Mathematics College

Given f(x) =1/(x^2+4) and g(x) = square root (x+1) Find g(f(x)).

Answers

Answer 1

Step-by-step explanation:

all steps are in the picture above.

Note:if you have any question let me know about.thanks

Given F(x) =1/(x^2+4) And G(x) = Square Root (x+1) Find G(f(x)).

Answer 2

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Answer:

g(f(x)) = √((x²+5)/(x²+4))

Step-by-step explanation:

[tex]g(f(x))=g(\dfrac{1}{x^2+4})=\sqrt{\dfrac{1}{x^2+4}+1}=\sqrt{\dfrac{1+x^2+4}{x^2+4}}\\\\\boxed{g(f(x))=\sqrt{\dfrac{x^2+5}{x^2+4}}}[/tex]

I prefer this compact form, but some may want the denominator rationalized. This means the expression becomes ...

[tex]g(f(x))=\sqrt{\dfrac{(x^2+5)(x^2+4)}{(x^2+4)^2}}\\\\\boxed{g(f(x))=\dfrac{\sqrt{x^4+9x^2+20}}{x^2+4}}[/tex]

Related Questions

help me plz now plz help me asap

Answers

[tex]\\ \sf\longmapsto 0.49=\dfrac{49}{100}[/tex]

[tex]\\ \sf\longmapsto 0.093=\dfrac{93}{1000}[/tex]

[tex]\\ \sf\longmapsto 0.021=\dfrac{21}{1000}[/tex]

[tex]\\ \sf\longmapsto 0.103=\dfrac{103}{1000}[/tex]

Determine the range of the following graph:
y
12
11
10
9
8
7
2
1
-12-11-10-9-8-7-6-5-4-3-2-11
1 2 3 4 5 6 7 8 9 10 11 12
- 2
-3
-4
-8
-9
-10
-11
-12

Answers

Answer:

r = (-4,9]

Step-by-step explanation:

hope this will help

Answer:

-4<y≤2

Step-by-step explanation:

The range of a graph is the range of the y values.

Given f(x) = x − 7 and g(x) = x2 .

Find g(f(4)).

g(f(4)) =
]

Answers

9514 1404 393

Answer:

g(f(4)) = 9

Step-by-step explanation:

Put the argument value where the variable is and do the arithmetic.

g(f(4)) = g(4 -7) = g(-3) = (-3)^2

g(f(4)) = 9

[tex]-7+1[3+8(2^2-8)][/tex]-7+1[3+8(2^2-8)]

Answers

Answer:

-36

Step-by-step explanation:

-7+1[3-32]

= -7-29

= -36

19. The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is (a) 20 (b) 23 (c) 169 (d) None of these

Answers

Answer:

Step-by-step explanation:

Let the two numbers be a and b.

The product of the two is 120 and their sum of their squares is 289. In other words:

[tex]\displaystyle ab = 120 \text{ and } a^2 + b^2 = 289[/tex]

And we want to find the sum of the two numbers.

We can use the perfect square trinomial. Recall that:

[tex]a^2 + 2ab + b^2 = (a+b)^2[/tex]

From the first equation, multiply by two:

[tex]2ab = 240[/tex]

Add the two equations together:

[tex](a^2+b^2)+(2ab) = (289)+(240)[/tex]

Simplify and rewrite:

[tex]a^2+2ab+b^2 = 529[/tex]

Factor using the perfect square trinomial pattern:

[tex](a+b)^2 = 529[/tex]

And take the square root of both sides:

[tex]\displaystyle a + b = \pm\sqrt{529} = \pm23[/tex]

Hence, the sum of the two numbers is 23 or -23.

In conclusion, our answer is B.

Subtract. Write your answer in simplest form.
5/- 10/5

Answers

Answer:

-1/10

Step-by-step explanation:

(5/(-10))/5 = -(5/10)/5 = 1/10

(Hopefully this helped you out!)

Help meeeeeeeeeeeeeeeee

Answers

Answer:

x-3

Step-by-step explanation:

the inverse is x-3

this is the answer

PLS HELP :( i’ve been trying to understand this but i cant. please explain this if you know how to do it pleaseee

Answers

Answer:

[tex]\huge\boxed{\sf x = 17}[/tex]

Step-by-step explanation:

Since m is a straight line, its measure is 180 degrees.

So,

2x + 5 + 8x + 5 = 180

2x + 8x + 5 + 5 = 180

10x + 10 = 180

10x = 180 - 10

10x = 170

Divide both sides by 10

x = 17

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807Peace!

A coin is flipped two times and the number of heads is counted. Which of the following is a valid assignment
of probabilities for the number of heads observed in two flips?
8.
Number of heads
Probability
0
1/10
1
5/10
2
4/10
b.
Number of heads
0
1
2
Probability
1/4
2/4
1/4
C.
0
1
Number of heads
Probability
2
1/3
1/3
1/3
d. All answer options are correct

Answers

Answer:

5/10, 1, 2/4,

Step-by-step explanation:

One number exceeds another by 12 and their sum is 44 find the two numbers you

Answers

Answer:

Step-by-step explanation:

x - first

x + 12 - second

x + (x + 12) = 44

2x=44-12

x=16

first number is 16

second number is 16+12=28

two numbers are 16 and 28

16 and 28 are the required two numbers when one number exceeds another by 12 and their sum is 44

One number exceeds another by 12 and their sum is 44

We need to find the two numbers

What is equation?

Two expressions with equal sign is called equation.

Let x be the first number

x + 12 be the second number

x + (x + 12) = 44

2x=44-12

x=16

Therefore first number is 16

second number is 16+12=28

To learn more about solving equation click here: https://brainly.com/question/24638714

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HELP PLS!! PLS BRO LOLOLOLOL

Answers

Answer and Step-by-step explanation:

An easy way of doing this is to first square root the numerator and the denominator.

[tex]\sqrt{\frac{36}{81} } =\frac{\sqrt{36}}{\sqrt{81} } =[/tex] ±[tex]\frac{6}{9} =[/tex] ±[tex]\frac{2}{3}[/tex] <- This is the answer.

#teamtrees #PAW (Plant And Water)

I hope this helps!

Consider the sequence of numbers 50,48,46,44….
(A) What are the next three numbers in this sequence?
(B) Using n to represent the position of a number in this sequence, write an expression that allows you to calculate the nth number.
(C) use your expression to find the 100th number in this sequence

Answers

Step-by-step explanation:

(A) 42,40

(B) T(n) = 50 + (n-1)(-2)

= 50+2-2n

= 52-2n

= 52- 200

= - 148

Plz help ASAP need fast plz will mark Brainlyist

Answers

Answer:

The correct answer is the third one. CIRCUMFERENCE

75 is what percent of 96?

Answers

75 is what percent of 96? = 78.13.

Let x be 75% of 96
x = 75/100 * 96 [Since % = 1/100]
x = 7200/100
x = 72
Thus, 75% of 96 is 72.

12. A jet stream can move a particle of air
11 miles in 5 minutes. At this rate, how far
will the particle move in 1 hour?
(5 minutes = 1 hour) (Example 1)

Answers

Answer:

132 particles

Step-by-step explanation:

5 minutes = 11 miles

1 hour (60 minutes)

11*x = 11 x 60 = 660

11x = 660/5=132

The distance of a jet stream can move a particle of air 132 miles in 1 hour.

Here,

A jet stream can move a particle of air 11 miles in 5 minutes.

We have to find, The distance of particles move in 1 hour.

What is distance?

The length along a line or line segment between two points on the line or line segment.

Now,

A jet stream can move a particle of air 11 miles in 5 minutes.

5 minutes = 11 miles

Then, for 1 minute a jet stream can move a particle of air = 11 / 5 miles

Hence, In 1 hour ( 60 minutes) a jet stream can move a particle of air;

⇒ [tex]\frac{11}{5} * 60 = 132[/tex]

So, The distance of a jet stream can move a particle of air 132 miles in 1 hour.

Learn more about the distance visit:

https://brainly.in/question/20602441

#SPJ2

Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction. 4/3 divided 7/4

Answers

Answer:

so we have 4/3 divided by 7/4

= 4/3 * 4/7

= 4*4/3*7

= 16/21

Step-by-step explanation:

answer from gauth math

16/21 is the answer to the question

HELP ME PLEASEEEEEEEE

Answers

Answer:

Step-by-step explanation:

i search it up

What is this number sentence equal to?

If you could help, thank you so much!

Answers

the answer is 18.63 :)

Answer:

18.63

Step-by-step explanation:

[tex] \frac{6}{10} = 0.6 \\ \frac{3}{100} = 0.03[/tex]

[tex]10 + 8 + 0.6 + 0.03 = 18.63[/tex]

How many different sets of answers are possible on a true-false test that has 11
questions?

Answers

2048 different sets are possible

Find the coordinates of the point 7/10 of the way from A to B A -3,-7 B 11,4

Answers

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Answer:

(6.8, 0.7)

Step-by-step explanation:

That point is ...

A + (7/10)(B -A)

= (-3, -7) +(7/10)(11 -(-3), 4 -(-7)) = (-3, -7) +7/10(14, 11)

= (-3, -7) +(9.8, 7.7) = (6.8, 0.7)

The point 7/10 from A to B is (6.8, 0.7).

How is the expression 3 x 1/10 written as a decimal

A)3

B).3

C).03

D).003

Answers

Answer:

Step-by-step explanation:

3.0 / .1 = 0.3

Answer:

3×1/10=0.3 in decimals.

Step-by-step explanation:

3×1÷10

3÷10

0.3

Order the numbers from least to greatest

Answers

Answer:

Step-by-step explanation:

It just is

In ΔPQR, sin P = 0.2, sin R = 0.2 and r = 12. Find the length of p.

Answers

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Answer:

p = 12

Step-by-step explanation:

The sines of the opposite angles are the same, so the lengths of the sides are the same.

p = 12

_____

The law of sines tells you ...

p/sin(P) = r/sin(R)

p/0.2 = 12/0.2 . . . . . . substitute given values

Multiply by 0.2 to get ...

p(0.2/0.2) = 12(0.2/0.2)

p = 12

Write the number in standard form.

ninety-two billion, seventy thousand,
one hundred eight

Answers

92.000.070.108

Step-by-step explanation:

Thousand has 3 zeros, a million has 6 and a billion has 9.

So for ninety-two billion, you take 92 and add 9 zeros behind it because a billion has 9 zeros

(92.000.000.000)

-1/3 - (-1/2) plz help I am confused

Answers

Answer:

[tex] \frac{ - 1}{3} - ( - \frac{1}{2} ) \\ \frac{ - 1}{3} + \frac{1}{2} ( - \times - = + ) \\ = \frac{ - 2 + 3}{6} \\ = \frac{1}{6} \\ thank \: you[/tex]

Answer:

[tex] \frac{1}{6} [/tex]

Step-by-step explanation:

[tex] - \frac{1}{3} - ( - \frac{1}{2} )[/tex]

[tex] - \frac{1}{3} + \frac{1}{2} [/tex]

[tex] \frac{ - 2 + 3}{ 6} [/tex]

[tex] = \frac{1}{6} [/tex]

Which describes the relationship between the distance and the difference?

Answers

Answer:

Which describes the relationship between the distance and the difference? The distance is always the opposite of the difference. ... The distance is the absolute value of the difference.

The vertical side of a right triangle measures 6 inches, and the horizontal side measures 8 inches
1.Write the ratio of the distance of the vertical side to the distance of the horizontal side as a reduced fraction
2.If the original triangle were enlarged by 3 times, what would the new dimensions be?
3.Does the ratio of vertical side to horizontal side change when scaling up? Explain.

Answers

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Answer:

3/4vertical: 18 in; horizontal: 24 inno change

Step-by-step explanation:

1. The ratio is ...

(6 in)/(8 in) = 6/8 = 3/4

2. The scaled dimensions are ...

6 in × 3 = 18 in (vertical side)

8 in × 3 = 24 in (horizontal side)

3. You know from your process of reducing the fraction in part 1 that multiplying numerator and denominator by the same value does not change the reduced ratio.

Is quadrilateral DEFG a parallelogram? Why or why not?
Question 2 options:

A)

Yes, because adjacent angles aren't supplementary.

B)

No, because adjacent angles aren't congruent.

C)

There isn't enough information.

D)

Yes, because opposite angles are congruent.

Answers

Answer:

D ig?

Step-by-step explanation:

Because opposite angles are equal in parallelogram

Two trains leave towns 1285 kilometers apart at the same time and traveled towards each other. One train travels 17 km/h faster than the other. If they meet in 5 hours what is the rate of each train

Answers

Distance = (Rate)(Time)

Let x = speed of slower train

x + 17 = speed of faster train

The trains meet when the sum of the distances = 1285

5x + 5(x+17) = 1285

(5 came from 5 hours)

10x + 85 = 1285

10x = 1200

x = 120 mph

The speeds are 120 mph and 137 mph

wyzant

the result of a multiplication of two or more
terms

Answers

Answer:

Product

Step-by-step explanation:

Product is the result of a multiplication of two or more terms.

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Answer:

B=Product

C=polynominal

D=distirbutive property

Step-by-step explanation:

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