Answer:
Answer:
Domain is
All real number except at x=0
Step-by-step explanation:
We are given
Firstly, we will find (fog)(x)
now, we can plug back g(x)
Domain:
we know that domain is all possible values of x for which any function is defined
and we know that denominator of any function can not be zero
so, we set denominator =0
so, function will be defined for all values of x except at x=0
So, domain will be
All real number except at x=0
Hope this helps!
The domain of the function ( f o g ) ( x ) is given by all the real numbers greater than 0 and x ≥ 0
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the first be represented as f ( x )
Now , the value of f ( x ) = 2x
Let the second function be represented as g ( x )
Now , the value of g ( x ) = √x
And , the composition of functions is
( f o g ) ( x ) = f ( g ( x ) )
On simplifying , we get
f ( g ( x ) ) = f ( √x )
f ( √x ) = 2√x
Therefore , the value of ( f o g ) ( x ) = √x
And , the domain of the relation h ( x ) = y = 2√x is all the real numbers greater than 0
Hence , the domain is x ≥ 0
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Image attached: geometry
===================================================
Explanation:
For me, I find it easier to find the exterior angle first. For any convex polygon, the sum of the exterior angles is 360 degrees. When we talk about regular polygons with n sides, each exterior angle is 360/n degrees. In this case, we have a nonagon with 9 sides. So n = 9 is plugged into 360/n to get 360/9 = 40 as the exterior angle measure
exterior angle = 40
We could stop here since we can see the answer must be choice A. But let's keep going. To get the interior angle, we subtract the result we got from 180
interior angle = 180-(exterior angle) = 180-40 = 140
This is because any adjacent pair of interior and exterior angles must form a straight angle of 180 degrees.
--------------------
side note: you could use the formula [tex]i = \frac{180(n-2)}{n}[/tex] to find the measure of the interior angle.
*PLEASE ANSWER* The radius of a salad bowl is 7.2 inches. What is the surface area of the bowl? (Assume the bowl is half a sphere). a.) 325.72 in2 b.) 651.44 in2 c.) 81.43 in2
Answer:
a) 325.72
Step-by-step explanation:
A=4pir^2
A=4x3,14x7.2x7.2
a=651.44
1/2a=1/2x651.44
=325.72
In how many ways can the letters of the word PROBABLY be arranged using all of the letters?
Answer:
20160
Step-by-step explanation:
If there is no repeat of the alphabets, the answer will simply be 8! = 40320 (8 words)
but, there is B which repeated 2 times.
So, 8!/2!
Answer:
20160
Step-by-step explanation:
Let's write the word PROBABLY. There are 8 letters in total, but the letter B repeats twice. So, instead of just doing 8! or 1*2*3*4*5*6*7*8, you have to exclude the two B's.
So, you have to do 8! / 2! because the 2! is the two B's.
Hope this helps!! :)
Which triangle is a regular polygon? right triangle equilateral triangle scalene triangle obtuse triangle
Answer:
Step-by-step explanation:
In a regular polygon, all sides and angles are equal.
So, an equilateral triangle is an example for regular polygon
Answer:
equilateral triangle should be the correct answer
Step-by-step explanation:
can someone help me solve this problem?
and the answer is 4a + 5
Step-by-step explanation:
the value of a in the second is 1 so 3a + a is 4a
and 3 + 2 is 5Find the number of vertices on this solid.
Answer:
5
Step-by-step explanation:
Vertices are points where lines intersect. A pyramid has 5 vertices.
Answer:
5
Step-by-step explanation:
A square-based pyramid has 5 vertices, 1 on the top and 4 on the base.
Trinity created a game that uses 8 cards numbered 1 to 8 and a six-sided cube numbered 1
to 6. Each player chooses one card and rolls the cube to determine the number of spaces to
move on the game board.
What is the probability that Trinity will choose a card greater than 6 and roll a 6 on the
cube?
Done -
The probability that Trinity will choose a card greater than 6 and roll a 6 on the cube will be 4.167%.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Trinity created a game that uses 8 cards numbered 1 to 8 and a six-sided cube numbered 1 to 6.
Each player chooses one card and rolls the cube to determine the number of spaces to move on the game board.
Then the probability that Trinity will choose a card greater than 6 and roll a 6 on the cube will be
[tex]\rm P = \dfrac{2}{8}\times \dfrac{1}{6}\\\\\\P = \dfrac{1}{24}\\\\\\P = 0.04167 \ or \ 4.167\%[/tex]
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simplify -9/6 divided by 3/-2. A: 3 B: 1 C: -1 D: -3
Answer:
B. 1
Step-by-step explanation:
-9/6 ÷ 3/-2
Reciprocal and it becomes multiplication.
-9/6 × -2/3
Multiply the fractions.
18/18
= 1
Answer:
1 is the answerStep-by-step explanation:
-9/6/3/-2
Made the second number the reciprocal =
-9/6 / -2/3
Switch the sign to a multiplication sign =
-9/6 * -2/3
Simplify the numerator =
-9*-2 = 18
Simplify the denominator =
3*6 = 18
Place the numerator and denominator together =
18/18
Simplify the answer =
18/18 = 1
Hope this helped,
Kavitha
If F(x) =5x/3 +5
+5, which of the following is the inverse of F(x)?
O A. F'(x) = 5(x+5)
3
O B. F'(x) = 3(x+5)
5
C. F1(x) = 5(x-5)
O D. F'(x) = 3(-5)
Answer:
[tex]f^{-1}(x)=\frac{3(x-5)}{5}[/tex]
Step-by-step explanation:
[tex]f(x)=y=\frac{5x}{3}+5\\y-5=\frac{5x}{3}\\3(y-5)=5x\\x=\frac{3(y-5)}{5}\\ => f^{-1}(x)=\frac{3(x-5)}{5}[/tex]
The inverse of the linear function, f(x), f(x) =5x/3 +5 is f⁻¹(x) = 3 (x -5) / 5. The correct option is f⁻¹(x) = 3 (x -5) / 5
What is the inverse of a function?The inverse of a function is a function that reverses the effect the original function.
Here, we have,
The original function is; f(x) =5x/3 +5
The inverse of f(x) can therefore be found by making x the subject of the equation as follows;
f(x) = 5x/3 +5
f(x) -5 = 5x/3
(f(x) -5) 3 = 5·x
x = (f(x) -5) 3 / 5
x = 3 (f(x) -5) / 5
Plugging in x = f⁻¹(x) and f(x) = x, in the above equation, we get;
f⁻¹(x) = 3 ((x) -5) / 5
f⁻¹(x) = 3 (x -5) / 5
The correct option that is an inverse of f(x) is f⁻¹(x) = 3 (x -5) / 5.
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Put the following numbers in order from greatest to least 7 030 400, 70 000 200, 78 330, 790 300, 709 400, 70 800
Answer:
70 000 200, 7 030 400, 790 300, 709 400, 78 300, 70 800
Step-by-step explanation:
Greatest is always the number with the most digits.
Answer:
70 000 200, 7 030 400, 790 300, 709 400, 78 330, 70 800
Step-by-step explanation:
To answer this I simply needed to know the orders of numbers from ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, tens of millions, and hundreds of millions. You must also know which digits hold the most value.
[tex]1\\10\\100\\1,000\\10,000\\100,000\\1,000,000\\10,000,000\\100,000,000[/tex]
The formula for an arithmetic series is shown below, where n = 1, 2, 3 ...
f(n + 1) = f(n) + 8
If f(1) = 5, what are the fourth, fifth, and sixth terms in the sequence?
Answer:
4th term = 28
5th term = 37
6th term = 45
Step-by-step explanation:
f(n + 1) = f(n) + 8
f(1) = 5
f(1 + 1) = f(1) + 8 = 5+8 = 13
f(2) = 13
f(2 + 1) = f(2) + 8 = 13+8 = 21
Thus, series is 5, 13, 21......
In arithmetic series
Nth term is given by
n th term = a + (n-1)d
where a is the first term
and d is the common difference.
common difference d = nth term - (n-1)th term
For this series
a = 5
lets take nth term as 2nd term and 1st term as (n-1)th term
d = 13-5 = 8
n th term = a + (n-1)d
using the formula for nth term
4th term = 5 + (4-1)8 = 29
5th term = 5 + (5-1) 8= 37
6th term = 5+ (6-1)8 = 45
Thus, 4th term = 28
5th term = 37
6th term = 45
Note this, problem can be solved using f(n + 1) = f(n) + 8 by putting n = 3,4,5 as well but for learning concept of arithmetic series, i have used above process. Hope it helps.
Does anyone know this need help! Thanks!
the formula for the circumference of a cirlce is πd. the diameter is 2r which in this case is 0.5. therefore the circumference is 0.5π, or 1.5708 (rounded)
Answer:
C= 157
Step-by-step explanation:
The formula for the circumference of a circle is 2 · pi · r (radius)
So your problem would look something like this:
C= 2 · pi · r
C= 2 · 3.14 · 25
C= 157 in.
What is the number of possible outcomes for the tree diagram below?
w
w
w
A. 8
B. 6
C. 4
0
D. 2
Answer:
4
Step-by-step explanation:
£80 is divided between Fiona, Pip & Sara so that Fiona gets twice as much as Pip, and Pip gets three times as much as Sara. How much does Fiona get?
Answer:
Fiona got £48
Step-by-step explanation:
let Sara=x
Pip=3x
Fiona=2(3x)
x+3x+2(3x)=£80
4x+6x=£80
10x=£80
10x/10=£80/10
x=£8
therefore Sara(x) got £8
Pip=3x
=3(8)
=£24
Fiona=2(3x)
=2(24)
=£48.
The sales tax on clothing in Nebraska is 5.5%. Calculate how much tax you need to pay on a shirt if it costs $36.60 before tax. Round your answer to the nearest cent.(plz answer asap)
Answer:
$2.01.
Step-by-step explanation:
Tax paid = 5.5% * 36.60
= 0.055 * 36.60
= 2.013
Given the equation y ^2 − 4y = 3, what constant must be added to both sides so the left side is the square of a binomial?
Answer:
4
Step-by-step explanation:
y² − 4y = 3
y² - 2*2*y =3
y² - 2*2*y + 2² = 3 + 2²
(y - 2)² = 3 + 4
what's the slope of a line that passes through (-8,-16) and (18,5)?
Answer:
C. 21/26
Step-by-step explanation:
Slope Formula: [tex]m = \frac{y2-y1}{x2-x1}[/tex]
Plug in our coordinates:
m = (5 + 16)/(18 + 8)
m = 21/26
Answer:
C. 21/26
Step-by-step explanation:
Slope is determined by the change (or difference) in the y-coordinates divided by the change (or difference) in the x-coordinates.
Here, our y-coordinates are -16 and 5, so:
5 - (-16) = 5 + 16 = 21
Our x-coordinates are -8 and 18, so:
18 - (-8) = 18 + 8 = 26
Now, we divide: 21/26.
The answer is thus C.
~ an aesthetics lover
PLEASE HELP ME!! I NEED AN ANSWER ASAP PLZ! Given the quadrilateral inscribed in the circle, what is m∠L?
Answer:
97 degrees
Step-by-step explanation:
The length of a rectangle is three times its width.
The perimeter of the rectangle is 24cm
Calculate the area
Area of a rectangle is 27 cm²
Given:
Perimeter of a rectangle = 24 cm
Length = 3x
Width = x
p = 2(l + w)
24 = 2(3x + x)
24 = 6x + 2x
24 = 8x
24/8 = x
3 = x
Width = 3 cm ; Length = 3x = 3(3) = 9 cm
Area = length * width
= 9cm * 3 cm
Area = 27 cm²
Answer:
Area of a rectangle is 27 cm²
Step-by-step explanation:
What is the solution to (5m)² - (2n-3m)³ if m=-3 and n=5
Answer:
-6634
Step-by-step explanation:
(5m)² - (2n-3m)³ if m=-3 and n=5
= (5 * (-3))^2 - (2 * 5 - 3 * (-3))^3
= (-15)^2 - (10 - (-9))^3
= 225 - (19)^3
= 225 - 6859
= -6634
Please Help 100 points
Which graph shows the solution set for Negative 1.1 x + 6.4 greater-than negative 1.3?
A number line going from negative 10 to 0. An open circle is at negative 7. Everything to the left of the circle is shaded.
A number line going from negative 10 to 0. An open circle is at negative 7. Everything to the right of the circle is shaded.
A number line going from 0 to 10. An open circle is at 7. Everything to the left of the circle is shaded.
A number line going from 0 to 10. An open circle is at 7. Everything to the right of the circle is shaded.
Answer:
see below
Step-by-step explanation:
-1.1 x + 6.4 >- 1.3
Subtract 6.4 from each side
-1.1 x + 6.4 -6.4 >- 1.3-6.4
-1.1x > -7.7
Divide each side by -1.1, remembering to flip the inequality
-1.1x/-1.1< -7.7/-1.1
x < 7
There is an open circle at 7 and a line going to the left
Hey there! :)
Answer:
C.
Step-by-step explanation:
Given:
-1.1x + 6.4 > -1.3
Subtract 6.4 from both sides:
-1.1x > -7.7
Divide both sides by -1.1. Flip the sign because you are dividing by a negative sign.
-1.1x/ (-1.1) < -7.7/(-1.1)
x < 7.
Therefore, C is the correct answer. Since the sign used is < without the equal to, an open circle would be used.
Find the points of intersection of the following function graphs: y=14−2.5x and y=1.5x−18 PLEASE HELP ONLY HAVE 20 MINUTES
Answer:x=8 Y=-6
Step-by-step explanation:
14-2.5x=1.5x-18
+18. +18
32-2.5x=1.5x
+2.5x =2.5x
32= 4x
Divide 4 to both sides you get
8=x
Y=14-2.5(8)
Y=14-20
Y=-6
2. Below is a circle with centre C. A, B, D, and E
are points on the circumference. BD is a diameter of
the circle.
Angle CDA is 18° Find the size of angle EDA.
You must show your workings
Answer:
Step-by-step explanation:
45-37
8x17 = 136
A computer randomly generates a 5-digit string using numbers between 0 and 9 inclusive. What is the probability that the first two digits in the string are a 4 and a 2 , in that order?
Answer: 0.01.
Step-by-step explanation:
Given: A computer randomly generates a 5-digit string using numbers between 0 and 9 inclusive.
i.e. each place in 5 digit number has 10 choices.
Total ways to make such a number = [tex]10^5=100000[/tex].
If the first two digits in the string are a 4 and a 2, in that order, then the number of ays to make this kind of number = 1 x 1 x 10 x 10 x 10 = 1000 [as 4 and 2 can be put on first and second place in 1 way ]
Now, the probability that the first two digits in the string are a 4 and a 2 , in that order = [tex]\dfrac{1000}{100000}=\dfrac{1}{100}=0.01[/tex]
Hence, the probability that the first two digits in the string are a 4 and a 2 , in that order = 0.01.
Which statement is true?
A) |-45| = 45 and |-96| = -96.
B) -|-451 = 45 and -|-96| = -96.
C) |-45| = 45 and |-96| = -96.
D) |-45| = 45 and |-96| = 96.
The statement that is true is |-45| = 45 and |-96| = 96.
Option D is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
|-45| = 45
|-96| = 96
-|-45| = - 45
-|-96| = - 96
|-45| = 45
|-96| = 96
|-45| = 45
|-96| = 96
Thus,
|-45| = 45 and |-96| = 96 is true.
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Which of the following functions best describes this graph
Answer: its c i took the test
Step-by-step explanation:
What is 4.3 as a fraction in simplest form
-5/7 times 1/5 please help answer
Answer:
-1/7
Step-by-step explanation:
-5/7 × 1/5
Multiply.
-5/35
Simplify.
-1/7
Answer:
[tex] \frac{ - 1}{7} [/tex]
solution,
[tex] \frac{ - 5}{7} \times \frac{1}{5} \\ = \frac{ - 5 \times 1}{7 \times 5} \\ = \frac{ - 5}{ 35} \\ [/tex]
divide 5 and 35 by 5, you will get:
[tex] = \frac{ - 1}{7} [/tex]
hope this helps...
Good luck on your assignment
What is the recursive formula for the geometric sequence with this explicit formula?
Answer:
[tex]a1 = 9 \\ an = a(n - 1) \times ( \frac{ - 1}{3} )[/tex]
A small airplane can fly 12 miles in 3 minutes. At this rate, how far can it fly in 7 minutes? In an hour?
Answer:
28 miles in 7 minutes, 240 miles in an hour
Step-by-step explanation:
We can first simplify the rate to miles per minute. Since the plane goes 12 miles in 3 minutes, we can divide it by 3 to find how much it travels in one minute. 12 divided by 3 is 4 and 3 divided by 3 is 1
The plane travels 4 miles a minute
To find how much it travels in 7 minutes, multiply by 7
4x7 is 28
28 miles in 7 minutes
To find an hour, multiply by 60
4x60= 240
240 miles in an hour