2. What is the composition f(g(x)) and the inverse of the composite (fog)
given f(x) = 2x + 3 and g(x) = x-5?​

Answer:

B. 73°

Step-by-step explanation:

The triangle is an isosceles triangle as it has 2 equal sides. This implies that the angles opposite to the two equal sides are of the same measure.

Therefore,

x = (180 - 34) ÷ 2

x = 146 ÷ 2

x = 73°

Answer:

c, a, d

Step-by-step explanation:

I think?

Answer:

Step-by-step explanation:

[tex] step - 1 : define[/tex]

[tex] \sin( {30}^{o} ) = \frac{a}{12} [/tex]

[tex] step - 2 : solve[/tex]

Answer:

The function [tex]y = x[/tex] is shifted downwards by 8 units

Step-by-step explanation:

Given

[tex]y = x[/tex]

Required

Determine the transformation that gives: [tex]y = x-8[/tex]

When a function f(x) is shifted by b units, the new function g(x) is g(x) = f(x) - b

In this case:

[tex]y = x[/tex]

[tex]b = 8[/tex]

So, the new function is:

[tex]y = x - b[/tex]

Substitute 8 for b

[tex]y = x - 8[/tex]

Hence, the function is shifted 8 units downward

Answer:

16.21 degrees

f(x) = 1/x

for rational function

Answer:

11/25

Step-by-step explanation:

Answer:

11/25

Step-by-step explanation:

44/100  →   22/50→   11/25

Answer:

108 calories per cup

Step-by-step explanation:

Answer:

6.28 m^2  

Step-by-step explanation:

4^2 x Pi=area of full circle

45 degree segment =1/8 of a full circle

16x3.14159=50.27 m^2                  area of full circle

50.27/8=6.28 m^2             area of 1/8 circle

Answer:

90 square meters

Step-by-step explanation:

Formula for sector area--- SECTOR AREA=r^2 a/2

*Multiply the central angle by the radius squared- 45×4=180squred meter

*then, Divide by 2- 180÷2=90

Answer:

112 ft.

Step-by-step explanation:

This shape is a trapezoid. To find the area of a trapezoid, use the formula: [tex]\frac{b_{1} + b_{2} }{2} h[/tex]. First find base one. The shape in the middle is a square, so the top side of the trapezoid will be worth 8 ft as well. Now add the two bases 8 + 20 to get 28 and then divide by 2 to get 14. Now multiply 14 by the height (8). 14 x 8 is 112 ft.

Hope it helps and is correct!

Answer:

Answer:

ANS;;;; 45 ...........................

Answer:

[tex]g(9) = \frac{2048}{3}[/tex]

Step-by-step explanation:

Given

[tex]g(x) = \frac{1}{6}(8)^{x-5}[/tex]

[tex]x = 9[/tex]

Required

Solve

Substitute 9 for x in [tex]g(x) = \frac{1}{6}(8)^{x-5}[/tex]

[tex]g(9) = \frac{1}{6}(8)^{9-5}[/tex]

[tex]g(9) = \frac{1}{6}(8)^{4}[/tex]

Remove bracket

[tex]g(9) = \frac{1}{6}* 8^4[/tex]

[tex]g(9) = \frac{1}{6}* 4096[/tex]

[tex]g(9) = \frac{1* 4096}{6}[/tex]

[tex]g(9) = \frac{4096}{6}[/tex]

Simplify fraction

[tex]g(9) = \frac{2048}{3}[/tex]

9514 1404 393

Answer:

  21.8 cm

Step-by-step explanation:

A useful way to write the Law of Sines relation when solving for side lengths is ...

  a/sin(A) = b/sin(B)

Then the solution for 'a' is found by multiplying by sin(A):

  a = sin(A)(b/sin(B)) = b·sin(A)/sin(B)

__

We need to know the angle A. Its value is ...

  A = 180° -75° -31.8° = 73.2°

Then the desired length is ...

  a = (22 cm)sin(73.2°)/sin(75°) ≈ (22 cm)(0.9573/0.9659)

  a ≈ 21.8 cm

_____

I like to use the longest side and largest angle in the equation when those are available. That is why I chose 75° and 22 cm.

Answer:

.

Step-by-step explanation:

Answer:

da answerr is six

if DF is 6 and all sides are equal in length the EF side is going to be 6 as well

Answer. 32

Step-by-step explanation:

20+4+2+6=32

Answer:

1:4:1.5

Step-by-step explanation:

Answer:

(-1,-1),(1,-4)

Step-by-step explanation:

it is the wright answer

Answer:

1,2,4

Step-by-step explanation:

I just took the test and got it right and its the only logical answer.

If ΔXYZ, after reflection and dilation by a scale factor of 1/2, ΔX'Y'Z' is created, the following would be true:

1. △XYZ ~ △X'Y'Z'

2. AngleXZY ≅ AngleY'Z'X'

4. XZ = 2X'Z'

Thus, if ΔXYZ, after reflection and dilation by a scale factor of 1/2, ΔX'Y'Z' is created, the following would be true:

1. △XYZ ~ △X'Y'Z'

2. AngleXZY ≅ AngleY'Z'X'

4. XZ = 2X'Z'

Learn more about dilation on:

https://brainly.com/question/10253650

Answer:

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c[/tex]

Step-by-step explanation:

Given

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx[/tex]

Required

Solve

Let

[tex]u = \frac{x^2}{4}[/tex]

Differentiate

[tex]du = 2 * \frac{x^{2-1}}{4}\ dx[/tex]

[tex]du = 2 * \frac{x}{4}\ dx[/tex]

[tex]du = \frac{x}{2}\ dx[/tex]

Make dx the subject

[tex]dx = \frac{2}{x}\ du[/tex]

The given integral becomes:

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{x}{x^4 + 16}} \, * \frac{2}{x}\ du[/tex]

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{1}{x^4 + 16}} \, * \frac{2}{1}\ du[/tex]

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du[/tex]

Recall that: [tex]u = \frac{x^2}{4}[/tex]

Make [tex]x^2[/tex] the subject

[tex]x^2= 4u[/tex]

Square both sides

[tex]x^4= (4u)^2[/tex]

[tex]x^4= 16u^2[/tex]

Substitute [tex]16u^2[/tex] for [tex]x^4[/tex] in [tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du[/tex]

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16u^2 + 16}} \,\ du[/tex]

Simplify

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16}* \frac{1}{8u^2 + 8}} \,\ du[/tex]

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{2}{16}\int\limits {\frac{1}{u^2 + 1}} \,\ du[/tex]

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du[/tex]

In standard integration

[tex]\int\limits {\frac{1}{u^2 + 1}} \,\ du = arctan(u)[/tex]

So, the expression becomes:

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du[/tex]

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(u)[/tex]

Recall that: [tex]u = \frac{x^2}{4}[/tex]

[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c[/tex]

Answer:

Step-by-step explanation:

The teacher has 7/8 pounds of clay given.

gives out 1/16 per station

7/8= 0.875 pound

7/8 / 1/16 pound= 14 maximum stations

14 stations divided by 2 classes = 7 in each room

Answer:

9 cans of soup and the 4 frozen dinners were purchased

Step-by-step explanation:

Let x represent the number of cans of soup purchased.

Let y represent the number of frozen dinners purchased.

Lincoln purchased a total of 13 cans of soup and frozen dinners. This means that

x + y = 13

Each can of soup has 250 mg of sodium and each frozen dinner has 550 mg of sodium. The 13 cans of soup and frozen dinners which he purchased collectively contain 4450 mg of sodium. This means that

250x + 550y = 4450 - - - - - - - - -1

Substituting x = 13 - y into equation 1, it becomes

250(13 - y) + 550y = 4450

3250 - 250y + 550y = 4450

- 250y + 550y = 4450 - 3250

300y = 1200

y = 1200/300

y = 4

Substituting y = 4 into x = 13 - y, it becomes

x = 13 - 4 = 9

Answer:

I believe that 15% of 34.95 would be 5.24

Step-by-step explanation:

Answer:

1.7254

Step-by-step explanation:

(3.9)(0.27)+0.6724

= 1.053+0.6724

= 1.7254

hope I helped!!

Answer:

Your answer is A

Step-by-step explanation:

The graph of y = f(x) will shift left 2 units.

Answer:

y = -x + 1

Step-by-step explanation:

y=mx+b

m:slope= rise/run, the line goes down 1 and over 1 so it would be -1/1 which is -1

b:y-intercept: the line crosses the y-axis at 1

plug in m=-1 and b=1 into y=mx+b

y=-1x+1

y=-x+1

Answer:

= -1/2

Step-by-step explanation:

F=1/4(-2)

F=-1/4(2)

F=-1(2)/4

F=-2/4

F= -1/2