find the average rate of change of the function f ( x ) = 6 3 x 6 , on the interval x ∈ [-3,5]. average rate of change = give an exact answer.

Answer:

The image of the point is (-27, 6)

Step-by-step explanation:

Let us talk about the dilation

∵ Point (-9, 2) is dilated by a scale factor 3

∴ k = 3

∵ The center of dilation is the origin

→ Multiply the coordinates of the point by 3 to find the image

∴ The image = (3 × -9, 3 × 2)

∴ The image = (-27, 6)

The image of the point is (-27, 6)

The volume of the given triangular prism is 315 cm³.

The volume of a triangular prism, we need to multiply the base area of the triangular base by the height of the prism.

The triangular base has a base length of 5 cm and a height of 7 cm, and the height of the prism is 9 cm.

Calculate the area of the triangular base.

The area of a triangle can be calculated using the formula:

Area = (base length × height) / 2

Plugging in the values, we have:

Area = (5 cm × 7 cm) / 2

Area = 35 cm²

Calculate the volume of the prism.

The volume of a prism can be calculated by multiplying the base area by the height of the prism.

Volume = Base area × Height

Volume = 35 cm² × 9 cm

Volume = 315 cm³

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Answer:

x=53°

(x+2)=55°

Step-by-step explanation:

Add all the angles up to equal 180, because all triangles equal 180.

(x+2)+x+72=180

Simplify and solve for x.

2x+74=180

-74=-74

2x=106

2 = 2

x=53.

Plug x in to the inequalities. Hope this helps.

The solution to the equation using quadratic formula is n= -1±√11

A formula that provides the solution to a quadratic issue is the quadratic formula in elementary algebra. Other approaches to solving quadratic equations outside the quadratic formula comprise factoring, solving the square, graphing, and others.

Given expression= 2 + 13n = 9n + 20

Rearranging the equation we get

= 2n²+13n-9n-20=0

= 2n²+4n-20 =0

Taking out the common factor 2, we get

= 2 (n²+2n-10) = 0

Dividing both side with same factor 2, we get

= n²+2n-10 = 0

Use the quadratic formula:

n= \(\frac{-b +/- \sqrt{b^{2} -4ac} }{2a}\)

In the given expression n²+2n-10 = 0, a=1, b=2, c=-10

Therefore, n= \(\frac{-2 +/- \sqrt{2^{2} -4*1(-10)} }{2*1}\)

After evaluating the exponents, multiplying the numbers, adding the numbers, evaluating the square root and final multiplication we get:

n= \(\frac{-2 +/- 2\sqrt{11}}{2}\)

Separating the equations and rearranging them we get:

n= -1+√11

n= -1-√11

The solution to the equation using quadratic formula is n= -1±√11

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Answer:

Leonardo emiliano Castañeda

Answer:

Your answer is correct.

Answer:duhhh equal 4

Step-by-step explanation:duhhh equal 4

Answer:

$41.05

Step-by-step explanation:

\(\frac{40}{100} =\frac{16.42}{x}\)

\(40x=1642\)

\(x=41.05\)

So, the original price is $41.05.

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

The solution to the expression 6x - 2x + 8y - 6y is 4x + 2y

From the question, we have the following parameters that can be used in our computation:

6x - 2x + 8y - 6y

Collect the like terms in the expression

So, we have the following representation

6x - 2x + 8y - 6y = 6x - 2x + 8y - 6y

Evaluate the like terms in the expression

So, we have the following representation

6x - 2x + 8y - 6y = 4x + 2y

Hence, the simplified expression is 4x + 2y

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b) 52/25

is the right answer

Answer:

46.6667%

Step-by-step explanation:

Divide 7 by 15 because that's how you calculate the chance of receiving marbles

7/15 is equal to 0.466667 approx..

To convert to Percent form, multiply by 100

0.466667 *100=46.6667

According to the given data we have the following:

Shift the function f(x)=x^2 to the right 2, vertical stretch by 4, and a shift

up 1 unit.*

If we Shift the function f(x)=x^2 to the right 2, hence the right option would be:

f(x)=4(x+2)^2+1

Hence, the right option would be option 1.

Answer:its 11

Step-by-step explanation:

$:!

The surface area of this locker is 432 square centimeters .

The right rectangular prism shown in the figure has dimensions 8 cm (length) x 6 cm (width) x 12 cm (height).

1. The top and bottom faces are both rectangles with dimensions 8 cm (length) x 6 cm (width). The area of each face is:

A = length x width = 8 x 6 = 48 cm²

Since there are two of these faces, the total area is:

2 x 48 = 96 cm²

2. The front and back faces are also rectangles with dimensions 8 cm (length) x 12 cm (height). The area of each face is:

A = length x height = 8 x 12 = 96 cm²

the total area is:

2 x 96 = 192 cm²

3. The left and right faces are rectangles with dimensions 6 cm (width) x 12 cm (height). The area of each face is:

A = width x height = 6 x 12 = 72 cm²

the total area is:

2 x 72 = 144 cm²

4. Therefore, the total surface area of the locker is the sum of all the faces:

Total surface area = 96 + 192 + 144 = 432 cm²

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Answer:

A

Step-by-step explanation:

I'm certain the answer is this, and I understand that you are in a hurry. I can update it anytime you'd like to see the explanation

Answer:

a. 5

Step-by-step explanation:

Taking two points, (0,0) and (1,5), find the slope using \(\frac{y_2-y_1}{x_2-x_1}\). Plugging the two points in, we have \(\frac{5-0}{1-0}=5\) as the slope.

Answer:

Slope = 5

Step-by-step explanation:

We will use 2 points on the line.

(1 , 5) and (2 , 10)

formula for slope = y2 - y1/x2 - x1

10 - 5/2 - 1

= 5/1

= 5

The slope is 5.

Answer:

Below

Step-by-step explanation:

12 C 2  = 12! / ( 10! 2!) = 66 ways

Answer: x= 60

Step-by-step explanation:

In the given figure

These are vertically opposite angle so, 2x=120

x=60

the price per ticket that will give maximum revenue is $6.5, and the maximum revenue in dollars per ticket is $2.925.

As given,If club members charge $3 admission to a classic car show, 1000 people will attend, and for each $1 increase in price, 100 fewer people will attend.

We need to determine the price that will give the maximum revenue for the show and the maximum revenue in dollars per ticket.

Let the number of $1 increases in price be x. Then the number of people attending will be (1000 - 100x), and the price per ticket will be $(3 + x).The total revenue will be:

Revenue = Price × Quantity= $(3 + x) × (1000 - 100x)= $3000 - $100(x^2 + 7x)

The revenue function is quadratic, with the coefficient of the x^2 term being negative. Hence the graph of the function is a parabola which opens downwards, with a maximum at the vertex of the parabola.To find the value of x that will give maximum revenue, we first find the x-coordinate of the vertex.

For a quadratic function of the form f(x) = ax^2 + bx + c, the x-coordinate of the vertex is given by x = -b / (2a).In this case, a = -100, and b = -100(7) = -700. Therefore, the x-coordinate of the vertex is:x = -b / (2a)= 7/2= 3.5

Therefore, the value of x that will give maximum revenue is 3.5. Substituting this value of x in the revenue function, we get:Revenue = $3000 - $100(x^2 + 7x)= $3000 - $100(3.5^2 + 7(3.5))= $2925

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Answer:

24.6

Step-by-step explanation:

take 72 degree as reference angle

using tan rule

tan 72 = opposite / adjacent

3.07 = x/8

3.07 * 8 = x

24.56 = x

24.6 = x

\(\frac{2}{x}\)

\(\frac{x}{2}\)

\(\frac{4x^4}{y^3}\)

a. 2x^-3 • 4x^2

To solve this using only positive exponents, follow these steps:

i. Rewrite the expression in a clearer form

2x⁻³ . 4x²

ii. The position of the term with negative exponent is changed from denominator to numerator or numerator to denominator depending on its initial position. If it is at the numerator, it is moved to the denominator. If otherwise it is at the denominator, it is moved to the numerator. When this is done, the negative exponent is changed to positive.

In our case, the first term has a negative exponent and it is at the numerator. We therefore move it to the denominator and change the negative exponent to  positive as follows;

\(\frac{1}{2x^3} . 4x^2\)

iii. We then solve the result as follows;

\(\frac{1}{2x^3} . 4x^2\) = \(\frac{2}{x}\)

Therefore, 2x⁻³ . 4x² = \(\frac{2}{x}\)

b. 2x^4 • 4x^-3

i. Rewrite as follows;

2x⁴ . 4x⁻³

ii. The second term has a negative exponent, therefore swap its position and change the negative exponent to a positive one.

\(2x^4 . \frac{1}{4x^3}\)

iii. Now solve by cancelling out common terms in the numerator and denominator. So we have;

\(\frac{x}{2}\)

Therefore, 2x⁴ . 4x⁻³ = \(\frac{x}{2}\)

c. 2x^3y^-3 • 2x

i. Rewrite as follows;

2x³y⁻³ . 2x

ii. Change position of terms with negative exponents;

\(2x^3.\frac{1}{y^3} .2x\)

iii. Now solve;

\(\frac{4x^4}{y^3}\)

Therefore, 2x³y⁻³ . 2x = \(\frac{4x^4}{y^3}\)

The company profile and goals are briefly mentioned in the company's mission statement. This statement encapsulates the essence of the organization, outlining its purpose, values, and objectives.

It serves as a guiding principle for the company's actions and decisions, providing a clear direction for employees, stakeholders, and customers. The mission statement typically highlights the company's core competencies, target market, and desired impact on society. It is often crafted to be concise, memorable, and inspirational, reflecting the company's vision for the future. By summarizing the company profile and goals, the mission statement acts as a compass, aligning all aspects of the organization towards a common purpose.

The mission statement is a concise declaration that captures the essence of the company's identity, values, and ambitions. It outlines the company's goals and aspirations in a brief and compelling manner. Typically, the statement includes key elements such as the company's core values, unique selling proposition, target audience, and desired impact on society. It communicates what the company aims to achieve and how it intends to make a difference in the world. The mission statement serves as a unifying force, providing a clear sense of direction and purpose to employees, stakeholders, and customers. It helps to define the company's profile by highlighting its distinctive attributes and long-term objectives.

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Answer:

250 pennies

Step-by-step explanation:

50 x 8 = 250

The interaction plot consistent with the combination of main effects and interactions described is Plot D, which shows an interaction between squirrels and location.

An interaction occurs when the effect of one independent variable (in this case, squirrels) on the dependent variable (cone sizes) depends on the level of another independent variable (location).

Based on the given information, we have the following main effects and interactions:

1. Main effect of location: This means that the location (island vs. mainland) has an independent effect on cone sizes. It suggests that there is a difference in cone sizes between the two locations.

2. Main effect of squirrels: This means that the presence or absence of squirrels has an independent effect on cone sizes. It suggests that the presence of squirrels may influence cone sizes.

3. Interaction between squirrels and location: This means that the effect of squirrels on cone sizes depends on the location. In other words, the presence or absence of squirrels may have a different impact on cone sizes depending on whether the trees are on an island or the mainland.

Among the given interaction plots, Plot D is consistent with these main effects and interactions. It shows that the effect of squirrels on cone sizes differs between the island and mainland locations, indicating an interaction between squirrels and location.

Therefore, Plot D is the interaction plot that aligns with the combination of main effects and interactions described in the question.

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To find the standard deviation of the data summarized in the given frequency distribution, we can perform the following calculations. The table provides the necessary calculations for the standard deviation of the data summarized in the given frequency distribution:

Waiting time (minutes) Number of customer Midpoint (x) of Class Boundary of Class

f(x) 0-39 (0+3)/2=1.5 -0.5, 3.5+1.5 (9) (1.5) (9) = 13.5

4-7 16(4+7)/2=5.5 -3.5, 7.5+3.5 (16) (5.5) (16) = 88.0

8-11 15(8+11)/2=9.5 -7.5, 11.5+7.5 (15) (9.5) (15) = 213.75

12-15 8(12+15)/2=13.5 -11.5, 15.5+11.5 (8) (13.5) (8) = 91.875

16-20 2(16+20)/2=18 -16, 20+16 (2) (18) (2) = 92

Sum 60 (363.2)

Mean = Sum of (f(x)) / Sum of (f) = 363.2 / 60 = 6.0533

The variance, σ², can be calculated using the formula [Sum of (f(x²)) - {Sum of (f(x))² / Sum of (f)}] / (Sum of (f) - 1). Plugging in the values, we get:

σ² = [1103.2 - {363.2² / 60}] / (60 - 1) = 104.36

The standard deviation, σ, can be calculated using the formula √σ². Hence, the standard deviation of the data summarized in the given frequency distribution is approximately 10.2 minutes.

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Translation involves changing the position of a shape or line or point.

The value of k is -3

The given parameter is:

\(\mathbf{g(x) = f(x) + k}\)

From the attached graph, we can see that the line of f(x) is shifted down by 3 units to form g(x).

This means that:

\(\mathbf{g(x) = f(x) - 3}\)

By comparing: \(\mathbf{g(x) = f(x) - 3}\) and \(\mathbf{g(x) = f(x) + k}\)

We have:

\(\mathbf{k = -3}\)

Hence, the value of k is -3

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Answer:c

Step-by-step explanation:

i did the test