what’s the value of k that transforms f into g

The length of DC is √102, which is the simplest radical form.

The proportion of corresponding sides in similar triangles is the same. This is known as the similar triangles theorem.

In other words, if two triangles are similar, then the ratio of the lengths of any two corresponding sides is the same.

Since DE is parallel to AB, we can use similar triangles to set up the following proportion:

DC/AC = DE/AB

Substituting the given values, we get:

DC/17 = 6/AB

Since AB is the same length as DC, we can replace AB with DC:

DC/17 = 6/DC

Cross-multiplying and simplifying, we get:

DC^2 = 17 * 6

DC^2 = 102

DC = √102 in simplest radical form

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The recursive definition for the function f given by f(x) = 500 * (1/5)⁽ˣ⁻¹⁾, for x = 1, 2, 3 is a definition that describes how the value of f for a given x can be calculated from its inputs.

A recursive definition of a function is when the definition of the function involves the function itself. This type of definition is used to express complex operations in a simpler form. It is an effective way to break down a complicated problem into simpler, manageable parts. It allows us to define a set of rules in terms of smaller versions of itself, which can then be worked out using a series of steps.

A recursive definition for the function f is a process by which the value of f for a given input can be defined in terms of the values of f for smaller inputs. In other words, a recursive definition for f is a definition that describes how f can be calculated from its inputs.

In this case, the recursive definition for the function f is given by:

f(x) = 500 * (1/5)⁽ˣ⁻¹⁾, for x = 1, 2, 3

This means that the value of f for a given x can be calculated by multiplying 500 (the value of f for x = 1) by 1/5 raised to the power of x-1. This is because f(1) = 500, f(2) = 100 (1/5 * 500), and f(3) = 20 (1/5 * 1/5 * 500).

This recursive definition can also be expressed in a more general form as:

f(x) = a * b⁽ˣ⁻¹⁾, for x = 1, 2, 3

Where a and b are constants. In this case, a is 500 and b is 1/5.

In conclusion, the recursive definition for the function f given by f(x) = 500 * (1/5)⁽ˣ⁻¹⁾, for x = 1, 2, 3 is a definition that describes how the value of f for a given x can be calculated from its inputs. This definition can also be expressed in the more general form of f(x) = a * b⁽ˣ⁻¹⁾, for x = 1, 2, 3.

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The next three terms in the sequence are 1/81, -1/243, and 1/729.

What is the geometric sequence?

A geometric sequence is a sequence of numbers in which each term is obtained by multiplying the previous term by a fixed number called the common ratio. The general form of a geometric sequence is:

a, ar, ar^2, ar^3, ...

where a is the first term, r is the common ratio

To identify the next three terms in the sequence, we need to first determine the pattern. Looking at the sequence, we can see that each term is obtained by multiplying the previous term by -1/3, which means that this is a geometric sequence with a common ratio of -1/3.

Using this common ratio, we can find the next three terms in the sequence as follows:

-1/3 * (-1/27) = 1/81

1/81 * (-1/3) = -1/243

-1/243 * (-1/3) = 1/729

Therefore, the next three terms in the sequence are 1/81, -1/243, and 1/729.

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The coordinates of point B' after the translation are given as follows:

B'(1,-2).

A translation happens when either a figure or a function are moved horizontally or vertically.

The meaning of the translation for this problem is given as follows:

The coordinates of point B are given as follows:

B(5,1).

Hence the coordinates of point B' are given as follows:

Meaning that the last option is correct.

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Answer:

Multiply the numerator and denominator by the conjugate.

a with a small 3 b with a small 5 and check under it will be a small a and small b

Step-by-step explanation:

Answer: B

Step-by-step explanation:

The correct answer is O for some discrete probability distributions but not all.

This is because the probability of a random variable X being less than 8 can vary depending on the type of distribution it follows. For some discrete distributions, such as a binomial distribution, the probability of X < 8 can be calculated by summing the probabilities of all possible values of X that are less than 8. However, for other discrete distributions, such as a Poisson distribution, the probability of X < 8 may not be as straightforward to calculate. Therefore, the statement that P(X < 8) = P(X < 8) is true for some discrete distributions but not all.

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The transformation applied to the function f(x) is a translation of 4 units up.

Here we can see that:

f(x) = √(x + 3)

and g(x) is a vertical translation of k units:

g(x) = f(x) + k

To get the value of k, just look how many units the graph has been translated up ( remember that each of the smalls squares in the coordinate axis represents a single unit), we can see that it is 4 units up, then k = 4

We have a vertical translation of 4 units up.

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Answer:

-0

Step-by-step explanation:

After solving the equation, the solution if the equation is -2 and -11/5.

To solve the rational equation we first express the given statement in the form of mathematical equation. After that we solve the equation.

As the statement is 5 over X + 2. It can be written as 5/(x + 2)

Then the second statement is -11 over X to the 2nd + 2X which is written as -11/(x² + 2x).

There have equal sign between both expression. So the expression is

5/(x + 2) = -11/(x² + 2x)

Now solve it.

Multiply by (x² + 2x) on both side, we get

5(x² + 2x)/(x + 2) = -11

Multiply by (x + 2) on both side, we get

5(x² + 2x) = -11(x + 2)

Now simplify using the distributive property

5x² + 10x = -11x - 22

Add 11x on both side, we get

5x² + 21x = - 22

Add 22 on both side, we get

5x² + 21x + 22 = 0

Now we factor the equation

5x² + (11 + 10)x + 22 = 0

5x² + 11x + 10x + 22 = 0

x(5x + 11) + 2(5x + 11) = 0

(5x + 11)(x + 2) = 0

Now equating equal to 0.

5x + 11 = 0                     x + 2 = 0

5x = -11                          x = -2

x = -11/5

The solution if the equation is -2 and -11/5.

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The complete question is:

Solve the rational equation 5 over X + 2 equals -11 over X to the 2nd + 2X.

The exact number for tan(t + 71) is -0.5846.

To find tan(t + 71), we can use the formula for the sum of two angles:
tan(t + 71) = (tan t + tan 71)/(1 - tan t * tan 71)

Given that tan t = 5, we can substitute this value into the formula:
tan(t + 71) = (5 + tan 71)/(1 - 5 * tan 71)

To find the exact number for tan 71, we can use a calculator or a table of trigonometric values. The exact value of tan 71 is approximately 2.9042.

Substituting this value into the formula, we get:
tan(t + 71) = (5 + 2.9042)/(1 - 5 * 2.9042)

Simplifying the expression, we get:
tan(t + 71) = (7.9042)/(1 - 14.521)
tan(t + 71) = (7.9042)/(-13.521)
tan(t + 71) = -0.5846

Therefore, the exact number for tan(t + 71) is -0.5846.

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Answer:

20%

Step-by-step explanation:

Formula - multiply decimal by 100

0.2- Word form= two tenths

Fraction * 2/10 *

0.2 (multiply by 100)

0.2 x 100 = 20

20% is 0.2 as a percent

( hope this helps I’m online so ask any questions you need)

The permutation ([1,2,3,4,5,6],[6,5,4,3,1,2]) can be written as a product of disjoint cycles as (A) ([1,6,2,5])([3,4]).

To find the product of disjoint cycles, we can start by looking at the first element in the first cycle, which is 1. We see that 1 maps to 6 in the given permutation, so we write ([1,6. Next, we see that 6 maps to 2, so we write ([1,6,2. Finally, 2 maps to 5, so we write ([1,6,2,5. Since 5 maps back to 1, we can close the cycle and write ([1,6,2,5]).

Next, we look at the remaining elements, which are 3 and 4. We see that 3 maps to 4 and 4 maps back to 3, so we write ([3,4]).

Therefore, the permutation ([1,2,3,4,5,6],[6,5,4,3,1,2]) can be written as a product of disjoint cycles as ([1,6,2,5])([3,4]). The correct answer is (A) ([1,6,2,5])([3,4]).

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The statements that are true about the function when graphed on a coordinate plane include the following:

C. The relative minimum of the function is (3, 0)

E. When t > 3, the function is increasing.

In order to determine the minimum and maximum of this function, we would have to determine the critical points where the derivative of the function is equal to zero or undefined, and then evaluate the function at these critical points and at the endpoints of the interval.

By taking the first derivative of the given function and factorizing, we have:

f(t) = t³ - 6t² + 9t

f'(t) = 3t² - 12t + 9  

3t² - 12t + 9 = 0

t² - 4t + 3 = 0

(t - 3)(t - 1) = 0

t = 3 and t = 1

Therefore, the critical points of the function are at t = 1 and t = 3.

By taking the second derivative of the given function and factorizing, we have:

f''(t) = 6t - 12

At point t = 1, we have:

f''(1) = 6(1) - 12 = -6 (it is less than zero).

Therefore, f(t) has a local maximum at t = 1.

At point t = 3, we have:

f''(3) = 18 - 12 = 6 (it is greater than zero).

Therefore, the function f(t) has a local minimum at t = 3.

At t = 4, f''(4) = 24 - 12 = 12

At t = 5, f''(5) = 30 - 12 = 18

In conclusion, the relative minimum of the function is (3, 0) and when t > 3, the function would increase.

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Answer:

Second option

Step-by-step explanation:

Check the relationship between the x digits and compare with y digits. It must be the same all through

In the second option x =2y for all the digits

4:2, 7:3.5,8:4,10:5

The expressions that are equivalent to 2(-2m+7)-9m are C: 2(-8m+6m+7)-9m and D: 2(-6m+4m+7)-9m.

To see why, let's simplify the original expression:

2(-2m+7)-9m = -4m+14-9m = -13m+14

Now let's simplify the other expressions:

(-2m+7)2-9m = -4m+14-9m = -13m+14

2(-8m+6m+7)-9m = -16m+12m+14-9m = -13m+14

2(-6m+4m+7)-9m = -12m+8m+14-9m = -13m+14

So we can see that the expressions 2(-8m+6m+7)-9m and 2(-6m+4m+7)-9m are equivalent to the original expression.

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The 95% confidence interval for the population proportion of defective calculators is (0.0015, 0.0069).

Hence, (0.0015 < p < 0.0069).

According to the given information

we can use the formula for calculating the confidence interval for a population proportion,

⇒ P ± z√(P(1-P )/n)

Where,

P = sample proportion of defective calculators = 5/1200

                                                                              = 0.0042

n = sample size = 1200

z = z-score for 95% confidence level = 1.96 (from standard normal distribution table)

Substituting the values in the formula, we get,

⇒ 0.0042 ± 1.96√(0.0042(1-0.0042)/1200)

Simplifying the expression gives us the confidence interval,

⇒ (0.0015 < p < 0.0069)

Therefore,

The 95% confidence interval for the population proportion of defective calculators is (0.0015, 0.0069).

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Answer:

∠ A = 19.8°

Step-by-step explanation:

the 3 angles of the triangle sum to 180°

sum the 3 angles and equate to 180

5x - 18 + 4x + x = 180

10x - 18 = 180 ( add 18 to both sides )

10x = 198 ( divide both sides by 10 )

x = 19.8

Then

∠ A = x = 19.8°

By following this process, we were able to evaluate each expression and get the answers of 590, 181, 25, and 6 respectively.

a) (fog)(4) = (f(g(4)) = f(7(4)^2+6) = 5(7(16)+6) = 5(118) = 590

b) (gof)(2) = (g(f(2)) = g(5(2)) = 7(5)^2+6 = 7(25)+6 = 181

c) (fof)(1) = (f(f(1)) = f(5(1)) = 5(5) = 25

d) (gog)(0) = (g(g(0)) = g(7(0)^2+6) = 7(0)+6 = 6

To find the expressions given, we need to first use the definition of a function composition. This means that when we have a function \(f\) composed with a function \(g\), this is represented by \(f\circ g\). When we use a function composition, we evaluate the function \(g\) first, then plug the result into the function \(f\).

For example, in part (a) we have the expression \(f\circ g(4)\). We need to first evaluate \(g(4)\), which gives us \(7(4)^2+6\). Then we plug this result into the function \(f\) to get \(f(7(4)^2+6)= 5(7(4)^2+6) = 590\). We can repeat this process for the rest of the parts. For part (b) we have \(g\circ f(2)\). Evaluating \(f(2)\) gives us \(5(2)\), which we then plug into \(g\) to get \(g(5(2))= 7(5)^2+6 = 181\).

For part (c) we have \(f\circ f(1)\), so evaluating \(f(1)\) gives us \(5(1)\) and then plugging this into \(f\) gives us \(f(5(1))= 5(5) = 25\). Finally, for part (d) we have \(g\circ g(0)\), so evaluating \(g(0)\) gives us \(7(0)^2+6\), which we plug into \(g\) to get \(g(7(0)^2+6) = 7(0)+6 = 6\).

In conclusion, we can use function composition to find the expressions given. We start by evaluating the inner function, then plugging the result into the outer function.

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The width of the rectangle is 4 2/3 yards.

The area of a rectangle is the measure of the total region that the rectangle occupies in two-dimensional space.

It is calculated by multiplying the length of the rectangle by its width.

The formula for the area of a rectangle is:

Here we have

The area of a rectangular tablecloth is 8 3/4 square yards.  

The width of the tablecloth is 1 7/8 yards

For simple calculation convert given fractions into improper fractions

=> 8 3/4 = 35/4 yards

=> 1 7/8 = 15/8  yards  

Let 'x' be the breadth of the rectangle

As we know Area of the rectangle = Length ×  width

=> x × 15/8 = 35/4

=> x = 35/4 × 8/15

=> x = 14/3

Here, 14/3 = 4 2/3 yards  

Therefore,

The width of the rectangle is 4 3/2 yards.

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Simplifying the expression (2x³ – 2x² – 40x )/(2x² + 5x - 12) ÷ (6x⁴ – 150x²)/(8x³ - 27) will result to (x - 5)/(3x(x - 3)(x + 5)).

To simplify the given expression completely, we need to factor the numerator and denominator of each fraction, and then simplify by canceling out common factors.

(2x³ – 2x² – 40x )/(2x² + 5x - 12) ÷ (6x⁴ – 150x²)/(8x³ - 27)

= (2x(x² - x - 20))/(2x^2 + 5x - 12) ÷ (6x^2(x^2 - 25))/(8x^3 - 27)

= (2x(x - 5)(x + 4))/(2x² + 8x - 3x - 12) ÷ (6x²(x - 5)(x + 5))/(8x³ - 27)

= (2x(x - 5)(x + 4))/(2x(x + 4)(x - 3)) ÷ (6x²(x - 5)(x + 5))/(8x³ - 27)

= (2x(x - 5)(x + 4))/(2x(x + 4)(x - 3)) × (8x³ - 27)/(6x²(x - 5)(x + 5))

= (x - 5)/(x - 3) × (8x³ - 27)/(6x²(x - 5)(x + 5))

= (x - 5)/(x - 3) × (2x - 3)(4x² + 6x + 9)/(6x²(x - 5)(x + 5))

= (x - 5)/(x - 3) × (2x - 3)/(6x(x - 5)(x + 5))

= (x - 5)/(3x(x - 3)(x + 5))

Therefore, the simplified expression is (x - 5)/(3x(x - 3)(x + 5)).

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Answer:

ABD = 75 degrees

Step-by-step explanation:

ABD is the same as ABC + CBD

ABC = 30

CBD = 45

30+45 = 75 degrees

Therfore, ABD = 75 degrees

There are 8 possible ways for the first 2 finishers to complete the marathon with different genders. There are 20 possible ways for Chantal to finish the race before David.

There are a couple of different ways to approach this problem, but one common method is to use the multiplication principle, which states that if there are A ways to do one thing and B ways to do another, then there are A*B ways to do both. We can apply this principle to both parts of the question.

a) If the first 2 finishers must have different genders, then we can think about the possible combinations of boys and girls. There are 2 options for the first finisher (either a boy or a girl), and then there are 4 options for the second finisher (either a boy or a girl, but not the same gender as the first finisher).

So, using the multiplication principle, we can find the total number of ways for the first 2 finishers to complete the marathon with different genders:

2 * 4 = 8

Therefore, there are 8 possible ways for the first 2 finishers to complete the marathon with different genders.

b) If Chantal must finish the race before David, then we can think about the possible positions for Chantal and David. There are 5 possible positions for Chantal (first, second, third, fourth, or fifth), and then there are 4 possible positions for David (second, third, fourth, or fifth, but not before Chantal).

So, using the multiplication principle, we can find the total number of ways for Chantal to finish before David:

5 * 4 = 20

Therefore, there are 20 possible ways for Chantal to finish the race before David.

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answer = c

its not a or b because the range starts at y = 2

Answer:

We can use the concept of percentage to solve this problem.

Let's represent the total number of cards sold for Mother's Day by "x". We know that one salesman sold 47 cards, which was 4% of the total number of cards sold. So we can set up an equation:

0.04x = 47

Solving for "x", we divide both sides by 0.04:

x = 47 / 0.04

Using a calculator, we get:

x = 1175

Therefore, the total number of cards sold for Mother's Day was 1175.

Vοlume οf the Pyramid is 21 cm³

A prism is a sοlid shape with twο identical parallel bases and flat sides that cοnnect the bases. The sides οf a prism are usually rectangles, but they can alsο be triangles οr οther pοlygοns.

A pyramid is a sοlid shape with a pοlygοnal base and triangular sides that meet at a single pοint called the apex.

When a prism have same base area and height as that οf a pyramid the vοlume οf the prism is three times that οf the pyramid.

=> Vοlume οf prism = 3 Vοlume οf pyramid

Here we have

The prism and pyramid abοve have the same width, length, and height.  

The vοlume οf the prism is 63 cm³  

As we knοw,

Vοlume οf prism = 3 Vοlume οf pyramid

The vοlume οf the Pyramid = [ Vοlume οf prism ]/ 3

= [ 63 cm³]/3 = 21 cm³  

Therefοre,

Vοlume οf the Pyramid is 21 cm³

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The extra number of people that should be engaged to reap the field in 10 days is given by A = 21 people

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the extra number of people that should be engaged to reap the field in 10 days be represented as A

Now , the number of people that should be engaged to reap the field in 10 days = n

The number of people that can reap the field in 17 days = 30 persons

So , the proportion is

30 x 17 = n ( 10 )

On simplifying , we get

Divide by 10 on both sides , we get

n = ( 30 x 17 ) / 10

n = 3 x 17

n = 51

And , the number of extra persons A = n - 30

So , the extra number of people that should be engaged to reap the field in 10 days A = 21 people

Hence , the proportion is A = 21 people

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The concept time and work is used here to determine the number of people required to reap the same field in 10 days. The number of people required is 51.

The time and work represents the time taken by an individual or a group of individuals to complete a piece of work and the efficiency of the workdone by each of them.

If 30 persons can reap a field in 17 days

1 person can reap = 30 × 17 = 510 days

In 10 days, number of persons needed = 510 / 10 = 51 persons

Thus 51 persons can reap the field in 10 days.

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The total amount will Perri need when she gets the keys for the house at closing is $41,860.

Perri is making a 7% down payment on the $364,000 purchase price of the condominium, so her down payment will be

0.07 x $364,000 = $25,480.

Perri estimates her closing costs to be 4.5% of the purchase price, which is 0.045 x $364,000 = $16,380.

Therefore, the total amount Perri will need when she gets the keys for the house at closing is the sum of the down payment and the closing costs, which is $25,480 + $16,380 = $41,860.

So the answer is (C) $41,860.

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Answer:

x = -5.5

Step-by-step explanation:

-2x - 4 + 2x + 32 - 2x - 21 = 18​

-2x - 4 + 32 - 21 = 18

-2x + 7 = 18

-2x = 11

x = -5.5

So, the answer is x = -5.5

A blue token is worth 15 points and a yellow token is worth 5 points.

Two or more expressions with an Equal sign is called as Equation.

Let b  represent the point value of a blue token and

y represent the point value of a yellow token.

We can set up two equations:

4b + 7y = 95 (Jillian's score)

4b + 3y = 75 (Jacob's score)

Subtracting the second equation from the first, we get:

4b + 7y - (4b + 3y) = 95 - 75

Simplifying this, we get:

4y = 20

Dividing both sides by 4, we get:

y = 5

So a yellow token is worth 5 points.

Now we can substitute this value of "y" into one of the original equations and solve for "b".

4b + 7y = 95

4b + 7(5) = 95

4b + 35 = 95

4b = 60

b = 15

So a blue token is worth 15 points.

Therefore, a blue token is worth 15 points and a yellow token is worth 5 points.

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