Which of these pairs of functions are inverse functions? A) f(x) = 2 ^ (x - 1) + 1 and g(x) = log2 (x - 1) - 1 b) f(x) = 1/2 * (ln(pi/2) - 1) and g(x) = 2e ^ (2x + 1) 1 c) f(x) = (4ln(x ^ 2))/(e ^ 2) g(x) = e ^ ((e ^ 2 * x)/8) d) f(x) = 10 ^ (x - 10) - 10 and g(x) = log10 (x + 10) - 10

Given :

A crafter is making a triangular flag.

She has two sides of length 24 inches and 36 inches.

To Find :

The length possibilities (in whole inches) for the third side.

Solution :

We know, the sum of two sides of any triangle is always greater than the length of the third side.

Let, third side is d.

So, d is always less than the sum of other sides i.e. ( 24 + 36 ) = 60 .

d < 60

Also, difference between the difference of length is always less than the side.

So, d > 36 - 24

d > 12

Therefore, the length possibilities for the third side is between 13 inches and 59 inches.

Answer:

-7x^3+8x^2+x-5

Step-by-step explanation:

We are simply adding the two functions:

f(x) + g(x) = (2x^2-5x^3+x-7) + (6x^2-2x^3+2) = 8x^2-7x^3+x-5 = -7x^3+8x^2+x-5

Answer:

368= 280-h

Step-by-step explanation:

Answer:

368 = 280 - h

Answer:

To plot an inequality, such as x>3, on a number line, first draw a circle over the number (e.g., 3). Then if the sign includes equal to (≥ or ≤), fill in the circle. If the sign does not include equal to (> or <), leave the circle unfilled in.

Answer:

To plot an inequality, such as x>3, on a number line, first draw a circle over the number (e.g., 3). Then if the sign includes equal to (≥ or ≤), fill in the circle. If the sign does not include equal to (> or <), leave the circle unfilled in.

Step-by-step explanation:

Answer:

31/5 or 6 1/5

Step-by-step explanation:

Answer:

B = 34.2°

C = 58.2° or 121.8°

c= 10.6

Step-by-step explanation:

Step 1

Finding c

We calculate c using Pythagoras Theorem

c²= a² + b²

c = √a² + b²

a= 8, b = 7

c = √8² + 7²

c = √64 + 49

c = √(113)

c = 10.630145813

Approximately c = 10.6

Step 2

Find B

We solve this using Sine rule

a/sin A = b/sin B

A = 40°

a = 8

b = 7

Hence,

8/sin 40° = 7/sin B

8 × sin B = sin 40° × 7

sin B = sin 40° × 7/8

B = arc sin (sin 40° × 7/8)

B ≈34.22465°

Approximately = 34.2°

Step 3

We find C

Find B

We solve this using Sine rule

b/sin B = c/sin C

B = 34.2°

b = 7

c = 10.6

C = ?

Hence,

7/sin 34.2° = 10.6/sin C

7 × sin C = sin 34.2 × 10.6

sin C = sin 34.2° × 10.6/7

C = arc sin (sin 34.2° × 10.6/7)

C = arcsin(0.85)

C= 58.211669383

Approximately C = 58.2°

Or = 180 - 58.2

C = 121.8°

Answer:

C=105.8 degrees. c=12

Step-by-step explanation:

Answer:

Number of game lose = 29 games (Approx)

Step-by-step explanation:

Given:

Winning part = 5/12

Total game = 49

Find:

Number of game lose

Computation:

Lose part = 1 - 5/12

Lose part = 7/12

Number of game lose = Total game x Lose part

Number of game lose = 49 x [7/12]

Number of game lose = 28.58

Number of game lose = 29 games (Approx)

They would lose 29 games if they play 49 games

They won 5 out of their first 12 games.

Hence the number of game lost in their first 12 games = 12 - 5 = 7  games

The rate at which they lose = 7 games / 12 games

Given that they played 49 games, hence:

Number of games lost = (7 games / 12 games) * 49 = 28.58

They would lose 29 games if they play 49 games

Find out more at: brainly.com/question/21105092

Answer: 18080!

Step-by-step explanation:400 x 450

1. Multiplying from the oneths place ( turning 45.2 into 450)

      2x0=0  2x0=0  2x4=8 = So the first answer is 800

2. Multiply from the tenths place

5 x 0 = 0   5 x 0 = 0   5 x 4 = 20 = the second answer is 2000

Multiplying the hundredths place

4 x 0 = 0  4 x 0 = 0   4 x 4 = 16  = The third answer is 1600

800 + 2000 + 1600 = 18080    Hope this helped! :)

I think the answer might be y=4

Answer:

4x+x=40

5x+40

x=8

8, 32

Step-by-step explanation:

Answer:

8 and 32 are the numbers

Step-by-step explanation:

4x + x = 40

4x + x= 5x

5x + 40

40/5= 8

x= 8

and

40-8= 32

x= 32

Answer:

Supplementary angles

Step-by-step explanation:

Definition of supplementary angles :

"If the sum of two adjacent angles is 180°, angles are said to be supplementary angles."

m∠ABC + m∠CBD = 90° + 90° [Given]

m∠ABC + m∠CBD = 180°

Therefore, both the angles are supplementary angles.

B, 1 2/5

Step-by-step explanation:

By subtracting that amount from 3, using a common facotor. You would get B.

Answer:

Full moon. I hope you have a good day!

Answer:

Any numbers when we add or subtract or divide or multiply that can give as -28

Step-by-step explanation:

For example, -9x3= -28

10-38=-28

Answer:

-28

Step-by-step explanation:

easy

Answer:

Most reasonable: 16°, 20° and 22°

If Emma is very short, 25°

Step-by-step explanation:

This is trigonometry using Tangent and arc-tan

Tan=opp/adj

The length of the adjacent is 20 yards. The opposite lengths given are the bottom, 6 yards and the top, 10 yards. Assuming Emma is of average height, it seems reasonable to subtract about 1.7 to 1.9 yards, the distance of her eyes above ground level, for accuracy. But that may not be necessary, given the range of angles.

I subtracted 1.8, about 5'6"

Calculating tangent from the top:

8.2/20 = .41. arc-tan .41= 22.3°

tangent for the bottom:

4.2/20= .21 arc-tan .21 = 11.8°

If you are using a scientific calculator, once you have the ratio of the opp to adj in decimal form, use the tan- key then the decimal to convert to degrees.

Answer:

j=x3 .......................

Answer:

27/64

Step-by-step explanation:

(7×16)+(5×64)64×16

=112+3201/024

=432/1024

Simplifying 432/1024, the answer is

=27/64

Answer:

a). 3 and 4/7

b). 3/10 and 4/13

Step-by-step explanation:

These are already in like fraction.

HOPE This Helps You

pls mark as brainliest

give thanks

Answer: -4 and 4

Step-by-step explanation:

In mathematics, the Pythagorean theorem, or Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

Answer:

leg a is 3 units and leg b is 8 units

Step-by-step explanation:

[tex]3^{2} + 8^{2} =73[/tex]

[tex]\sqrt{73} = 8.5[/tex]

so the hypotenuse is 8.5 hope this helps

Final Answer: [tex]b = -18[/tex]

Steps/Reasons/Explanation:

Question: Solve [tex]-21 = -9 + \frac{2}{3}b[/tex].

Step 1: Simplify [tex]\frac{2}{3}b[/tex] to [tex]\frac{2b}{3}[/tex].

[tex]-21 = -9 + \frac{2b}{3}[/tex]

Step 2: Regroup terms.

[tex]-21 = \frac{2b}{3} - 9[/tex]

Step 3: Add [tex]9[/tex] to both sides.

[tex]-21 + 9 = \frac{2b}{3}[/tex]

Step 4: Simplify [tex]-21 + 9[/tex] to [tex]-12[/tex].

[tex]-12 = \frac{2b}{3}[/tex]

Step 5: Multiply both sides by [tex]3[/tex].

[tex]-12[/tex] × [tex]3 = 2b[/tex]

Step 6: Simplify [tex]-12[/tex] × [tex]3[/tex] to [tex]-36[/tex].

[tex]-36 = 2b[/tex]

Step 7: Divide both sides by [tex]2[/tex].

[tex]-\frac{36}{2} = b[/tex]

Step 8: Simplify [tex]-\frac{36}{2}[/tex] to [tex]-18[/tex].

[tex]-18 = b[/tex]

Step 9: Switch sides.

[tex]b = -18[/tex]

~I hope I helped you :)~

Answer:

The inverse of function [tex]f(x)= (x+7)^5[/tex] is [tex]\mathbf{f^{-1} (x)=\sqrt[5]{x}+7}[/tex]

Option A is correct option.

Step-by-step explanation:

For the function [tex]f(x)= (x+7)^5[/tex], Find [tex]f^{-1} (x)[/tex]

For finding inverse of x,

First let:

[tex]y=(x+7)^5[/tex]

Now replace x with y and y with x

[tex]x=(y+7)^5[/tex]

Now, solve for y

Taking 5th square root on both sides

[tex]\sqrt[5]{x}=\sqrt[5]{(y+7)^5}\\\sqrt[5]{x}=y+7\\=> y+7=\sqrt[5]{x}\\y=\sqrt[5]{x}-7[/tex]

Now, replace y with [tex]f^{-1} (x)[/tex]

[tex]f^{-1} (x)=\sqrt[5]{x}+7[/tex]

So, the inverse of function [tex]f(x)= (x+7)^5[/tex] is [tex]\mathbf{f^{-1} (x)=\sqrt[5]{x}+7}[/tex]

Option A is correct option.

Answer:

like

Step-by-step explanation:

Answer:

[tex]x = 2\pi /3 + 2\pi n\\x= 4\pi /3 + 2\pi n[/tex]

Step-by-step explanation:

Radian: x = 2\pi /3 + 2\pi n\\x= 4\pi /3 + 2\pi n

Degree:  x = 120 + 360n , x = 240 + 360n

Answer:

0<x<5

Step-by-step explanation:

I assume based on the question that you are in a geometry class, so you should understand this. Based on the triangle inequality theorem, the sum of two sides of a triangle are greater than the third side. Using this, we can say that x+3+3 should be greater than 5. since 3+3 is already six regardless of what x is, we know that as long as x is greater than 0 it meets this requirement. Also, if 5 and 3 are added they should be greater. 5+3=8, so x must be less than 5 for the 5 and 3 sides to be greater.

Answer:

the slope is 2/3

Step-by-step explanation:

the line starts at 5(b) and to get a whole number point you go up 2 and over 3.

Answer:

2/3

Step-by-step explanation:

rise over run