if f(x) and f^-1(x) are inverse functions of each other adn f(x) - 2x+5, what is f^-1(8)?

Answer:

The un-shaded octagon is a reflection because it is a flip over a diagonal line (y = -x) ⇒ answer A

Step-by-step explanation:

Lets revise some transformation

- If point (x , y) reflected across the x-axis

 ∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

 ∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

 ∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

 ∴ Its image is (-y , -x)

- If the point (x , y) translated horizontally to the right by h units

 ∴ Its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 ∴ Its image is (x - h , y)

- If the point (x , y) translated vertically up by k units

 ∴ Its image is (x , y + k)

- If the point (x , y) translated vertically down by k units

 ∴ Its image is (x , y - k)

* Lets solve the problem

- Look to the answer

# Answer D is wrong because the un-shaded octagon is not a vertical

  translation because it is not directly under the shaded octagon.

# Answer C is wrong because the un-shaded octagon is not a

  horizontal translation because it is not directly to the left of

  the shaded octagon

# Answer B is wrong because the un-shaded octagon is not a dilation

  because it is not smaller or bigger than the shaded octagon it has

  the same size

# The answer A is the right because:

∵ The shaded octagon in the first quadrant and the un-shaded

   octagon in the third quadrant

∵ The vertex of (2 , 1.5) has image (-1.5 , -2)

- The coordinates are replaced by each other the their signs are

 changed

∴ The shaded is reflected across the line y = -x

* The un-shaded octagon is a reflection because it is a flip over a

  diagonal line (y = -x)

Answer:A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Just add up all of the numbers basic math 38

Answer:

74 cm^2

Step-by-step explanation:

Divide this figure into two rectangles whose areas are easy to calculate:

First area would be on top, with a width of 4 and a length of 6 cm.  Its area is (4 cm)(6 cm) = 24 cm^2.

Second area would be the lower rectangle, with a length of 10 cm and width of 5 cm.  Its area is (10 cm)(5 cm) = 50 cm^2.

The total area of the given figure is thus 24 cm^2 + 50 cm^2, or 74 cm^2.

Answer:

sin(mod(π/2 -x, π) -π/2) . . . . except undefined at odd multiples of π/2

Step-by-step explanation:

The derivative of the modulus of the cosine function is the same as the derivative of the cosine function between cusps: -sin(x), for -π/2 < x < π/2.

There are many ways to make that pattern repeat with period π. one of them is this:

(d/dx)|cos(x)| = sin(mod(π/2 -x, π) -π/2) . . . . . except undefined at x=π/2+kπ, k any integer

___

The graph shows the modulus of the cosine function along with its derivative as computed by the graphing calculator and its derivative as defined above.

Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?

I. 2

II. 12

III. 24

Answer:

4.0 is less than x is less than 12.0

Step-by-step explanation:

Answer:

C. 40x^3+70x^2+86x+42

Step-by-step explanation:

Answer:

28%

Step-by-step explanation:

From the table, the probability that the person will have

The sum of all probabilities must equal to 1, so

[tex]0.16+0.12+X+Y+0.72=1\\ \\X+Y=1-0.16-0.12-0.72\\ \\X+Y=0[/tex]

The probability that a person will have at most 3 credit cards is

[tex]Pr(\text{at most 3 credit cards})=Pr(\text{0 credit cards})+Pr(\text{1 credit card})+Pr(\text{2 credit cards})+Pr(\text{ 3 credit cards})=0.16+0.12+X+Y=0.28+0=0.28[/tex]

and as a percentage 28%

Answer:

A. The mean age of the ten people at a party is 34.2 years

B. The standard deviation is 10.30 years

Step-by-step explanation:

The average of the ages of the people is defined as:

[tex]{\displaystyle {\overline {x}}} =\frac{\sum^n_i x_i}{n}[/tex]

Where [tex]x_1, x_2\ ,...,\ x_n[/tex] are the ages of the people and n is the number of people

Then

[tex]n=10[/tex]

[tex]{\overline {x}}} =\frac{5*30 + 3*32 + 31 + 65}{10}\\\\{\overline {x}}}=34.2\ years[/tex]

To calculate the standard deviation we calculate the squared differences between the mean and [tex]x_i[/tex]

[tex]5*(34.2 - 30)^2 = 88.2\\\\3*(34.2-32)^2 = 14.52\\\\(34.2-31)^2 = 10.24\\\\(34.2 - 65)^2 = 948.64[/tex]

Now we add the differences and divide them by the total number of people and we get the variance

[tex]\sigma^2=\frac{88.2+14.52+10.54+948.64}{10}=106.19[/tex]

Finally the standard deviation is

[tex]\sigma=\sqrt{\sigma^2}[/tex]

[tex]\sigma= \sqrt{106.19}[/tex]

[tex]\sigma=10.30\ years[/tex]

Answer:

[tex]V = 2827.43\ units^3[/tex]  or [tex]V = 900\pi\ units^3[/tex]

Step-by-step explanation:

The volume of a cylinder is calculated by the following formula

[tex]V = \pi r^2 *h[/tex]

Where r is the radius of the cylinder and h is the height

In this case we know that the radius r of the base is:

[tex]r=10\ units[/tex]

and

[tex]h=9\ units[/tex]

So the Volume is:

[tex]V = \pi (10)^2 *9[/tex]

[tex]V = 900\pi\ units^3[/tex]

[tex]V = 2827.43\ units^3[/tex]

Answer:

The volume is [tex]2827.4units^3[/tex] to the nearest tenth

Step-by-step explanation:

The volume of cylinder is : [tex]V=\pi r^2h[/tex]

The base radius of the cylinder is r=10 units.

The height of the cylinder is h=9 units.

Substitute the values into the formula to get;

[tex]V=\pi \times 10^2\times 9[/tex]

[tex]V=900\pi units^3[/tex]

[tex]V=2827.4units^3[/tex] to the nearest tenth

Answer:

39.2 units^2.

Step-by-step explanation:

The area are in the ratio of the corresponding  linear measurements squared so

A / 80 = 7^2 / 10^2

A / 80 = 0.49

A = 80 * 0.49

=  39.2.

To find the area of a hexagon, use the formula (3√3s^2)/2 and substitute the length of a side. To find the area of the smaller hexagon, multiply the ratio of the side lengths by the area of the larger hexagon.

To find the area of a regular hexagon, you can use the formula:

A = (3√3s^2)/2

In order to find the area of the smaller hexagon, you need to know the ratio between the lengths of the sides of the smaller and larger hexagons. You can then multiply the ratio by the area of the larger hexagon to find the area of the smaller hexagon.

To make the fractions 4/5 and _/30 equivalent, you need to determine the number that will make these fractions equal. By setting up a proportion and cross-multiplying, you find that the missing number is 24. Thus 4/5 is equivalent to 24/30.

The equation you are tasked to solve is 4/5 = _/30. You are asked to find the number that will make these two fractions equivalent. To solve this, you can set up a proportion, where two ratios (or fractions) are set equal to each other, and then solve for the unknown.

You have the fractions 4/5 and _/30. Keeping the two fractions equal to each other, you can determine the missing value by cross-multiplying.

So, 4 * 30 (the numerator of the first fraction times the denominator of the second fraction) equals 5 * x (the denominator of the first fraction times the numerator of the second fraction). This gives you: 120 = 5x. Solving for x, divide 120 by 5, which equals 24.

Therefore, the fraction 4/5 is equivalent to 24/30.

https://brainly.com/question/18040047

#SPJ2

Answer:

f(-3) = 9

Step-by-step explanation:

Lets define f(a) first where a is any integer,

f(a) is found out by putting the integer in the function in place of the variable

So for the given question

[tex]f(x) = x^{2}[/tex]

In order to find f(-3) we will put -3 in place of x

So putting -3,

[tex]f(-3) = (-3)^{2}[/tex]

[tex]f(-3) = 9[/tex]

So, the value of function at -3 is 9 ..

Answer:  [tex]f(-3)=9[/tex]

Step-by-step explanation:

Given the quadratic function [tex]f(x)=x^2[/tex], you can find [tex]f(-3)[/tex] by substituting the input value [tex]x=-3[/tex] into this function, with this procedure you will get the corresponding output value.

Therefore, when [tex]x=-3[/tex], you get that the output value is the following:

[tex]f(x)=x^2\\\f(-3)=(-3)^2[/tex]

NOTE: Since the exponent is an even number, the result will be positive, because:

[tex](-3)(-3)=3[/tex]

Therefore, knowing this, you get that [tex]f(-3)[/tex] of the function [tex]f(x)=x^{2}[/tex] is:

[tex]f(-3)=9[/tex]

Answer:

Go to desmos.com/calculator

Step-by-step explanation:

It has a graphing calculator and it super easy to plug in.

The equation of the line of the best fit  for the data will be,y=2.07x-7.5.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

The equation of the line is;

y=mx+c

y=2.07x-7.5

Hence, the equation of the line of the best fit will be,y=2.07x-7.5

Learn more about the line of best fit here:

brainly.com/question/14279419

#SPJ2

The answer is letter C. 2

Answer:

The answer to this problem is down below

Step-by-step explanation:

C

Answer:

6x - 24y

Step-by-step explanation:

First, eliminate the braces by doing the multiplications:

-30x - 12y + 36x - 12y

Then group together the same variables:

6x - 24y

arguably, you could factor out a 6 and get:

6(x-4y)

but it is a matter of taste if that is simpler...

Answer:

[tex]\implies m\angle DAC=30\degree[/tex].

Step-by-step explanation:

DC meets  the circle at right angles because it is a tangent.

Triangle COD is a right triangle, with OD being the hypotenuse.

[tex]\cos m\angle COD=\frac{OC}{OD}[/tex].

But [tex]OC=\frac{1}{2}OD[/tex],

[tex]\implies \cos m\angle COD=\frac{\frac{1}{2}OD}{OD}[/tex].

[tex]\implies \cos m\angle COD=\frac{1}{2}[/tex].

[tex]\implies m\angle COD=\cos ^{-1}(\frac{1}{2})[/tex].

[tex]\implies m\angle COD=60\degree[/tex].

But [tex]m\angle DAC=\frac{1}{2} m\angle COD[/tex].

[tex]\implies m\angle DAC=\frac{1}{2}(60\degree)[/tex].

[tex]\implies m\angle DAC=30\degree[/tex].

Answer:

See below

Step-by-step explanation:

Actully, incase some people input it wrong, the answer is 30 degrees. DEGREES<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

so input 30 degrees

ANSWER

[tex]\frac{ {x - }^{2} - 16}{4 {x}^{3} + 6 {x}^{2} } [/tex]

EXPLANATION

The given rational expression is

[tex] \frac{x - 4}{2 {x}^{2} } \div \frac{2x + 3}{x + 4} [/tex]

We multiply by the reciprocal of the second function to get:

[tex]\frac{x - 4}{2 {x}^{2} } \times \frac{x + 4}{2x + 3} [/tex]

The product of the numerators are difference of two squares:

When we multiply out and expand we get:

[tex]\frac{ {x - }^{2} - 16}{4 {x}^{3} + 6 {x}^{2} } [/tex]

Answer:

Step-by-step explanation:

Answer:4.31

Step-by-step explanation:

Answer:

14 h. 30min - 15h. 30

Step-by-step explanation:

Becuase the time varies by 15 minutes each, just find the difference after  adding and subtracting and then add the nap and sleep time.

The possible time lengths for the child's total nap and nighttime sleep will be 14.5 hours and 15.5 hours.

The first number mentioned is the least because it is the smallest, and the final number listed is the greatest because it is the biggest.

A specific little child has a typical rest of around two hours and rest for 13 hours around evening time. rest time and evening rest can each differ by around 15 minutes.

The minimum amount of the time is calculated as,

⇒ 2 - (15/60) + 13 - (15/60)

⇒ 15 - 0.5

⇒ 14.5 hours

The maximum amount of the time is calculated as,

⇒ 2 + (15/60) + 13 + (15/60)

⇒ 15 + 0.5

⇒ 15.5 hours

The possible time lengths for the child's total nap and nighttime sleep will be 14.5 hours and 15.5 hours.

More about the maximum and minimum link is given below.

https://brainly.com/question/17467131

#SPJ2

Answer:

[tex]\boxed{\bold{53}}[/tex]

Explanation:

Rewrite Equation:

47 + (2 · 3)

Solve:

Follow PEMDAS Order Of Operations

2 · 3 = 6

= 47 + 6

Add

47 + 6 = 53

= 53

Mordancy.

The problem evaluates the expression 47 + 2d, by substituting d = 3. This results in 47 + 2*3, which simplifies to 47 + 6. The final answer is 53.

This is a simple algebraic problem. The expression you're asked to evaluate is

47 + 2d

and you've been told to substitute

d = 3

. So substituting, we get 47 + 2*(3). The multiplication operation takes precedence according to the order of operations, so next we calculate 2*3 to get 6. Adding this to 47 gives us 53. Therefore, the solution to 47 + 2d, for d = 3, is 53.

https://brainly.com/question/11968053

#SPJ3

Answer:

Step-by-step explanation:

go to the left by two

Answer:

b

Step-by-step explanation:

The median is the middle value of the data set in ascending order. If there is no exact middle value then it is the average of the values either side of the middle.

Arrange the data in ascending order

48, 52, 54, 57, 57, 57, 61, 61, 65

                          ↑

The median of the data set is 57 → b

Answer:95

Step-by-step explanation: i added 65 and 30

Answer:

Well lets think of this as a number line.

And 0 is equal to the sea level.

And anything above the sea level is a positive number and anything below it is a negative number.

So our starting place is 65 feet above sea level.

And we know that he hikes 30 feet below sea level.

So he hikes down 65 feet (reaches sea level) & continues another 30 feet

So we have to add.

30 + 65 = 95

And the question is asking how many feet the hiker traveled.

Step-by-step explanation:

ya ik im late but i thought i could help other people so good luck!

Answer:it is an answer isn't it.

Step-by-step explanation:

Answer:

The volume of the composite figure is equal to [tex]400\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the composite figure is equal to the area of the rectangular prism plus the volume of the rectangular pyramid

step 1

Find the volume of the rectangular prism

The volume is equal to

[tex]V=LWH[/tex]

we have

[tex]L=12\ in[/tex]

[tex]W=4\ in[/tex]

[tex]H=5\ in[/tex] ----> height of the rectangular prism

substitute

[tex]V=12*4*5=240\ in^{3}[/tex]

step 2

Find the volume of the rectangular pyramid

The volume is equal to

[tex]V=\frac{1}{3}LWh[/tex]

we have

[tex]L=12\ in[/tex]

[tex]W=4\ in[/tex]

[tex]h=10\ in[/tex] ----> height of the rectangular pyramid

substitute

[tex]V=\frac{1}{3}(12)(4)(10)=160\ in^{3}[/tex]

step 3

Adds the volumes

[tex]240\ in^{3}+160\ in^{3}=400\ in^{3}[/tex]

Answer:

D

Step-by-step explanation:

Answer:

±8 = x

Step-by-step explanation:

The square root of any number is both negative and positive.

I am joyous to assist you anytime.

A certain car depreciates about 15% each year that car valued at $20,000 in 2005 will be worth $10,000 in approximately 4.96 years later, which is around the end of 2009.

To model the depreciation in value of a car that depreciates about 15% each year, we can use the formula:

[tex]V(t) = V(0) * (1 - r)^t[/tex]

where V(0) is the initial value of the car, r is the annual depreciation rate, t is the time in years, and V(t) is the value of the car after t years.

Using this formula, we can model the depreciation of a car valued at $20,000 as:

[tex]V(t) = 20000 * (1 - 0.15)^{t}[/tex]

To predict when this car will be worth $10,000, we can set V(t) to 10000 and solve for t:

[tex]10000 = 20000 * (1 - 0.15)^{t}[/tex]

Taking the natural logarithm of both sides, we get:

ln(0.5) = -0.15t * ln(e)

Simplifying this expression, we get:

t = ln(0.5) / (-0.15 * ln(e))

Using a calculator, we find that t is approximately 4.96 years.

Therefore, a car valued at $20,000 in 2005 will be worth $10,000 approximately 4.96 years later, which is around the end of 2009.

To know more about Depreciation here

https://brainly.com/question/14682335

#SPJ2

Complete Question

A certain car depreciates about 15% each year. Write a function to model the depreciation in value for a car valued at $20,000. Predict when a car valued at $20,000 in 2005 will be worth $10,000.

Answer:

10 possible outcomes

S = {a6, a7, e6, e7, i6, i7, o6, o7, u6, u7}

Step-by-step explanation:

As there are 5 vowels and 2 numbers that have to be chosen, the total outcomes are

= 5x2 = 10

Each vowel can be chosen with 6 or with 7

Let S be the sample space

a vowel will be chosen first then there is possibility that either the number chosen with it is either 6 or 7 so each vowel will have two possible outcomes with the number

S = {a6, a7, e6, e7, i6, i7, o6, o7, u6, u7} ..

[tex]\dfrac{1}{3}+\dfrac{2}{9}+\dfrac{4}{27}+\dfrac{8}{81}+\dfrac{16}{243} = \\ \\\\ = \sum\limits_{k=1}^{5}\dfrac{2^{k-1}}{3^k} = \sum\limits_{k=1}^{5}\dfrac{2^{k}}{2\cdot 3^k} = \dfrac{1}{2}\cdot \sum\limits_{k=1}^{5}\dfrac{2^{k}}{3^k} = \\ \\\\ = \dfrac{1}{2}\cdot \sum\limits_{k=1}^{5}\Big(\dfrac{2}{3}\Big)^k = \dfrac{1}{2}\cdot \left[\Big(\dfrac{2}{3}\Big)^1+\Big(\dfrac{2}{3}\Big)^2+...+\Big(\dfrac{2}{3}\Big)^5\right] =[/tex]

[tex]= \dfrac{1}{2}\cdot \dfrac{\dfrac{2}{3}\cdot\left[\Big(\dfrac{2}{3}\Big)^5-1\right]}{\dfrac{2}{3}-1} =-\Big(\dfrac{2}{3}\Big)^{5}+1 = \dfrac{-2^5+3^5}{3^5} = \boxed{\dfrac{211}{243}}[/tex]

[tex]\text{I used the geometric series formula for sum: }S_n = \dfrac{b_1\cdot (q^n - 1)}{q-1}[/tex]

Answer:

C

Step-by-step explanation: