Given f(x) =1/(x^2+4) and g(x) = square root (x+1) Find g(f(x)).
Answers
Step-by-step explanation:
all steps are in the picture above.
Note:if you have any question let me know about.thanks
9514 1404 393
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
Can some one please help -18-17 simplified
Answers
Answer:
-35
Step-by-step explanation:
-(18+17)
-35
that should be the answer but don't quote me on it
-18+-17
=-35
that’s the answer
What is the length of an edge of a cube whose total surface area is equal to 150 square feet? A. 7.5 ft B. 5 ft C. 10 ft D. 25 ft
Answers
Answer:
5 ft
Step-by-step explanation:
Using the formula,
A = 6a²
a² = A/6
a = √(A/6)
a =√(150/6)
a = √25
a = 5
The area of a 2D form is the amount of space within its perimeter. The length of the edge of the cube is 5 ft. The correct option is B.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The total surface area of a cube is 6 times the area of a face which is equal to the square of side of the cube. Therefore, the total surface area of the cube is,
Total surface area of cube = 6a²
Given that the total surface area of the cube is 150 square feet. Therefore, the length of the side of the cube can be written as,
Total surface area of cube = 6a²
150 square feet = 6a²
150 square feet / 6 = a²
25 ft² = a²
a = √(25 ft²)
a = 5 ft
Hence, the length of the edge of the cube is 5 ft.
Learn more about Area here:
https://brainly.com/question/1631786
#SPJ2
3.
THREE
THREE
+ ONE=
SEVEN
Answers
9514 1404 393
Answer:
multiple solutions, see the attachment
Step-by-step explanation:
If you allow any digits 0-9, there are 11 possible solutions. Of these, two have the leading digit O = 0, so you may not agree that is an allowable solution.
Each row in the attachment is a possible solution. (Rows 4 and 10 have O=0.)
__
Found by exhaustive search using a computer program. Note that E=7 and N=1 are not hard to find by hand.
If ST = 3x + 8, SU = 24 and
TU = 2x – 4, what does ST = ?
Answers
Step-by-step explanation:
For TU is it -2x-4 or 2x-4 cause the question and what on your paper are different
Answer:
20
Step-by-step explanation:
ST= SU - TU
=24 - (2x-4)
=24-2x+4=28-2x
but. 2x-4+3x+8 = 5x+4 = 24
5x=24-4=20
x=20/5=4
so ST=28-2x= 28-2(4)
ST=20
How high is a tree that cast a 33ft shadow at the same time a9ft post casts a shadow w
Answers
let x=height of the tree
x/33=5/12
x=5*33/12
x=13.75
Find the measure of ∠Z.
Answers
Answer:
105+105+2x=360 and x=75
Step-by-step explanation:
z=75
Answer:
Step-by-step explanation:
John is playing a game with a standard deck of playing cards. He wants to draw a jack on the first try. Which of the following statements is true?
a. The probability that John draws a jack on the first try is 1/13. If John replaces the card, re- shuffles, and draws again, the probability that he will pull another jack increases.
b. The probability that John draws a jack on the first try is 3/13. If John replaces the card, re- shuffles, and draws again, the probability that he will pull another jack stays the same.
c. The probability that John draws a jack on the first try is 1/13. If John replaces the card, re- shuffles, and draws again, the probability that he will pull another jack decreases.
d. The probability that John draws a jack on the first try is 1/13. If John replaces the card, re- shuffles, and draws again, the probability that he will pull another jack stays the same.
Answers
Answer:
d
Step-by-step explanation:
It is a 1/13 chance but even if you shuffle and replace it, its still a 1/13 chance.
The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and draws again, the probability that he will pull another jack stays the same. Hence, statement d is correct.
What do we mean by the probability of an event?The probability of an event is the ratio of the number of favorable outcomes to the event to the total number of outcomes for the experiment.
If we have an event A, the number of favorable outcomes to event A is n, and the total number of outcomes in the experiment is S, then the probability of the event A is given by,
P(A) = n/S.
How do we solve the given question?We are given that John is playing a game with a standard deck of playing cards.
We are said that he wants to try to draw a jack on the first try.
Let the event of drawing a jack be A.
The number of outcomes favorable to the event A (n) = 4 (number of jacks)
The total number of outcomes in the experiment of drawing a card (S) = 52 (the total number of cards)
∴ The probability of the event A is given by,
P(A) = n/S = 4/52 = 1/13.
∴ The probability of drawing a jack on the first try is 1/13.
When he replaces the card and re-shuffles it, the probability will be the same as the number of favorable outcomes and the total number of outcomes remains the same.
∴ The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and draws again, the probability that he will pull another jack stays the same. Hence, statement d is correct.
Learn more about the probability of an event at
https://brainly.com/question/7965468
#SPJ2
Given a function described as the equation y = 4x - 4, what is y when x is 1, 2, and 3?
Answers
Answer:
f(1) = 0
f(2) = 4
f(3) = 8
Step-by-step explanation:
Substitute the values for the variable x.
[tex]f(1)=4(1)-4\\f(1)=4-4\\f(1)=0\\\\f(2)=4(2)-4\\f(2)=8-4\\f(2)=4\\\\f(3)=4(3)-4\\f(3)=12-4\\f(3)=8[/tex]
When x= 1
y = 4(1) - 4
y = 0
when x = 2
y = 4(2) - 4
y = 4
when x = 3
y = 4(3) - 4
y = 8
Which expression represents -8x^2+54x+140 in factored form?
A. (x-70)(-8x+2)
B. (x+1)(8x- 140
C. (x-8)(2x+70)
D. (x+2)(-8x+70)
Answers
Answer:
D. (x+2)(-8x+70)
Step-by-step explanation:
-8x^2+54x+140
Factor out -2
-2(4x^2+27x+70)
Factor
-2(x+2)(4x-35)
Option D is the same answer if we multiply -2 in the second term
(x+2) (-8x+70)
I need help question:how many questions would you need to get correct on a test that has 30 questions to get at least 70% correct?
Answers
Answer:
25
Step-by-step explanation:
Answer:
21 answers.
Step-by-step explanation:
First, change the percentage into a decimal point. Move the decimal point to the left two place values and drop the percentage sign:
70% = 70/100 = 0.70
Next, multiply 0.70 with the total amount of questions (30):
30 x 0.70 = 21
21 answers must be correct.
Check:
Divide 21 with 30:
21/30 = 0.70 = 70%
~
Convert 3250 ml to l
Answers
3250 mL = 3.25 L
* 1 mL = 0.001 L
I hope I helped you^_^
Which equation represents the graph?
y = 5|x| + 3
y = 3|x + 5|
y = 3|x| + 5
y = 5|x + 3|
Answers
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Answer:
(c) y = 3|x| + 5
Step-by-step explanation:
The vertex is at (0, 5), so the basic function has been translated up 5 units.
The slope of each line has a magnitude of 3, so the basic function has been scaled vertically by a factor of 3.
The transformation ...
g(x) = c·f(x) +h
is a vertical scaling by a factor of c, and a translation upward by h units. Here, we have c=3 and h=5. The basic function is f(x) = |x|, so the transformed function shown on the graph is ...
y = 3|x| +5
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!If a cubic inch of gold weighs 316 grams, how much does a cubic centimeter of gold weigh?
Answers
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Answer:
19.3 g/cm³
Step-by-step explanation:
There are 2.54 cm in one inch, so the weight of 1 cm³ is ...
(316 g/in³) ÷ (2.54 cm/in)³ = 19.3 g/cm³
How do I do this, is the equation 40=ksqrt(65)?
Answers
Answer:
Step-by-step explanation:
Start a little more generally. Carefully find k
distance = k * speed ^2
112 = k*40^2
112 = k * 1600 Divide by 1600
112/1600 = k
k = 0.07
Now do the question you are asked to do.
distance = k * speed^2
distance = 0.07 * 65^2
distance = 295.75
Now having done that, you can set up a proportion.
d1 / d2 = k speed1^2/kspeed2^2 Cancel the ks
112/d2 = 40^2 / 65^2 Cross multiply
112 * 65^2 = 40^2 * d2 Divide by 40^2
112 * 65^2/40^2 = d2 Expand the squares
112 * 4225 / 1600 = d2
295.75 = d2
The second way is shorter, but I suggest the long way until you get comfortable with it.
A state lotto has a prize that pays $1,600 each week for 20 years.
The total value of the prize: $1,664,000
If the state can earn 9% interest on investments, how much money will they need to put into an account now to cover the weekly prize payments?
--
I'm so stuck on this question! I've tried every single formula I can remember from the textbook, but I just don't get it! Apparently the answer is "$771,396.86" but I can't for the life of me understand how! Please help!
Answers
Answer:
Step-by-step explanation:
Start by calculating the effective rate of interest:
.09/52= .0017307
(we divide by 52 because there are 52 weeks in a year)
Then just use the annuity formula
[tex]1600(\frac{1-(1+.0017307)^{-(20*52)}}{.0017307})=771396.864393[/tex]
Which equation is represented by the table?
Which equation is represented by the table?
Answers
Answer:
The choose A.
y= – | x+1|–4
I hope I helped you^_^
Find the area of the triangle
Answers
Answer:
12.7 m
Step-by-step explanation:
use pythagorean theorem
[tex]13^{2} + b^{2} = 18.2^{2}[/tex]
rounds to 12.73735
not fully sure if that's right
What is the coordinate of point A?
Answers
Answer:
The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane.
Hope it is helpfully.Keisha bought these supplies for school:
4 packs of pencils that cost $0.85 each
6 packs of pens for $1.25 each
5. What was the total cost of the pencils and pens, including a 6% tax?
A
$13.35
B
$10.90
C
$11.55
D
$2.23
.
Answers
Answer:
C. $11.55
Step-by-step explanation:
First, multiply 4 by $0.85 to get an answer of $3.40. Next, multiply 6 by $1.25 to get an answer of $7.50. Add up the cost of the pencils and pens by adding $3.40 and $7.50 to get $10.90. Next, we have to add the tax. Multiply $10.90 by 0.06 to get $.65. Add the $.65 to the $10.90 for a grand total of $11.55. Hope this helps!
Select all the correct answers. Which vectors are unit vectors?
Answers
Answer:
Step-by-step explanation:
[tex](-\frac{1}{3} \sqrt{\frac{7}{2} } )^2+(\frac{1}{3} \sqrt{\frac{13}{2} } )^2\\=\frac{1}{9} (\frac{7}{2} +\frac{13}{2} )\\=\frac{1}{9} (\frac{7+13}{2} )\\=\frac{1}{9} \times10\\=\frac{10}{9} \neq 1[/tex]
not a unit vector.
b.
[tex](\frac{1}{\sqrt{3} } )^2+(-\sqrt{\frac{2}{3} } )^2\\=\frac{1}{3} +\frac{2}{3} \\=\frac{1+2}{3} \\=\frac{3}{3} \\=1[/tex]
it is a unit vector.
c.
[tex](\frac{1}{2} \sqrt{\frac{5}{3} } )^2+(-\frac{1}{2} \sqrt{\frac{7}{3} } )^2\\=\frac{1}{4} (\frac{5}{3} +\frac{7}{3} )\\=\frac{1}{4} (\frac{5+7}{3} )\\=\frac{1}{4} (\frac{12}{3} )\\=\frac{1}{4} (4)\\=1[/tex]
it is a unit vector.
d.
[tex](\frac{3}{\sqrt{7} } )^2+(-\frac{2}{\sqrt{7} } )^2\\=\frac{9}{7} +\frac{4}{7} \\=\frac{9+4}{7} \\=\frac{13}{7} \neq 1[/tex]
it is not a unit vector.
1/2+1/3+1/6+1/2+1/8+1/4= see problem as an addition problem
Answers
Answer:
1 7/8
Step-by-step explanation:
Solve For x.
(-4x+5)-(6x+7)=0
(Pls Explain Your Answer in Simple Terms)
Answers
Answer:
[tex] - 4x + 5 - (6x + 7) = 0\\ - 4x + 5 - 6x - 7 = 0 \\ - 10x - 2 = 0 \\ 10x + 2 = 0 \\ 10x = - 2 \\ x = \frac{ - 2}{10} \\ x = - .2 \\ thank \: you[/tex]
-4x-6x=-7-5
-10x=-12
10x=12
X=1.2
Two cars start at the same point. One travels north at 65 km/h and the other travels east at 50 km/h. How far are they apart after 30 minutes?
Answers
Answer:
1they are 15 kilometers apart
The inner dimensions of an in-ground swimming pool are: width = 13.0 ft, length = 18.0 ft, and depth = 9.0 ft. The pool walls and the bottom are uniformly 1.0 ft thick and made of concrete. What is the weight, W (in pounds) of the concrete used to construct the pool, if one cubic inch of concrete weighs 0.25 pounds? (Note: You may find it useful to draw a labeled diagram of the pool.
a. 386208
b. 32184
c. 3582
d. 2682
Answers
And you can see the method solution
Note: don't forget put heart ♥️ .
6 4/5 + 3 2/3
add and simplify
Answers
Answer:
10 3/5
Step-by-step explanation:
6 4/5 + 3 4/5
First convert to improper fraction,
34/5 + 19/5
Then add the improper fractions,
=>53/5
Then convert improper fraction to mixed fraction,
=> 53/5 = 10 3/5
The number 0,1,2,3,4 and so on are called
Answers
Hope this helps *smiles*
Help Please!
Find the value of x for which ABCD must be a parallelogram.
Answers
Answer:
2
Step-by-step explanation:
We know that the opposite sides of a parallelogram are equal so:
25x+1=7x+37
18x=36
x=2
Angles R and S are complementary. If angle R is = 4x - 20 and angle S = 6x - 7, then angle R measures ___ degrees.
Answers
Answer:
26.8°
Step-by-step explanation:
4x - 20 + 6x - 7 = 90
10x -27 =90
10x = 90+27
10x= 117
x = 11.7
so, the angle R = 4x-20 =4(11.7)-20
= 46.8-20 = 26.8°
A straight driveway leading to a hotel is 150 feet long and 12 feet wide. It is pave with concrete 6
inches thick. At a cost of $6.25 per cubic foot, how much did the concrete cost.