequality  −2(n − 3.5) > 15. That is, to find the possible values for n.

−2(n − 3.5) > 15

Dividing throughout by 2,

-(n - 3.5) > 15/2

⇒ -n +3.5 > 7.5

Subtracting 3.5 from both sides,

⇒ -n > 7.5 - 3.5

⇒ -n > 4

Multiply -1 on both sides of the inequality and the inequality will be reversed,

⇒ n < -4 is the solution for n.

The solution is the values of n less than -4.

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Answer:

Step-by-step explanation:

The two angles are vertically opposite. Vertically opposite angles are equal.

2 + 3x = 62              Subtract 2 from both sides

2-2+3x = 62-2

3x = 60                    Divide by 3

3x/3 = 60/3

x = 20

The unknown part of the angle = 20

Answer:

vertical angles

X=20

Step-by-step explanation:

I know that the two angles have to be congruent because they are vertical angles. Congruent means that they equal each other so then the equation would be, 2+3x= 62

X=20

Given the topological spaces X = {D, O, R, K} with the topology Tx and Y = {M, A, T, H} with the topology Jy, we are asked to determine whether the set E = {0, K} is open in X and open in Y.

To determine whether the set E = {0, K} is open in the topological spaces X and Y, we need to check if E belongs to the respective topologies, Tx and Ty.

In X, the topology Tx is given by: Tx = {Ø, {0}, {D, O}, {O, R}, {D, O, R}, X}. We can see that E = {0, K} is not explicitly listed in Tx. Therefore, E is not open in X since it does not belong to the topology.

In Y, the topology Ty is given by: Jy = {0, {M}, {M, A}, {M, A, T}, Y}. Again, E = {0, K} is not explicitly listed in Ty. Hence, E is not open in Y as it does not belong to the topology.

In both cases, the set E = {0, K} is not open in the respective topological spaces X and Y because it is not a member of the defined topologies.

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Answer:

The area of the circle is 18.84.

Step-by-step explanation:

You multiply pi (3.14) by the radius of the circle, which is 6, to get the area of any circle.

Step 1: Let's evaluate the following expression

Step 2: Solve the exponent expression:

The correct answer is 16.

For the second case, we apply the same principle:

The correct statement about the center of both box plots is: the median for Town A, 30° is greater median for Town B, 25°

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. The two lines are known as whiskers. The end of the first line represents the minimum number and the end of the second line represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile.

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The area of the triangle is expressed as 2.718cm²

The formula for calculating the area of a triangle is expressed as:

A = 0.5absinФ

Given the following

Substitute the given parameters to have:

Area = 0.5(2.5)(2.3)sin71

Area = 2.718cm²

Hence the area of the triangle is expressed as 2.718cm²

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The coordinates of point O of the given Reflection is; 5, 5

What is coordinates of point ?

A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).

According to my investigation, the coordinate points are shown on the picture below.

The junction of these two lines should tell us the location of point O because N is the reflection of B and O is the reflection of C.

If we were to draw a line to the right of N and a vertical line below C, this intersection would reveal the location of point O.

By doing so, point O is located at (5,5).

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