The inverse of f(x) is a function

Answer:

4.243

Step-by-step explanation:

To calculate the diagonal of a square, multiply the length of the side by the square root of 2:

d = a√2

d = 3√2=4.24264068

Answer:

The slope is 3/8

The y intercept is 75/8

Step-by-step explanation:

The slope is found by

m= (y2-y1)/(x2-x1)

   = (9-6)/(-1- -9)

   = (9-6)/(-1+9)

    =3/8

The y intercept is found by

y = mx+b where m is the slope and b is the y intercept

y = 3/8 x+b

9 = 3/8(-1) +b

Getting a common denominator

72/8 = -3/8 +b

Add 3/8 to each side

75/8 = b

The y intercept is 75/8

Answer:

3/8, 9 3/8

Step-by-step explanation:

y= mx+b

m=(y2-y1)/(x2-x1)

L (-9, 6) and M(-1, 9)

slope is:

y- intercept is:

Answer:

Eva swam 400 meters in 1/5 hour. Her average swimming speed was 2000 meters per hour.

Step-by-step explanation:

Eva swam 2/3*600 meters in 1/5 hour. 2/3*600=400. She swam 400 meters in  1/5 hour, which means she swims 5*400 meters in a whole hour. Eva swims 2000 meters per hour.

Answer: Wheres the table

Step-by-step explanation:

Answer:

Step-by-step explanation:

40

Answer:

[tex] 2 \sqrt{71} \: units[/tex]

Step-by-step explanation:

Given is a right angled triangle in which third side is the hypotenuse.

Therefore, by Pythagoras theorem:

[tex]thid \: side = \sqrt{ {15}^{2} + ( \sqrt{59} )^{2} } \\ \\ = \sqrt{225 + 59} \\ \\ = \sqrt{284} \\ \\ = \sqrt{ {2}^{2} \times 71 } \\ \\ = 2 \sqrt{71} \: units[/tex]

Answer:

y = 8.5x

Step-by-step explanation:

A proportional relation in one in which change of value of y with respect to change of value of x remains proportional. It can be represented by equation

y = kx, where k is constant of proportionality

________________________________________________

Let  the  relation be

y = kx

but we have a as 3 and b as 25.5

thus

substituting value of and a and b in y = kx , we have

25.5 = k*3

=> k = 25.5/3 = 8.5

Thus, equation which can represent this relation is y = 8.5x

Answer:

A

Step-by-step explanation:

Answer:

4^3

11>6

y>2

13-x

Step-by-step explanation:

4 is to the third power

11 is greater than 6 which means u use this sign >

y is greater than 2

13 subtract x

Answer:

(C) ¹/₂

Step-by-step explanation:

Given;

A standard number cube with the numbers 1 through 6 = 1, 2, 3, 4, 5, 6

The probability of rolling a number less than 4 = 3, 2, 1

The probability of rolling 3, P(3) = ¹/₆

The probability of rolling 2, P(2) = ¹/₆

The probability of rolling 1, P(1) = ¹/₆

Probability of rolling a number less than = P(3) or P(2) or P(1)

                                                                   = ¹/₆ + ¹/₆ + ¹/₆

                                                                   = ³/₆

                                                                   = ¹/₂

Therefore, the probability of rolling a number less than 4 is ¹/₂

Option (C) ¹/₂

Answer:

2/255

Step-by-step explanation:

In total, there are 18 books on the shelf.

The probability that person A will pick a novel is 6/18 = 1/3

There are now 5 novels and 17 total books on the shelf

The probability that person A then picks a mystery is 4/17.

There are now 3 mysteries and 16 total books on the shelf.

The probability that person B then picks a mystery is 3/16.

There are now 2 mysteries and 15 total books on the shelf.

The probability that person B then picks a poetry book is 8/15.

The probability that all these events occur back to back is the product of their individual probabilities. Therefore, the probability is:

1/3 * 4/17 * 3/16 * 8/15 = 2/255

Answer:

The inverse of the function is [tex]g (x)=-5x-4[/tex].

Step-by-step explanation:

The function provided is:

[tex]f^{-1}(x)=-\frac{1}{5}\ x-\frac{4}{5}[/tex]

Let us assume that:

[tex]y=f^{-1}(x)[/tex]

Then the equation will be:

[tex]y=\frac{-x-4}{5}[/tex]

To compute the inverse of the function substitute x as y and y as x.

[tex]x=\frac{-y-4}{5}[/tex]

Now solve for y as follows:

[tex]x=\frac{-y-4}{5}[/tex]

[tex]5x=-y-4[/tex]

[tex]y=-5x-4[/tex]

Thus, the inverse of the function is [tex]g (x)=-5x-4[/tex].

Answer:

The answer is "-5x-4"

Step-by-step explanation:

Given:

[tex]\bold{f^{-1} (x)=(-\frac{1x}{5}-\frac{4}{5})}[/tex]

solve the above equation:

[tex]\to f^{-1}(x)= \frac{-x-4}{5}\\\\\to f^{-1}(x)= -\frac{x+4}{5}\\[/tex]

Let

[tex]y= f^{-1} x= -(\frac{x+4}{5})\\\\[/tex]

inverse the above function:

[tex]\to x= -(\frac{y+4}{5})\\\\\to 5x= -(y+4)\\\\\to 5x= -y-4\\\\\to\boxed {y=-5x-4}\\\\[/tex]

Answer:

A) 3

Step-by-step explanation:

The range is the highest value - the lowest value from the data

The data given is 1,2,3,4

Highest value: 4

Lowest value: 1

So range = 4-1

= 3

Answer:

2.72

Step-by-step explanation:

the other one copied my answer from another website.

Explanation:

Move all the terms containing a to the left side of the equation

-0.5a+4.96=3.6

Subtract 4.96 from right side

-0.5a=3.6-4.96

Would be

-0.5a=-1.36

Divide each term by -0.5 and simplify

a= 2.72

[tex] \dfrac{126}{21} = \dfrac{2 \times 3 \times 3 \times 7}{3 \times 7} = 6[/tex]

Answer: 6

Answer:

A & D

Step-by-step explanation:

Vertical angles are equivalent angles made by intersecting lines. ISN and TSW, and TSN and ISW face each other and are equivalent.

Answer: Slope of 2.

Step-by-step explanation:

Start at where the line meets on the y-axis, -7. Then work your way upwards until you see the line align with a value of x, like (1,-5). Then you see a trend of it going up 2 units and over 1. 2/1 or 2 is your slope.

Answer:

[tex]33\%[/tex]

Step-by-step explanation:

To work out the percentage of the circle shaded blue, we first must work out the area of the whole circle.

Area of the whole circle = [tex]\pi r^2[/tex]

[tex]r=4+3+3\\\pi * (4+3+3)^2=\pi*10^2=100\pi[/tex]

Now we need to work out the area of the blue 2d torus, by finding out the area of the blue circle, then subtracting the area of the innermost white circle.

Blue shaded area = [tex]\pi(r_{0}{^2}-r_{1}{^2})[/tex]

[tex]r_0=4+3\\r_1 = 4\\\pi ((4+3)^2-(4)^2)= \pi (7^2-4^2)=33 \pi[/tex]

Now we have the total areas of each, we can work out the fraction of blue to non blue by dividing the blue area by the total area, and then working out the percentage by multiplying by 100.

[tex]\frac{33\pi}{100\pi}*100=\frac{33\pi}{\pi}=33\%[/tex]

Answer:

(2x+5)(x+4)

Step-by-step explanation:

After factoring we can find that it equals

(2x+5)(x+4)

Answer:

(2x +5) (x+4)

Step-by-step explanation:

2x*2+13x+20

(2x +   )(x+  )

Factoring 20 into 4 and 5  so we can get 13 in the middle

(2x +5) (x+4)

2*4 +5 = 13 for the middle term

Answer:

f⁻¹(f(6.022)) = 6.022

f⁻¹(-10) + f(-6) = -6 + -10 = -16

Step-by-step explanation:

f⁻¹(f(x)) = x

so  f⁻¹(f(6.022)) = 6.022

inverse function flips y and x coordinates so look at table where f(x)=-10 and read x so f⁻¹(-10) = -6

f⁻¹(-10) + f(-6) = -6 + -10 = -16

Answer:

X= 24

Step-by-step explanation:

Y was multiplied by 3 to equal 30, so same rules are applied and you multiply 8 by 3

Answer:

28 or 24 im not sure which

Answer:

its the fourth one on edg

Step-by-step explanation:

Answer:

The last option :)

Step-by-step explanation:

Answer:

a). A = -2x² + 200x

b). Widths = 40 feet and 60 feet

Step-by-step explanation:

It is given that length of the fencing material = 200 feet

a). Peg wants to cover the vegetable garden from three sides with the given fencing material.

If length of the garden = l

and width of the garden = x

l + x + x = 200

l + 2x = 200

l = (200 - 2x) feet

Therefore, area of the garden = Length × width

A = [tex](200-2x)\times x[/tex]

A = -2x² + 200x

b). Foe A = 4800 square feet,

4800 = -2x² + 200x

2x² - 200x + 4800 = 0

x² - 100x + 2400 = 0

x² - 60x - 40x + 2400 = 0

x(x - 60) - 40(x - 60) = 0

(x - 60)(x - 40) = 0

x = 40, 60 feet

Therefore, widths of Peg's garden will be 40 feet and 60 feet.

Answer:

7-x

Step-by-step explanation:

49 - x^2 is a perfect square so

it factors to :(7+x)(7-x)

since there is a negative in 49 - x^2, it would make sense that the answer would be a negative to get that negative answer in the first place (negative times a positive equals a negative)

Forgive me for my lame explanation :')

Answer:

The volume  is  191.3 [tex]cm^3[/tex]

Step-by-step explanation:

Recall that the formula for the volume of a pyramid is given by the formula:

[tex]Volume=\frac{B\,*H}{3}[/tex]

where B is the area of the pyramid's base, and H its height. So, in our case, the base is a square of length 7.5 cm, which gives 56.25 cm^2

Now, we use this value and the height 10.2 cm to find the volume:

[tex]Volume=\frac{B\,*H}{3}\\Volume=\frac{56.25\,*10.2}{3}\\Volume=191.25\,\,cm^3[/tex]

which rounded to the nearest tenth is: 191.3 [tex]cm^3[/tex]

Answer:

191.3

Step-by-step explanation:

Answer:

b & e

Step-by-step explanation:

The statements that are true of the given function are f(0)=3/2 and f(4)=7/2. This can be obtained by finding the function and checking the values of given in the question.

Given, f(-1/2)= -2

f(0)= 3/2

f(1)= -1

f(2)= 1

f(4)= 7/2

The function is of the form, f(x)= mx +b

where m is the slope of the line and b is the cutting point with the y axis.

For x=0, the value of the function is f(0)=3/2

⇒b=3/2   and m=1/2

∴ The function is f(x) = (1/2)x + 3/2

f(-1/2) = (1/2)(-1/2) + 3/2 =5/4

f(0) = (1/2)(0) + 3/2 = 3/2

f(1) = (1/2)(1) + 3/2 = 2

f(2) = (1/2)(2) + 3/2 = 5/2

f(4) = (1/2)(4) + 3/2 = 7/2

Hence the statements that are true of the given function are f(0)=3/2 and f(4)=7/2.

Learn more about functions here:

brainly.com/question/32813328

#SPJ2

Step-by-step explanation:

[tex]10x^2+2x-8\\2(5x^2+x-4)\\2(5x-4)(x+1)[/tex]

Answer:

[tex]2(5x-4)(x+1)[/tex]

You can check the answer by re-distributing the 2 and using the foil method :)

Answer:

(x+8)²-2=0

(x+8+√2)(x+8-√2)=0

x= - 8- √2 =  -9.41 lesser x

x= -8 + √2 = -6.59  greater x

Answer:

[tex]\mathrm{Decimal}:\quad x=-6.58578\ ,\:x=-9.41421[/tex]

Step-by-step explanation:

[tex]\left(x+8\right)^2-2=0\\\mathrm{Add\:}2\mathrm{\:to\:both\:sides}\\\left(x+8\right)^2-2+2=0+2\\Simplify\\\left(x+8\right)^2=2\\\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\mathrm{Solve\:}\:x+8=\sqrt{2}:\quad x=\sqrt{2}-8\\x+8=\sqrt{2}\\\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}\\x+8-8=\sqrt{2}-8\\\mathrm{Simplify}\\x=\sqrt{2}-8[/tex]

[tex]\mathrm{Solve\:}\:x+8=-\sqrt{2}:\quad x=-\sqrt{2}-8\\x+8=-\sqrt{2}\\\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}\\x+8-8=-\sqrt{2}-8\\\mathrm{Simplify}\\x=-\sqrt{2}-8\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=\sqrt{2}-8,\:x=-\sqrt{2}-8\\\mathrm{Decimal}:\quad x=-6.58578 ,\:x=-9.41421[/tex]

Answer:

(8-5)/(7-2)= 3/5

Step-by-step explanation:

proper fraction

Answer:

[tex]\dfrac{2s^3+136}{s}[/tex]

Step-by-step explanation:

Let the side length of the square base =s feet

Let the height of the box = h

Given that the volume of the box = [tex]34$ ft^3[/tex]

Volume of the box =[tex]s^2h[/tex]

Then:

[tex]s^2h=34$ ft^3\\$Divide both sides by s^2\\h=\dfrac{34}{s^2}[/tex]

Surface Area of a Rectangular Prism =2(lb+bh+lh)

Since we have a square base, l=b=s feet

Therefore:

Surface Area of our closed box[tex]= 2(s^2+sh+sh)[/tex]

[tex]S$urface Area= 2s^2+4sh\\Recall: h=\dfrac{34}{s^2}\\$Surface Area= 2s^2+4s\left(\dfrac{34}{s^2}\right)\\=2s^2+\dfrac{136}{s}\\$Surface Area in terms of length only=\dfrac{2s^3+136}{s}[/tex]