What is the scale factor from figure A to B???

For all values of x

Yuliya22 [10]

Answer:

A.) gf(x) = 3x^2 + 12x + 9

B.) g'(x) = 2

Step-by-step explanation:

A.) The two given functions are:

f(x) = (x + 2)^2 and g(x) = 3(x - 1)

Open the bracket of the two functions

f(x) = (x + 2)^2

f(x) = x^2 + 2x + 2x + 4

f(x) = x^2 + 4x + 4

and

g(x) = 3(x - 1)

g(x) = 3x - 3

To find gf(x), substitute f(x) for x in g(x)

gf(x) = 3( x^2 + 4x + 4 ) - 3

gf(x) = 3x^2 + 12x + 12 - 3

gf(x) = 3x^2 + 12x + 9

Where

a = 3, b = 12, c = 9

B.) To find g '(12), you must first find the inverse function of g(x) that is g'(x)

To find g'(x), let g(x) be equal to y. Then, interchange y and x for each other and make y the subject of formula

Y = 3x + 3

X = 3y + 3

Make y the subject of formula

3y = x - 3

Y = x/3 - 3/3

Y = x/3 - 1

Therefore, g'(x) = x/3 - 1

For g'(12), substitute 12 for x in g' (x)

g'(x) = 12/4 - 1

g'(x) = 3 - 1

g'(x) = 2.

5 0

3 years ago

Solve ΔABC with ABC=51°, c=8 and a=11. Draw a diagram.

Rashid [163]

To solve a triangle means to obtain al the missing parts of the triangle.

<h3>How do you solve a triangle?</h3>

To solve a triangle means to obtain al the missing parts of the triangle. Now we have the following information;

<ABC = 51°

c = 8

a = 11

Then;

b^2 = a^2 + c^2 - 2acCos B

b^2 = (11)^2 + (8)^2 - [2 * 11 * 8 * cos 51]

b^2 = 121 + 64 - 55.38

b = 11.39

Now;

a/sinA = b/sinB

asinB = bsinA

sinA = asinB/b

sinA = 11 * sin 51/11.39

A = 48.6 or 49°

C = 180 - (49 + 51)

C = 80°

Learn more about triangles:brainly.com/question/2773823

#SPJ1

7 0

2 years ago

Can anyone help me on this ?

andrew-mc [135]

Answer:

37.9

Step-by-step explanation:

21.600/21.6+16.3=37.9

8 0

3 years ago

A 90-inch length of ribbon is to be cut into three pieces. The longest piece is to be 30 inches longer than the shortest piece,

Free_Kalibri [48]

Lets name the shortest piece a, the medium b and the longest c

Together they are 90inches
$a + b + c = 90$
The longest is 30 inches longer than the shortest
$c = a + 30$
The third piece is half the lenght of the longest
$b = \frac{c}{2}$

So if you place c=a+30 in the other 2 equasions you get

$a + b + (a + 30) = 90 = 2a + b + 30$
And
$b = \frac{30 + a}{2}$
Now if you put this 2 toghether u get
$2a + \frac{30 + a}{2} + 30 = 90$
Multyplied by 2
$4a + 30 + a + 60 = 180$
$5a = 90$
Meaning that a=18inches

Now that we have the lenght of a we put it in the previous equasion

$b = \frac{30 + 18}{2}$
So b=48/2 which means b=24inches

And together they must be 90 so

$18 + 24 + c = 90$

C=48inches

6 0

3 years ago

Determine the missing angle.

yarga [219]

Answer: 130 degrees

Explanation: 180-50=130

4 0

3 years ago