Mathematics High School

For all values of x, f(x) = x^2 + 1 and g(x) = x-5
(a) Show that fg(x) = x^2 - 10x + 26
(b) Solve fg(x) = gf(x)

Answers

Answer 1

Answer:

a)  f g(x) =  x³ - 5 x² + x -5

b) g(f(x) =  x³ - 5 x² + x -5

Step-by-step explanation:

Step(i):-

Given that f(x) = x² + 1 and g(x) = x-5

a)

      f(g(x)) = f(x-5) = (x-5)²+1 = x² - 10x +25 +1 = x² - 10 x +26

Step(ii):-

a) f g(x)  = f(x) g(x) = (x² + 1 )(x-5) = x³ - 5 x² + x -5

b)   g(f(x)  = g(x) f(x) = (x-5) (x²+1) =  x³ - 5 x² + x -5

Related Questions

In the diagram below of circle 0, diameter AB is
parallel to chord CD.
A. 110°
B. 70°
C. 55°
D. 35°
If mCD= 70, what is mAC?

Answers

Answer:

C. 55°

Step-by-step explanation:

The computation of mAC is shown below:

Given that

Diameter AB would be parallel to CD

McD = 70

Based on the attached diagram and the above information

mAC is

= (180 - 70) ÷ 2

= 55 degrees

hence, the correct option is third

Find AY. (fill in the blank)

Answers

Answer:

its 9a

Step-by-step explanation:

AY= 9a=4 should be the answer!!!

Principal: $4,000
Rate: 7.25%
Time: 8 years
How much money will need to be paid back to the bank for this loan?

Answers

Answer:

the money required to pay back to the bank for the loan is $7,002

Step-by-step explanation:

The computation of the money required to pay back to the bank for the loan is given below:

= Principal × (1 + rate of interest)^number of years

= $4,000 × (1 + 0.0725)^8

= $4,000 × 1.0725^8

= $7,002

Hence, the money required to pay back to the bank for the loan is $7,002

The following week, clare earns $75 from delivering newspapers and deposits it in her account. What will her account balance be then

Answers

Answer: Whatever the original balance was + 75

Step-by-step explanation:

You never gave a concrete value of what the balance of her account was before the new deposit so it is impossible for me to tell you the exact answer, but just add $75 to whatever it was before and you will be correct!  If you tell me the original value I would be more than happy to help you further :)  Have a great rest of your day!

Which fraction is equivilent to -2/3

Answers

Answer:

-4/6, -6/9,- 8/12,-10/15

Step-by-step explanation:

hope it helps pls mark brainliest

Simon makes a model of a boat, using a scale of 1 : 30


If the model has a height of 40 cm, find the height of the real boat.


Give your answer in metres.

Answers

Answer: 12 metres

Step-by-step explanation:

The scale factor used for the model is 1 : 30.

This means that for any 1cm on the model, the real boat would be 30 cm.

If the height is 40 cm on the model, the real boat will be 30 times that:

= 40 * 30

= 1,200 cm

A metre is equivalent to 100cm.

1,200 cm would therefore be:

= 1,200/100

= 12 metres

Jamal has $15.00 to spend at the concession
stand. He buys nachos for $7.50, and he wants to
purchase some Sour Straws for $1.50 each. How
many Sour Straws can Jamal purchase with the
money that he has? What is the inequality
A. 7.50-150x ≤ 15
B. 7.50+ 150x ≤ 15
C. 7.50- 150x < 15
D. 7.50+ 150x >15

Answers

i think it’s B. 7.50+1.50x<_15
B is the answer I think

About how many times smaller is 6.05 x 10than 1.23 x 10?

Answers

Answer:

girl ion even kno

Step-by-step explanation:

lol

Answer:

none

Step-by-step explanation:

6.05 * 10 is about 5 times greater than 1.23 * 10, so the question is not correct.

PLEASE ANSWER ASAP !!!!!

Answers

Answer:

11

Step-by-step explanation:

well you have to multiply and divide

Answer:

-4

Step-by-step explanation:

what does 40 centimeters equals in meters

Answers

Answer:

Its 0.4 meters!

Step-by-step explanation:

The law of cosines find the missing side or angle

Answers

Step-by-step explanation:

[tex] \cos(x) = \frac{11}{17} \\ x = 49.68[/tex]

Answer:

[tex] \cos(x) = adj \div hyp \\ = 10 \div 17 = 0.58 \\ x = \cos { - 1 = 54.5}^{} [/tex]

....

The divisor times the quotient plus the remainder will give you the dividend.

True or False

Answers

Answer: True


Explain:
Trueeeeeeeeeeeeeeeeeeeeeeeeee

When we rewrite a fraction as a decimal, are we changing the value of the fraction? hi so my teacher is asking this question on this mini quiz thing and i have a horrible headache and dont feel like doing that right now. so pls help me out

Answers

Answer:

No, you are not changing the value.

Step-by-step explanation:

Answer:

No, because then it would have different values and it wouldn't be rewriting it.

Step-by-step explanation:

Ex. 1/2. The decimal for this would be 0.5, right?

We aren't changing the value of the fraction. It is just another way of writing the value.

Hope this helped. :)

Also, I hope your headache goes away. Feel better soon. :D

You select a letter at random from the letters shown. Express the following probabilities as a fraction, a decimal, and a percent. letters A B C D E


A) P (vowel)

B) P (consonant)

Answers

Answer:

B

Step-by-step explanation:

ou select a letter at random from the letters shown. Express the following probabilities as a fraction, a decimal, and a percent. letters A B C D E

A) P (vowel)

B) P (consonant)

Answer:

the fraction would be 1/5 chance for every letter.

Step-by-step explanation:

there is one of each letter and there is 5 letters, therefore there is a 1/5 chance of selecting A, B, C, D, or E.

Which two represent 10 cube? *

Answers

Answer:

5 cube and 5 cube = 10 cube..??

Step-by-step explanation: ok so can i have brainiest plaease::)

How many solutions does 5x - 3 = 5 (x - 1) have?
O A. 1 Solution
OB. Exactly 2 Solutions
OC. No Solutions
OD. Infinitely Many Solutions

Answers

Answer:

C. No solutions

Step-by-step explanation:

5x - 3 = 5 (x - 1)

5x - 3 = 5x - 5

* so they have the same slope but different y-intercepts. So they would be parallel lines and they would never intercept meaning. No Solutions!

The correct answer is c.No solutions.So I would say c. No solutions

What is the area of the border,or the shaded region,of this figure in square inches HELP ILL GIVE BRAINLIEST PLEASEEE

Answers

Answer:

60 i think

Step-by-step explanation:

Basketball Arcade Game
You're buying the basketball arcade game for $4,500.00 with 5% tax. How much
will you pay all together? *

Answers

Answer:

$4,725

Step-by-step explanation:

multiply 4,500x0.07=225 add that to 4,500

the answer is $4,725 good luck!

Least to greatest
75% 0.071 0.54

Answers

Answer:

0.071, 0.54, 75%

Step-by-step explanation:

75% is 0.75, so it’s 0.071, 0.54, then 75% hope that helps and have a great day!

The answer is
75%= 75/100= 0.75
%= 100
Least = 0.0071, 0.54, 0.75=greatest
So the answer is 0.0071, 0.54, 0.75

OU
Prove algebraically that 0.5 =
Write your proof in the box, below, and use x in the working.
The concluding line has been written for you.
Therefore x =
olu

Answers

Answer:

The prove is explained below:

Step-by-step explanation:

The computation is given below:

Here we needed two equations

Let us assume x = 0.555 --------------- (1)

Now if multiplied it by 10 to the both sides

So, it would be

10x = 5.555............(2)

Now deduct equation 1 from equation 2 in order to remove the recurring decimals  

(10x - x) = (5.5555 - 0.5555 )

9x = 5 (divided the both sides by 9 )

So x = 5 by 9

Find the formula for the nth term of these sequences:

(a) 2, 5, 10, 17, 26, …….

(b) 4, 10, 20, 34, 52, ………

Part of a geometric sequence is given below:

,,,,, -1, ,,,, , ,,,,,, 64, ,,,,,

Where uₙ means the nth term, hence, u₂ = -1, and u₅ = 64.

Second term is -1, and the fifth term is 64. Calculate:

(a) The common ratio (r)

(b) The value of the first term (a) or u₁

(c) The value of the 10th term.

I need it by today!! and please for the people who type to get points please dont do it with me

Answers

A child makes a pitcher of fruit punch by completely dissolving fruit- flavoured powder in water. The child drinks a glass and decides the punch needs to be sweeter, so she stirs in more powder. This time the powder does not all dissolve, but settles on the bottom of the pitcher. A) Is the fruit-flavoured powder a pure substance or a mixture? * helpme anyone?

Two sides of a triangle measure 25 cm and
35 cm. Which of the following could be
the measure of the third side?
0 11 cm
O 6cm
O 8 cm
O 3 cm

Answers

First one I believe

Pls help I’ll mark u brain.

Answers

Answer:

the value of B is 12 times more than a

b = a * 12

Answer: 1. 12 times the value of a

2. B=12a

Step-by-step explanation:

0 and 0 indicate that it cannot be more(there are other ways)

and the ratio 2:24 simplifies to 1(a):12(b)

Ken bought 3 3/4 pounds of apples at the farmers' market. Abby bought 2 1/8 pounds of apples. How many pounds of apples did Ken and Abby buy?

Answers

5 7/8 pounds of apples

The new club sticker is in the shape of a triangle. It has a height of 16 inches and a base of 14 inches. The area of the club sticker is ____ square inches.

Answers

Answer:

112 square inches

Step-by-step explanation:

Area of a triangle is B*h/2

14 x 16 = 224

224/2 = 112

simplify 9x + 18(2x - 6) + 13

Answers

Answer:

45x-95

Step-by-step explanation:

Step-by-step explanation:

9x + 36x - 108 + 13

45x - 95

I NEED HELP
Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.


2,7,12,...

Answers

Answer:

Arthmetic, it is a 5 difference

Step-by-step explanation:

Brainliest pls

find the linear relationships ​

Answers

Answer:

There is no linear relationship in this problem.

Step-by-step explanation:

When plotting the coordinates on the graph, the line curves and slopes upwards. It is not a straight line.

Solve for x. any help would be appreciated thanks

Answers

The correct answer is x=5
You have to set them equal
9x+47=16x+12
-12 -12
9x+35=16x
-9x -9x
35=7x
/7 /7
5=x

what does 35q = 5 equal

Answers

Answer:

q = 1/7 = 0.143

Step-by-step explanation:

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