Given that for all values of x,
f(x) = 3x + p
g(x) = px + 4
and fg(x) = 6x + 9
where p and q are constants.
Work out the values of p and q.

Answers

Answer 1
Question, where is q in the equations? Do you mean x?
Answer 2

The value of p is 2.

The value of q is 14

What is a function?

function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Two functions:

f(x) = 3x + p

g(x) = px + 4

Now,

f(g(x)) = 6x + 9

This means,

3(g(x)) + p = 6x + q

Substituting g(x) = px + 4.

3(px + 4) + p = 6x + q

3px + 12 + p = 6x + q

3px + (p - q) = 6x - 12

This means,

3p = 6

p = 2

p - q = -12

2 - q = -12

q = 2 + 12

q = 14

Thus,

p is 2 and q is 14.

Learn more about functions here:

https://brainly.com/question/28533782

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Related Questions

BRAINLIEST!!! Please help (ASAP)!!! (15 pts)
The average weight of adult males is 184.5 pounds, with a standard deviation of 19 pounds and a normal distribution. Micah weighs 203.4 pounds. What is the standardized score for Micah's weight?
a. -0.01
b. 0.01
c. -0.99
d. 0.99
e. Unable to determine the standardized score

Answers

Answer:

0.99

Step-by-step explanation:

z=x-mean/standard dev = 203.4-184.5/19 = 0.99

Recall that two angles are complementary if the sum of their measures is 90°
Find the measures of two complementary angles if one angle is 14º more than three times the other angle.

Answers

I’m I think 79% but I’m probably way off

Can you help me please

Answers

2.5

Step-by-step explanation:

Multiply 2.5 by y and you get x

what is 7.5% of 61.13​

Answers

Answer:

Step-by-step explanation:

61.13*7.5%=4.58

61.13+4.58=65.71

9. A woman makes 15% more than her husband. If her husband's annual salary is $45,000, what
is the combined annual income of the couple?

Answers

Answer:

6750

Step-by-step explanation:

15 ÷100×45000=6750

Use the graph to find the x-intercept for the equation ý +2 Graph: Y + 2 = 2(x+3)
= 2(x + 3).
ty
X
y
6
The x-intercept is
4
2
-4
-6
-2
4
6
-2
-4
16
Draw
y
Click or tap the graph to plot a point.

Answers

The x-intercept of the graph is given as (-2, 0)

The intercept of a line

Given the equation of a line expressed as:

y + 2 = 2(x+3)

We are to find the x-intercept of the line. The x-intercept occur at the point where y = 0

Substituting y = 0 into the equation will give;

y + 2 = 2(x+3)

0 + 2 = 2(x+3)

2 = 2x + 6

2x = -4

x = -2

Hence the x-intercept of the graph is given as (-2, 0)

Learn more on intercept here; https://brainly.com/question/24212383

Which Student is walking Faster E or F

Answers

Answer:

E

Step-by-step explanation:

the steeper the slope the faster the something

E sorry dude i may be wrong

What’s the value for y? PLEASE!!

Answers

Answer:

the answers Is c or 13 because 3*5=15-2=13

Find the area of a rectangle whose width is (x + 2) and whose length is (x + 3) .

Answers

Answer:

x² + 5x + 6

Step-by-step explanation:

x × x + 2x + 3x + 6

= x² + 5x + 6

−4(32x−12)=−15 as distribute property

Answers

rawr you should know that because that is very easy

Graph this compound inequality: I < 8.3 or 2 > 9.8
7
8
8
9
10
Drag a point to the number line.

Answers

Answer:

Here is a picture of the answer. I hope this helps!

Step-by-step explanation:

The graph of compound inequality [tex]x<8.3[/tex] and [tex]x>9.8[/tex] is shown in attached graph.

A compound inequality contains at least two inequalities that are separated by either and or "or".

Given compound inequality:

                                [tex]x<8.3[/tex] or [tex]x>9.8[/tex]

Above inequalities are shown in below attached graph.

Learn more:

https://brainly.com/question/11316045

what is the answer to 2x3=1x-4

Answers

Answer: x=10

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

Which expression represents an irrational number? A 0.18 repeating, b 2/3 ,

Answers

Answer:

I think it's A hope this helps

A cus it definitely ain’t B

Find the value of x that makes m
|| n

Answers

Answer:

X= 15

Step-by-step explanation:

3x - 15 + 150 = 180

X = 15

X=15 bdbdhsbbsbdbdbsbsbbsbsbsbsbsbbsbsbsbsbsbsbbsbsbsbsbsbbsbsbsbsbbsbsbsbsbbsbsbsbsbsbsbsbbsbsbsbsbsbbbs

10 points
What are a few things that help you focus while doing an assignment? (I need help focusing on a math test)
Please dont say unlogical answers, thanks!

Answers

Answer:

chewing gum can help

also taking breaks every time you feel like you need one, make sure you eat before doing a test as-well

Step-by-step explanation:

Answer:

i like to make sure i have a healthy breakfast and a big glass of water, that always helps. sometimes going for a 30 minute walk could help, listening to music also helps me

Step-by-step explanation:

hope this helps ;)

The table above shows how long Mariana worked on homework each day of the week.
How many total minutes did Mariana work on homework during the week? Show your work.

Answers

Answer:

443

Step-by-step explanation:

2 hours = 120 min

1,920/60= 32 min

120+98+134+32+59= 443 total minutes

The time spent to travel a certain distance varies inversely as a car's speed. If it takes 5½ hours to travel a certain distance at 60 miles per hour, how long will it take to travel the same distance at 50 miles per hour?

Select one:
a. 6.6 h
b. 6.9 h
c. 4.6 h
d. 4.2 h

Answers

Answer:

6.6h

Step-by-step explanation:

So it takes 5.5 hours going at a speed of 60 miles per hour, multiply these two and we get a distance of 330 milesUse this distance to find the time if speed is 50 miles per hour, so time is derived by dividing the distance by the speed330 miles divide by 50 miles per hour gives 6.6 hours

Arya travels at an average speed of 30 mph for 40 miles. Without stopping, Arya then travels 120 miles in 2.25 hours. Find her average speed for the entire journey to 2 dp.

Answers

Answer:

44.69 mph

Step-by-step explanation:

Speed = distance/time

Distance is:

40 miles + 120 miles = 160 miles

Time is:

40/30 + 2.25 = 3.58 hours

Average speed:

160/3.58 = 44.69 mph

If A(x) = -7x^2- 3, B(x) = - 4x +3 and C(x) = 5x² + 3x, form a simplified expression for B(x) – A(x).​

Answers

Answer:

aw baby naw that not cool

Step-by-step explanation:

During the life of a $2500 loan, the interest paid is $318.75. If the interest rate is 8.5%, how long was the loan?

Answers

Answer:

1.5 years

Step-by-step explanation:

Simple Interest I = PRT

Principal = 2500, Rate R= 8.5%, SI = 318.75, T = ?

Now, substituting the above value

318.75 = 2500*0.085 * T

T = 318.75 / 2500*0.085 years

T = 318.75 / 2500*0.085 years

T = 318.75 / 212.5 years

T = 1.5 years

how do I put 1000,000+200,000+50,000+4,000+300+80+9 in expanded form

Answers

If you mean making them a regular number, you add them all.

_______________

But, the expanded form of this is

1,000,000 - Millions Place

200,000 - Hundred Thousands

50,000 -Ten Thousands

4,000 -Thousands

300 - Hundreds

80 -Tens

9 - Ones

I hope this helps, if it doesn't let me know and I'll do my best.

3x4 + 20x3 + 14x2 + 170 + 30 and x + 6?

Answers

Answer:100x+200x+6= x+6 slope=1

11) maths question equations

Answers

Answer:

x= 12

Step-by-step explanation:

Multiply everything by 12 (making it easier to solve) to get

6x + 4x = 3x + 84

Simplify to get

7x = 84

Solve for x and get x=12

Answer
X=12
Explanation

Given: If you live in Orlando, then you live in Florida.

Given: Morgan does not live in Orlando.

Conclusion: Morgan does not live in Florida.

Is this sentence Law of Detachment, Law of syllogism, or invalid

Answers

Answer:

The law of detachment and syllogism is valid here

Explanation:

The law of detachment and syllogism is associated with inductive reasoning. This law states that a conclusion is valid if the premise or hypothesis is valid, therefore if a then b. In others a results in b.

The law of detachment is denoted

[(a→b)∧a]→b

The law of syllogism derives from the law of detachment. Syllogism says that if a results in b and b results in c, then a results in c. In other words since a causes b and b causes c, then if a then c.

It is denoted

[(a→b)∧(b→c)]→(a→c)

In the above example, given: If you live in Orlando, then you live in Florida

Morgan does not live in Orlando, therefore it is concluded that he does not live in Florida

please help asap nobody else has answered my other questions. thanks! answer question 2 please!

Answers

Answer:

15

Step-by-step explanation:

To find the y intercept set x=0

You are given two points: (7,-6)(-4,27)

y=mx+b

y2-y1=x2-x1

x1=7

y1=-6

x2=-4

y2=27

27-(-6)/-4-7=27+6/-4-7=33/-11=-3

y=-3x+b

-6=-3(7)+b

-6=-21+b

+21 +21

b=15 so, y=-3x+15

PLUG IN O TO THAT EQUATION

y=-3(0)+15

Your y intercept would be 15

Luka wants to buy peaches and a watermelon . Peaches cost $2.99 a pound, and watermelon costs $4.50. he has $15.00 to spend

Answers

Answer:

2.99: 3   4.50: 5

Step-by-step explanation:

5 plus 3 equals 8.

If he has 15.00 to spend he would get 7 dollars as change.

10 cm
5cm
5 cm
10 cm
10+10+5+5=
Find the perimeter

Answers

Answer:

30cm

Step-by-step explanation:

10+10=20

5+5=10

10+20=30

Answer:

30 cm

Step-by-step explanation:

10+5+10+5=30 cm

An ice cream factory makes 230 quarts of ice cream in 5 hours. What is the constant of proportionality?
A:41
B:46
C:225
D45

Answers

Answer:

C

Step-by-step explanation:

Ashley has a bag with 26 tiles, each with the letter of the alphabet. Ashley thinks our six tiles. What is the probability that the tile spell out her name?

Please answer ASAP

Answers

Answer:

a 6 out of 26 chance

Step-by-step explanation:

because when you grab 6 tiles they have to be the same exact letters which is pretty rare, plus there is 26 letters in the alphabet and well... that makes it a 6 out of 26 chance.

The function f is continuous on the interval (0,9) and is twice differentiable except at x = 6, where the derivatives do not exist (DNE). Information about the first and second derivatives of f for some values of x in the interval (0,9) is given in the table above. Which of the following statements could be false?

Answers

Answer:

The statement that could be false is;

(C) The function has a relative minimum at x = 6

Step-by-step explanation:

The given parameters are;

The function is continuous in the interval 0 ≤ x ≤ 9

The function is not differentiable at x = 6

f prime (x) = Negative for 4 < x < 6, and positive for 6 < x < 8

Therefore, at x = 6, the function is vertical

The statement that could be false is that the function has a relative minimum at x = 6.

A continuous function f(x) does not have discontinuity at any point

The statement that could be false is (c). The function f has a relative minimum at x = 6.

The interval is given as:

Interval = (0,9)

From the question, we understand that the function is not differentiable at x = 6.

This means that the function may or may not have a relative minimum at x = 6.

Hence, the statement that could be false is (c).

Read more about continuous functions at:

https://brainly.com/question/21447009

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