Graph the polygon and its image after a reflection in the line x=4.

The equations that  could represent f(x) and g(x) are f(x) = 6/x + 3 and g(x) = x

From the question, the equation of the function is given as

f of g of x is equal to 6 over the quantity x squared end quantity plus 3

Rewrite properly

So, we have

f(g(x)) = 6/x² + 3

The above equation can be rewitten as

f(g(x)) = 6/g(x)² + 3

This means that

g(x) = x

Remove the occurrence of g(x) from the equation f(g(x)) = 6/g(x)² + 3

So, we have

f(x) = 6/x + 3

Hence, the possible equations are f(x) = 6/x + 3 and g(x) = x

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The value of the expression (a[1] + a[3]) is "BD". In this array declaration and initialization, the variable "a" is an array of type String that contains four elements: "A", "B", "C", and "D". The square brackets notation is used to access specific elements of the array.

In this case, a[1] refers to the second element of the array (remember that array indices start at 0), which is "B". Similarly, a[3] refers to the fourth element of the array, which is "D".

Therefore, the expression (a[1] + a[3]) concatenates the strings "B" and "D" to form the string "BD". This is the final value of the expression.

It's worth noting that the other options listed in the question ("AC", "ABC", and "CD") are not correct. "AC" is the result of concatenating the first and third elements of the array (a[0] + a[2]). "ABC" is the result of concatenating all four elements of the array (a[0] + a[1] + a[2] + a[3]). And "CD" is the result of concatenating the last two elements of the array (a[2] + a[3]).

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The translation of the statements are (a) 25 > x and (b) 25 + x

Part (a)

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

25 more than a number

As an inequality, we have

25 > x

Where x is the number

Next, we have

Part (b)

Here, we have

25 is more than a number

As an expression, we have

25 + x

Hence, the translations are 25 > x and 25 + x

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The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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Answer:

Answer:

x=3

Step-by-step explanation:

7−3x=−x+1

Step 1: Simplify both sides of the equation.

7−3x=−x+1

7+−3x=−x+1

−3x+7=−x+1

Step 2: Add x to both sides.

−3x+7+x=−x+1+x

−2x+7=1

Step 3: Subtract 7 from both sides.

−2x+7−7=1−7

−2x=−6

Step 4: Divide both sides by -2.

−2x

−2

=

−6

−2

x=3

Decision Analysis is a mathematical method for making decisions in uncertain environment.

What is environment ?

Environment refers to the surrounding conditions, resources and factors that can have an impact on an organism, community, or system. This can include physical factors such as weather, terrain, and pollution, as well as biological factors such as other living organisms, and social or economic factors such as culture, laws and economic conditions.

The process of Decision Analysis can be broken down into several steps:

1) Define the decision problem: Clearly state the problem and the decision maker's objectives.

2) Identify the decision alternatives: List all the feasible options available to the decision maker.

3) Specify the probability distribution of the uncertain parameters: Assign probabilities to the possible outcomes of the uncertain parameters.

4) Evaluate the expected value or expected loss for each alternative: Compute the expected value or expected loss for each alternative, using the probability distribution of the uncertain parameters.

5) Choose the alternative with the highest expected value or the lowest expected loss: Select the alternative that maximizes the expected value or minimizes the expected loss.

6) Sensitivity analysis: Check the robustness of the decision by studying the effect of small changes in the model's assumptions.

Decision Analysis is a mathematical method for making decisions in uncertain environment.

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The total percentage increase in the investor's stock account is 3.7%.

What is the percentage increase?

Percentage increase refers to the amount by which a value or quantity has grown or increased, expressed as a percentage of its original value. It is calculated by dividing the difference between the new value and the original value by the original value, and then multiplying by 100 to express the result as a percentage. The formula for calculating percentage increase is:

Percentage increase = [(New value - Original value) / Original value] x 100%

To find the total percentage increase in the investor's stock account, we need to first calculate the new value of each stock and then add them together.

For Company A:

The stock has increased by 1%, which means its new value is 1% higher than $2000.

The increase in value is 0.01 * $2000 = $20.

The new value of the stock in Company A is $2000 + $20 = $2020.

For Company B:

The stock has increased by 5%, which means its new value is 5% higher than $4240.

The increase in value is 0.05 * $4240 = $212.

The new value of the stock in Company B is $4240 + $212 = $4452.

Now, we can find the total value of the investor's stock account by adding the new values of both stocks:

$2020 + $4452 = $6472

To find the percentage increase, we need to compare the total new value to the original total value:

The original total value was $2000 + $4240 = $6240

The total percentage increase is [(New total value - Original total value) / Original total value] x 100%

Plugging in the numbers: [(6472 - 6240) / 6240] x 100% = 3.7%

Therefore, the total percentage increase in the investor's stock account is 3.7%.

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By finding the average rate of change, we can see that:

a) The cost decreases.

b) The cost increases.

To check that, we need to find the average rate of change on the interval.

Remember that for function f(x) on an interval (a, b), the average rate of change is:

R = (f(b) - f(a))/(b - a)

Here the cost function is:

c(n) = 0.25*n² - 10n + 800

a) In the interval [10, 15] the average rate of change is given by:

R = (c(15) - c(10)/(15 - 10)

Where:

c(15) = 0.25*15^2 - 10*15 + 800 = 706.25

c(10) = 0.25*10^2 - 10*10 + 800 = 725

Then the average rate of change is:

R = (706.25 - 725)/(15 - 10) = -3.75

This means that between 10 and 15 light fixtures, the cost is decreasing.

b) Now we have the interval [20, 25], so let's do the same ting:

c(20) = 0.25*20^2 - 10*20 + 800 = 700

c(25) = 0.25*25^2  - 10*25 + 800 = 706.25

Here the average rate of change is:

R = (706.25 - 700)/(25 - 20) = 1.25

It is positive, which means that the cost is increasing.

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Answer:

0

Step-by-step explanation:

The answer would be 0

Answer: -4.3 is your answer. Hope it helps!

Answer:

x=2,y=−5

Step-by-step explanation:

1 Chinese yuan could purchase $0.12 and $0.15 in the year 2010 and 2012 respectively.

For the year 2010; we can calculate as follows;

1 US dollar = 8.24 Chinese yuan

x US dollar = 1 Chinese Yuan

using cross multiplication to find x;

8.24x = 1 ×1

8.24x = 1

x = 1 / 8.24

x = $0.12

For the year 2012; we can calculate as follows;

1 US dollar = 6.64 Chinese Yuan

x US dollar = 1 Chinese Yuan

Using cross multiplication to find x;

6.64x = 1

x = 1 / 6.64

x = $0.15

Therefore, one Chinese yuan could purchase $0.12 in 2010 and $0.15 in the year 2012.

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Answer: n+96

Step-by-step explanation:

Answer:

(n+8)x12

Step-by-step explanation:

You would take any letter (I used n) then add 8 then put that in parentheses then multiply by 12.

The Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

To solve the ODE using the Euler method, we divide the interval into smaller steps and approximate the derivative with a difference quotient. Given that the step size is h = 0.5, we will perform three steps to obtain the numerical solution.

we calculate the initial condition: y(0) = -2.

1. we evaluate the derivative at t = 0 and y = -2:

y' = 3(0) - 10(-2)² = -40

Next, we update the values using the Euler method:

t₁ = 0 + 0.5 = 0.5

y₁ = -2 + (-40) * 0.5 = -22

2. y' = 3(0.5) - 10(-22)² = -14,860

Updating the values:

t₂ = 0.5 + 0.5 = 1

y₂ = -22 + (-14,860) * 0.5 = -7492

3. y' = 3(1) - 10(-7492)² ≈ -2.2395 x 10^9

Updating the values:

t₃ = 1 + 0.5 = 1.5

y₃ = -7492 + (-2.2395 x 10^9) * 0.5 = -1.1198 x 10^9

Therefore, after performing three steps of the Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

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Answer:

12.5

Step-by-step explanation:

Keep dividing by 2, 25 divided by 2 is 12.5

Answer:

B

Step-by-step explanation:

16 + 6 ← factor out 2 from each number

= 2(8 + 3)

The worth of the equipment after 7 years will be $3145.7

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant.

Given is table with values of product for 3 years, we need to find its worth after 7 years, using the formula given,

aₙ = a₁rⁿ⁻¹

The given formula is of geometric sequence,

r = 9600 / 12000 = 0.8

a₁ = 12000

a₇ = 12000(0.8)⁷⁻¹

a₇ = 12000(0.8)⁶

a₇ = 3145.7

Hence, the worth of the equipment after 7 years will be $3145.7

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The unit rate in chapters per hour is 21/16 hours

Greg read 7/8 hours in 2/3 chapter

The unit rate can be calculated as follows

7/8= 2/3

1= x

cross multiply both sides

2/3x= 7/8

x= 7/8 ÷ 2/3

x= 7/8 × 3/2

x= 21/16

Hence 21/16 chapters is read in one hour

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The inequalities shown by the graph are y < 3, x > -1, x < 3, and y >-2.

The given graph has four lines showing different inequalities.

One undotted line is parallel to the x-axis and is at y = 3. The shaded region is below y = 3

Hence, the inequality will be y < 3

Another dotted line is parallel to the x-axis and is at y = -3. The shaded region is above y = -2

Hence, the inequality will be y > -2

Another dotted line is parallel to the y-axis and is at x = -1. The shaded region is to the right of x = -1

Hence, the inequality will be x > -1

Another dotted line is parallel to the y-axis and is at x = 3 The shaded region is to the left of x = 3

Hence, the inequality will be x < 3

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Answer:

the question has some problems

Answer:

Angle A = 102°

Angle B = 51°

Angle C = 27°

Step-by-step explanation:

angle A = 2b

angle B = b

angle C = 1/3 b + 10

Angle A + Angle B + Angle C = 180

2b + b + 1/3 b + 10 = 180

3 1/3 b + 10 = 180

10/3 b = 170

b = 51

a = 2b = 102

c = 1/3 b + 10 = 1/3 (51) + 10 = 17 + 10 = 27

Ok, so

Remember that the probability of an event is the relation between the favorable cases and all the possible cases.

In this case, we want to know the probability of landing on spaces 2 through 5.

We know that all the possible options for the spinner to land, are 10.

We also know that there's four positions between 2 and 5. (2,3,4,5).

Now, the probability will be:

Probability = 4/10 which is 2/5

The equivalent expression to 5z² + 10z is 5z(z + 2).

We have,

Expression: 5z² + 10z

Now, factories each term as

5z² = 5 x z x z

10z = 2 x 5 x z

So,  5z² + 10z

= 5 x z x z + 2 x 5 x z

= 5 x z( z + 2)

= 5z( z+ 2)

Thus, the required expression is 5z(z+2).

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Answer:

The roots of a polynomial are those values of the variable that cause the polynomial to evaluate to zero

Step-by-step explanation:

The first option (n − 1)s/ s1^2/s2^2 has an F distribution.

In statistics, the F-distribution is a probability distribution that is used to compare the variances of two independent samples. The F-distribution is defined as the ratio of two independent chi-square distributions, each divided by its degrees of freedom. The query lists three options: (n − 1)s/ s12/s22, (n − 1)s1/s2, and s1/s2, and asks which of these has an F-distribution. The correct option is (n − 1)s1/s2, which has an F-distribution with (n − 1) numerator degrees of freedom and (n − 1) denominator degrees of freedom [1]. The other options are not F-distributions.

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When the graph is decreasing, the rectangles give an underestimate and when the graph is increasing, they give an overestimate. These trends are accentuated to a greater extent by areas of the graph that are steeper.

We only need to add up the areas of all the rectangles to determine the area beneath the graph of f. It is known as a Riemann sum. The area underneath the graph of f is only roughly represented by the Riemann sum. The subinterval width x=(ba)/n decreases as the number of subintervals n increases, improving the approximation. Increased sections result in an underestimation while decreasing sections result in an overestimation. We now arrive at the middle rule. The height of the rectangle is equal to the height of its right edges for a right Riemann sum and its left edges for a left Riemann sum. The rectangle height is the height of the top edge's midpoint according to the midpoint rule, a third form of the Riemann sum.

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Answer:

4•(2+5)^2 -5^2 = 171

Step-by-step explanation:

Do BIDMAS
(brackets, indices, division, multipy, add, sub)

so brackets
4*7^2-5^2
then do the indices
4*49-25
then the multiply
196-25
= 171
Hope this helps

Answer: Brackets => 4 x (7)^2 - 5^2
               Indices/Orders => 4 x 49 - 25

               Multiplication => 196 - 25

               Subtraction => 171

Answer:

9, 81, 144

Step-by-step explanation:

Answer:

The answer is the last one or the one on the very bottom because y is above and touching the line so y must be greater than or equal to the slope plus the y-intercept or b. I figured out the slope by using rise over run meaning that you must first go up or down on a coordinate and then go left or right to meet the other coordinate. The y-intercept is just the place where the line touches the y axis and that is on -1. By piecing up these pieces of information one by one you will get D or the last one.

Hope this helped.