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____ [38]
3 years ago
8

Let $f(x) = 2x + 7$ and $g(x) = 3x + c$. find $c$ if $(f \circ g)(x) = (g \circ f)(x)$ for all $x$.

Mathematics
1 answer:
boyakko [2]3 years ago
5 0
Let me just rewrite the details in a more understandable manner

f(x) = 2x + 7
g(x) = 3x + c
f( g(x) ) = g( f(x) )

Proceeding to the problem, we have to find the value of c by making use of the relationship written by the third equation. The notation f( g(x) ) means that you have to replace x with g(x). So, you would have incorporate one equation to the other, and vice versa. By equating them, we can determine x. Let us start with f( g(x) ) .

f( g(x) ) = 2(3x + c) + 7
f( g(x) ) = 6x + 2c + 7

Next, we do the similar thing to g( f(x) ).
g( f(x) ) = 3(2x+7) + c
g( f(x) ) = 6x + 21 + c

Then, we equate both simplified equations
6x + 2c + 7 = 6x + 21 + c

Let's simplify further by placing c on one side, and the rest on the other side:
2c - c = 6x - 6x + 21 - 7
c = 14
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Where’s the question.
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I need some help on this question. Segment LM is the midsegment of trapezoid ABCD. AB=48, and DC=88. What is LM? I am not sure h
agasfer [191]
AB=48, DC=88

48+88=136
136÷2=68

Answer: LM=68
Remember that the length of the mid segment in a trapezoid is half the sum of the base lengths.
4 0
3 years ago
The minor arc measures of circle Z are shown in the figure.
DerKrebs [107]

The completed statement are:

  • Angle UZT is congruent to angle TZY.
  • Angle VZW is congruent to angle YZX.

<h3>What is the angle about?</h3>

Part A:

Angle UZT is congruent to angle TZY.

Using the image attached figure, we can see that:

∠UZT = 54°

∠TZY = 54°

Hence one can say that ∠TZY = ∠UZT are both congruent angles.

Part B:

Angle VZW is congruent to angle YZX.

Using the image attached attached, we can see that:

∠VZW = 71°

∠YZX = 71°

Hence, ∠YZX = ∠VZW are both  regarded as congruent angles .

Therefore, The completed statement are:

  • Angle UZT is congruent to angle TZY.
  • Angle VZW is congruent to angle YZX.

Learn more about Angles from

brainly.com/question/14684194

#SPJ1

6 0
1 year ago
In a recently administered iq test, the scores were distributed normally, with mean 100 and standard deviation 15. what proporti
iragen [17]

To solve for proportion we make use of the z statistic. The procedure is to solve for the value of the z score and then locate for the proportion using the standard distribution tables. The formula for z score is:

z = (X – μ) / σ

where X is the sample value, μ is the mean value and σ is the standard deviation

 

when X = 70

z1 = (70 – 100) / 15 = -2

Using the standard distribution tables, proportion is P1 = 0.0228

 

when X = 130

z2 = (130 – 100) /15 = 2

Using the standard distribution tables, proportion is P2 = 0.9772

 

Therefore the proportion between X of 70 and 130 is:

P (70<X<130) = P2 – P1

P (70<X<130) = 0.9772 - 0.0228

P (70<X<130) = 0.9544

 

Therefore 0.9544 or 95.44% of the test takers scored between 70 and 130.

6 0
3 years ago
Help me out hunnys ❤️
Alenkinab [10]

Answer:

g(x)=3(x+3)^2-8

Step-by-step explanation:

You can solve by using these acronyms.


H. orozontal.

I. nside.

O. pposite.


Meaning that a horozontal translation would be written inside the parenthesis and the poopsite sigh you would usually (Ex. Left is usually negitave but in this case it is positive).


The other acronym is,


V. erticle.

O. utside.

S. ame.


Meaning for a vrerticle translation the number would go on the outside of the parenthesis and tha sign would be normal (Ex. Negitave would be left and positive would be right).


For this one use H.I.O sinse you are moving on a horozontal plain. You are only working with the (x-2) nothing else matters.


Since you are moving left the number will move up 3 hence the O.


<h2><u>This transformation leaves you with g(x)=3(x+3)^2-8</u></h2>



3 0
2 years ago
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