Create a rational inverse function that has an original function with the following transformations, vertical compression, horizontal shift right, vertical shift up

Answer:

Tangent

Step-by-step explanation:

if the angle in question is the bottom of the ladder and the ground, then tangent is opposite over adjacent... or 12/5

Hope this is right

The Correct answer option D, which is is \(\sqrt[8]{10} ^{3x}\)

What are Square roots and cube root ?

The two most crucial areas in mathematics are square roots and cube roots. To calculate the square root of any number, one needs to find a number that, when multiplied twice by itself, equals the original value. Similar to this, to determine the cube root of any number, we need to find a number that, when multiplied three times by itself, equals the original value.

Symbol: The square root is represented by the character "√" whereas the cube root is represented by the character "∛" and so on.

According to question

⇒   \(\sqrt[]{10} ^{\frac{3}{4} x}\)

⇒  \(10^{\frac{3}{4}x .\frac{1}{2} }\)

⇒ \(10^{\frac{3}{8}x}\)

⇒ \(\sqrt[8]{10} ^{3x}\\\)

⇒    \(10^{\frac{3}{8}x} = \sqrt[8]{10} ^{3x}\\\)

hence, the \(\sqrt[8]{10} ^{3x}\\\) is equivalent to 10 square rooted 3/4x

To learn more about Square roots and cube root, check out

https://brainly.com/question/28259675

#SPJ1

Answer:

x(7y)x(7y)

Step-by-step explanation:

The given expression: 7(xy)7(xy)

i.e. a product of 7 and xy.

The operation used here: Multiplication.

Commutative property of multiplication :-

a\times b=b\times aa×b=b×a for any numbers a and b.

Associative property of multiplication :-

a\times(b\times c)=(a\times b\times c)a×(b×c)=(a×b×c) for any numbers a , band c.

Now, 7(xy)=(7x)y7(xy)=(7x)y [Associative property of multiplication]

=(x7)y=(x7)y [Commutative property of multiplication]

=x(7y)=x(7y) [Associative property of multiplication]

The sector areas of the grey and white areas are 159.09 in² and 41.87 in²

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

The area of shaded sector is calculated as

Area = Central angle/360 * π * Radius^2

Substitute the known values in the above equation, so, we have the following representation

Hence, the area is 159.09

Read mroe about area at

brainly.com/question/16656203

#SPJ1

Answer:

Step-by-step explanation:

Comment

The formula used to figure out the costs is

C(x) = 2885 + 30x

2885 is the total of the fixed costs -

Now the problem gets sort of complicated. If the company could print an unlimited amount of pages, the 2885 remains the same, no matter what.

But x gets larger and larger. and so C(x) gets larger and larger.

Answer

Therefore the average cost would approach infinity.

A

The zero of f is x = -2. C.

The equation of the linear function can be found using the point-slope formula:

y - y1 = m(x - x1)

m is the slope and (x1, y1) is a point on the line.

Plugging in the given values, we get:

y - 4 = 4(x + 1)

Expanding and simplifying, we get:

y = 4x + 8

The zero of f (where f(x) = y) set y = 0 and solve for x:

0 = 4x + 8

4x = -8

x = -2

The point-slope formula may be used to determine the equation of the linear function:

y - y1 = m(x - x1)

(X1, Y1) is a point on the line, and m is the slope.

With the above variables obtain:

y - 4 = 4(x + 1)

By enlarging and condensing, we obtain:

y = 4x + 8

y = 0, you may solve for x using the zero of f (where f(x) = y):

0 = 4x + 8 4x

= -8 x

= -2

For similar questions on zero

https://brainly.com/question/12730877
#SPJ11

Answer:

x,y,z=4,3,-4

Step-by-step explanation:

2x+4y-6x=44   =    x+2y-3z=22

x+2y-3z=22

x+2y+3z=-2

x+2y-3z=22

3x-4y+4z=-16

x+2y-3z=22         ------>

                                         2x+4y=20

x+2y+3z=-2          ------>

x+2y-3z=22                      ------>

                                                        13x-4y=40

3x-4y+4z=-16                    ------->

2x+4y=20

13x-4y=40

y=3

x=4

4+2x3-3z=22

z=-4

(x,y,z)=(4,3,-4)

2x4+4x3-6x(-4)=44

4+2x3+3x(-4)=-2

44=44

-2=-2

-16=-16

(x,y,z)=(4,3,-4)

I am so sorry if it is incorrect I  tried :<

The distance between point T (-5, 1) and point I (-1, 1) is 4 units.

To find the distance between two points, we can use the distance formula, which is derived from the Pythagorean theorem. The formula is:

Distance = √((x2 - x1)² + (y2 - y1)²)

Let's apply this formula to find the distance between point T (-5, 1) and point I (-1, 1):

x1 = -5, y1 = 1 (coordinates of point T)

x2 = -1, y2 = 1 (coordinates of point I)

Plugging these values into the formula, we have:

Distance = √((-1 - (-5))² + (1 - 1)²)

        = √(4² + 0²)

        = √(16 + 0)

        = √16

        = 4

Therefore, the distance between point T (-5, 1) and point I (-1, 1) is 4 units.

For more questions on Pythagorean theorem, click on:

https://brainly.com/question/231802

#SPJ8

Answer:1/2

Step-by-step explanation:

The system of equations that represent this situation is:

\(x + y + z = 356\)

\(9x + 4y + 4z = 1978\)

\(x = 2y\)

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

For our system, we say that:

Total of 356 people, thus:

\(x + y + z = 356\)

$9 for adults, $4 for students and teachers, total of $1978. Thus:

\(9x + 4y + 4z = 1978\)

Adults twice the number of students, thus:

\(x = 2y\)

The system is:

\(x + y + z = 356\)

\(9x + 4y + 4z = 1978\)

\(x = 2y\)

A similar problem is given at https://brainly.com/question/24823220

The answer is 3 I work it out

Descriptive statistics are the most useful in life. Descriptive statistics provide information about a data set and can help to summarize and interpret data. Specifically, I find the mean and median to be the most useful.

Descriptive statistics involves the use of measures such as the mean, median, mode, and range, as well as graphical representations of the data, such as histograms, box plots, and scatter plots.

The mean is the average of a set of data and is useful for summarizing and interpreting data. For example, when I am studying for a test, I often use the mean of my practice test scores to understand my overall performance.

The median is the middle value of a set of data and is useful for understanding the spread of the data. For example, when I am tracking my monthly expenses, I often use the median to understand how much I am spending each month. By taking the median of my monthly expenses, I can get an idea of which expenses are taking up the most of my budget.

For more questions related to median

https://brainly.com/question/26177250

#SPJ1

Answer:

4 1/2  and 7 1/4

Step-by-step explanation:

Answer:

Exact Form:

649/168

Decimal Form:

3.86309523…

Mixed Number Form:

3 145/168

Answer:

64

Step-by-step explanation:

2, 6, 28, 23,7.64.

because 64 is the furthest away from any other number

In the figure, the length of any line segment in the image is longer the length of the corresponding line segment in the preimage. The scale factor of the dilation is 2

The scale factor of dilation is defined as the change in size of a figure. Thus, a scale factor that is greater than 1 is referred to as an enlargement while a scale factor that is greater than 0 but less than 1 is referred to as a reduction.

Now, we are told that ΔABC has been dilated from center D to form ΔRST, This means that the lengths in ΔRST are longer than the lengths in ΔABC.

Secondly, by close inspection we can see that it was dilated by a scale factor of 2.

Read more about scale factor of dilation at; https://brainly.com/question/3457976

#SPJ1

The 500 sample size and 95% confidence level will both tend to increase the width of the confidence interval.

In this question, we have been given  the combinations of sample size and confidence level.

We need to select a combinations of sample size and confidence level that will give the widest interval.

We know that the confidence level is typically set in the range of 99% to 80%. The 95% confidence interval will be wider than the 90% interval and which will be wider than the 80% interval.

As we know increasing the confidence will increase the margin of error which results in a wider interval.

But increasing the sample size decreases the width of confidence intervals, as it decreases the standard error.

This means, for the widest interval we need to select a high confidence interval and small sample size.

Therefore, the sample size = 500 and the confidence interval = 95% will give the widest interval.

Learn more about the confidence interval here:

https://brainly.com/question/22851322

#SPJ4

Answer:

The answer to this is A.) 8/17

Answer:

See the attachment for the graph of the piecewise function.

Step-by-step explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

\(f(x)=\begin{cases}2x+2,\;\;\;0\leq x \leq 1\\4x^2,\;\;\;\;\;\;\;1 < x < 3\end{cases}\;[1,3]\)

Therefore, the function has two definitions:

When graphing piecewise functions:

Substitute the endpoints of the first function's domain 0 ≤ x ≤ 1 into the first function:

\(x=0\implies f(0)=2(0)+2=2 \implies (0,2)\)

\(x=1\implies f(1)=2(1)+2=4 \implies (1,4)\)

Therefore, place a closed circle at (0, 2) and a closed circle at (1, 4).

As this function is linear, join the two points with a straight line.

Substitute the endpoints of the second function's domain 1 < x < 3 into the second function:

\(x=1\implies f(1)=4(1)^2=4 \implies (1, 4)\)

\(x=3\implies f(3)=4(3)^2=36 \implies (3, 36)\)

Therefore, place an open circle at (1, 4) and an open circle at (3, 36).

As the function is quadratic (a parabola that opens upwards), join the points with a curve.

You will notice that both pieces of the function share the endpoint (1, 4).

As (1, 4) is included in the second piece of the function, the function is continuous at (1, 4) and the closed circle is optional at that point.

The solution is Option A.

The sum of the infinite geometric progression is S = -( 9/5 )

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the sum of the geometric progression be represented as S

Now , the equation will be

∑ n = 1 to ∝ ( -3 ( 3/8 )ⁿ )   be equation (1)

The sum of the infinite GP is S = a / ( 1 - r ) , where r is the common ratio

Substituting the values in the equation , we get

when n = 1

a₁ = -3 ( 3/8 )

a₁ = -9/8

when n = 2

a₂ = -3 ( 3/8 )²

a₂ = -27/64

So , the common ratio r = a₂ / a₁

The common ratio r = 3/8

Substituting the values in the equation , we get

The sum of the infinite GP is S = a / ( 1 - r )

The sum of the infinite GP is S = ( -9/8 ) / ( 1 - 3/8 )

The sum of the infinite GP is S = ( -9/8 ) / ( 5/8 )

The sum of the infinite GP is S = - ( 9/5 )

Hence , the sum of GP is - ( 9/5 )

To learn more about geometric progression click :

https://brainly.com/question/1522572

#SPJ1

Answer:

300

Step-by-step explanation:

The rectangles area is 200. (20*10) (though it might be 10*10 because 20 could be the length for it over all but there is the 10 for the triangles side so I think it's just 20).

The triangles area is 100. (1/2*10*20).

Answer:

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

Given function:

Graph it first (see attached).

Test the graph for symmetry.

We know the odd degree parent function y = x³ has an origin symmetry, whilst even degree functions may have axis symmetry.

The given function is a translation of cubic function 5 units up so the center of symmetry has translated as well. Therefore correct answer is 4.

Answer:

4. no origin symmetry

Step-by-step explanation:

Functions are symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, −b) on the graph:

To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.

\(\begin{aligned}&\textsf{Given}: \quad &y &= x^3 + 5\\&\textsf{Replace $y$ for $(-y)$}: \quad &-y &= x^3 + 5\\&\textsf{Simplify}: \quad &y &= -x^3 - 5\end{aligned}\)

Therefore, since the resultant expression is not equivalent to the original expression, it is not symmetric with respect to the x-axis.

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

Functions are symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph:

To determine if a graph is symmetric with respect to the x-axis, replace all the x's with (−x).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the y-axis.

\(\begin{aligned}&\textsf{Given}: \quad &y&=x^3+5\\&\textsf{Replace $x$ for $(-x)$}: \quad &y&=(-x)^3+5\\&\textsf{Simplify}: \quad &y&=-x^3+5\end{aligned}\)

Therefore, since the resultant expression is not equivalent to the original expression, it is not symmetric with respect to the y-axis.

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

Functions are symmetric with respect to the origin if for every point (a, b) on the graph, there is also a point (-a, -b) on the graph:

To determine if a graph is symmetric with respect to the origin, replace all the x's with (−x) and all the y's with (-y).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the origin.

\(\begin{aligned}&\textsf{Given}: \quad &y&=x^3+5\\&\textsf{Replace $x$ for $(-x)$ and $y$ for $(-y)$}: \quad &(-y)&=(-x)^3+5\\&\textsf{Simplify}: \quad &-y&=-x^3+5\\&&y&=x^3-5\end{aligned}\)

Therefore, since the resultant expression is not equivalent to the original expression, it is not symmetric with respect to the origin.

Answer:

80x+8y=232

Step-by-step explanation:

80 times however many days worked plus 8 times however many video games sold on Thursday

Answer: 24

Step-by-step explanation:

To find the area of the composite figure, we need to find the area of the sector and the area of the triangle and then add them together.

Area of sector = (θ/360) * π * r^2, where θ is the angle of the sector in degrees, r is the radius of the circle.

The angle of the sector can be found by subtracting the angle of the triangle from 360 degrees. The radius of the circle can be found by dividing the length of the arc by the angle of the sector.

Length of the arc = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 4 = 4.19

Radius of the circle = 4.19/60 = 0.07

Angle of sector = 360 - 60 = 300 degrees

Area of sector = (300/360) * 3.14 * 0.07^2 = 0.0041

The area of the triangle can be found using the formula:

Area of triangle = (1/2) * base * height = (1/2) * 8 * 6 = 24

Therefore, the total area of the composite figure is:

0.0041 + 24 = 24.0041

Rounding to the nearest hundredth, the area of the composite figure is approximately 24.00.

The statement, For every point on the graph of f(x), there is a point on the graph of F⁻¹(x) with reversed coordinates is false.

In relation to the original function f, the inverse function is denoted by the symbol f⁻¹, and both the original function's domain and its range are transformed into the inverse function's domain and range, respectively. Swapping (x, y) with (y, x) with reference to the line y = x yields the graph of the inverse function.

We know that inverse of function is NOT the reciprocal of f. The composition of the function f and the reciprocal function f inverse gives the domain value of x.

Hence, the statement, For every point on the graph of f(x), there is a point on the graph of F⁻¹(x) with reversed coordinates is false.

Learn more about inverse function here:

https://brainly.com/question/17872426

#SPJ1

The probability of the four events are: Event 1: 1/84Event 2: 3/14Event 3: 15/28 Event 4: 5/21

The total number of drinks = 9The number of sweet teas = 3The number of unsweetened teas = 6If you select 3 drinks at random, the following events can take place:

Event 1: All three drinks are sweet teas. The probability of event 1 = (Number of ways in which all three drinks can be sweet teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be sweet teas = 3C3 = 1 (because all three sweet teas are already fixed)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 1 = 1/84 = 1/84

Event 2: Exactly two drinks are sweet teas. The probability of event 2 = (Number of ways in which two drinks are sweet teas and one is an unsweetened tea) / (Number of ways to select 3 drinks)The number of ways in which two drinks are sweet teas and one is an unsweetened tea = (3C2 × 6C1) = 18 (because you can choose 2 sweet teas from 3 and 1 unsweetened tea from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 2 = 18/84 = 3/14

Event 3: Exactly one drink is a sweet tea. The probability of event 3 = (Number of ways in which one drink is a sweet tea and the other two are unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which one drink is a sweet tea and the other two are unsweetened teas = (3C1 × 6C2) = 45 (because you can choose 1 sweet tea from 3 and 2 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 3 = 45/84 = 15/28

Event 4: All three drinks are unsweetened teas. The probability of event 4 = (Number of ways in which all three drinks can be unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be unsweetened teas = 6C3 = 20 (because you can choose 3 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84 Therefore, the probability of event 4 = 20/84 = 5/21

For more question probability

https://brainly.com/question/25839839

#SPJ8

The monthly loan payment for a $60,000 loan with a $4,000 down payment, 13% interest rate, and a term of 60 months is approximately $1,289.49.

To calculate the monthly loan payment, we need to use the loan amount, down payment, interest rate, and term.

Loan amount: $60,000

Down payment: $4,000

Principal amount: Loan amount - Down payment = $60,000 - $4,000 = $56,000

Interest rate: 13% per annum (or 0.13 as a decimal)

Monthly interest rate: 13% / 12 = 0.0133 (approx.)

Term: 60 months (5 years)

Now, let's calculate the monthly loan payment using the formula for a fixed-rate loan:

Monthly payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

P = Principal amount

r = Monthly interest rate

n = Total number of payments

Substituting the values into the formula:

Monthly payment = $56,000 * (0.0133 * (1 + 0.0133)^60) / ((1 + 0.0133)^60 - 1)

Using a calculator, the approximate monthly loan payment comes out to be $1,289.49.

Therefore, the monthly loan payment for a $60,000 loan with a $4,000 down payment, 13% interest rate, and a term of 60 months is approximately $1,289.49.

For more questions on loan payment

https://brainly.com/question/25246413

#SPJ11

Answer: 62

Step-by-step explanation:

Given

p = 7, q = 2, r = 4

Solve

q ( 5p - r )

Substitute

(2) (5(7) - (4))

Simplify

(2) (35 - 4)

(2) (31)

62

Hope this helps!! :)

Please let me know if you have any questions

Answer:

start by putting in the y intercept, -4 on the y axis

then go up 5 and 1 right one to give your a slope of positive 5

Step-by-step explanation:

Answer:

512? Or you using the other way