Answers
Answer:
B
Step-by-step explanation:
[tex]y = \sqrt{x } - 4 \\ \sqrt{x} = y + 4 \\ x = (y + 4) {}^{2} \\ [/tex]
Domain of inverse = Range of f = x>-4
Hence B
The correct option is B which is f⁻¹(x) = ( x + 4 )² and x ≥ -4.
What is an inverse function?The inverse function of a function f in mathematics is a function that reverses the operation of f. If and only if f is bijective, the inverse of f is true.
A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
The given function is f(x) = √x - 4. The inverse function will be calculated as:-
y = √x - 4
√x = y + 4
Squaring on both sides.
x = ( y + 4 )²
Replace x with y.
y = ( x + 4 )²
The range of the function is x ≥ -4.
Therefore, the correct option is B which is f⁻¹(x) = ( x + 4 )² and x ≥ -4.
To know more about an inverse function follow
https://brainly.com/question/3831584
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Related Questions
13. For every 5 hours that he works, Andrew
is paid $60.20. How much is Andrew paid
in dollars per hour?
Answers
if f(1) = 2 – 2 anid 9(37)
and g(x) = x2 – 9, what is the domain of g(x) = f(x)?
Answers
Answer:
B
Step-by-step explanation:
Let divide g(x) by f(x)
[tex] \frac{ {x}^{2} - 9 }{2 - x {}^{ \frac{1}{2} } } [/tex]
The domain of a rational function cannot equal zero so let set the bottom function to zero.
[tex]2 - x {}^{ \frac{1}{2} } = 0[/tex]
[tex]x {}^{ \frac{1}{2} } = 2[/tex]
Square both sides
[tex]x = 4[/tex]
Also we can simplify the bottom denomiator into a square root function
[tex]2 - \sqrt{x} [/tex]
The domain of a square root function is all real number greater than or equal to zero because a square root of a negative number isn't graphable.
So we must find a answer that
Disincludes 4 from the intervalDoesnt range in the negative number or infinity)Range out in positve infinityThe answer to that is Bthe sherman family mad a down payment of $18,375 for a new house they mortaged the remaining cost of $129,625 the interest paid for 30 years was $273,116 what was the total cost of the house
Answers
Answer:
honestly this is a very poorly worded question...
it can be interpreted in several different ways....
the cost of the house (for them to purchase it) was
$129,625 + $18,375 = $148,000
The total amount that they paid for the house (money spent)
was
$129,625 + $18,375 + $273,116 = $421,116
all being said I think that the $148,000 is the answer that the question
is trying for you to figure out
Step-by-step explanation:
The perimeter of a square is 80cm
state the length of one of its side
Answers
Answer:
20cm
Step-by-step explanation:
a square has 4 equally long sides.
when we know its perimeter, that means we know the sum of all 4 sides.
since all sides are equality long, we only need to divide the perimeter by 4 to get the length of an individual side.
80/4 = 20cm
At the time of her grandson's birth, a grandmother deposits $3000 in an account that pays 9.5% compounded monthly.
What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period?
Answers
Answer:
74820
Step-by-step explanation:
9.5% of 3000 is 285
there are 12 months in a year
so 12 times 21 equals 252
so 285 times 252 add 3000 equals 74820
Question 17 (5 points)
Determine the value of x in the isosceles trapezoid.
2x
х
x = 60°
x= 65°
x= 180°
*= 90°
Answers
What is the length of each side of a square if its area is 121 ft??
11 feet
12 feet
10 feet
30 feet
Answers
Answer:
11 feet
Step-by-step explanation:
Given,
Area of square ( a^2 ) = 121 ft
To find : Length of each side ( a ) = ?
Formula : -
Area of square = a^2
a^2 = 121
a = √121
a = 11 feet
Answer:
11 ft = side length
Step-by-step explanation:
The area of a square is found by
A = s^2
121 = s^2
Taking the square root of each side
sqrt(121) = sqrt(s^2)
11 = s
Zachary's art club ordered a giant sub sandwich for a party. It was 6 feet long! When the sandwich arrived, Zachary cut it into 16 equal pieces.
How long was each piece?
Write your answer as a proper fraction or mixed number.
Answers
Answer:
3/8 feet long
Step-by-step explanation:
Find how long each piece was by dividing 6 by 16:
6/16
Simplify this by dividing each number by 2:
6/16
= 3/8
So, each piece was 3/8 feet long
which points lie in the second quadrant? check all that apply.
Answers
Point F
Point E
These lie in the second quadrant.
Rewrite the following expression using the properties of rational exponents. Be sure your answer is in simplest form.
Answers
Answer:
12^(3/2)
Step-by-step explanation:
(2x6)^3/2
2x6=12
12^3/2= 41.5692193817
Pls help this set question
Answers
1: True
2: False
3: False
4: True
5: False
6: True
A researcher is curious about the average IQ of registered voters in the state of Florida. The entire group of registered voters in Florida is an example of a ______.
Answers
Answer:
Population
Step-by-step explanation:
A population can be defined as the total number of living organisms living together in a particular place and sharing certain characteristics in common.
A sample survey is a statistical method used for the collection of data from a target population in order to draw an inference and reach a logical conclusion.
In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.
In this scenario, the entire group of registered voters in Florida is an example of a population.
A survey asked people of different ages whether they get their news by
reading the paper. What is the probability that a person surveyed is 40 or
above, given that he or she gets the news by reading the paper? If necessary.
round your answer to the nearest percent.
Answers
Answer:
A) 60%
Step-by-step explanation:
24/40
= 0.6
0.6*100
= 60%
I really hope this is right and it helps.
can someone do this step by step pls:)
Answers
Answer:
23
4* 4 = 16
cir = 2[tex]\pi[/tex]r = 2[tex]\pi[/tex](1.2) = 2.4[tex]\pi[/tex]
16 + 2.4[tex]\pi[/tex] = 23.53
Step-by-step explanation:
PLEASE ANSWER CORRECTLY FOR BRAINLIEST:
25.
26.
27.
29.
Answers
Step-by-step explanation:
25.
[tex] \frac{t}{5} = b[/tex]
where b is the no. if 5 dollar bills.
26.
[tex]x +( x + 2) +( x + 4) = x + (x + 2)[/tex]
[tex]3x + 6 + 9 = 2x + 2[/tex]
[tex]3x + 15 = 2x + 2[/tex]
[tex]x + 15 = 2[/tex]
[tex]x = - 13[/tex]
Since x=-13 the intergers are
[tex] - 13[/tex]
[tex] - 11[/tex]
[tex] - 9[/tex]
27.
Represent the function as
[tex]x + x + 6 = 44[/tex]
[tex]2x + 6 = 44[/tex]
[tex]2x = 38[/tex]
[tex]x = 19[/tex]
The shorter piece should be 19 inches.
28.
Solve for h.
[tex]s = 2\pi \times rh + 2\pi {r}^{2} [/tex]
[tex]s - 2\pi {r}^{2} = 2\pi \times rh[/tex]
[tex] \frac{s - 2\pi {r}^{2} }{2\pi \times r} = h[/tex]
29.
[tex] \frac{16 + x}{2} \times 6 = 108[/tex]
[tex] \frac{16 + x}{2} = 18[/tex]
[tex]16 + x = 36[/tex]
[tex]x = 20[/tex]
What is the simplified algebraic expression?
Answers
Solution: 3x + 2y – 2x + 6.
In the coordinate plane, two vertices of square ABCD are A (0, 0) and B (0, m). What are the coordinates of points C and D? Do not introduce any new variables.
Answers
Answer:
The coordinate of point C is (m,m) and the coordinate of point D is (m,0).
Step-by-step explanation:
Square:
In a square, all sides have the same length.
A (0, 0) and B (0, m).
This means that the length of the sides is m.
So:
From A, adding m vertically, we get point (0,m), which is B.
From A, adding m horizontally, we get point (m,0), which I will call D.
From B, adding m horizontally, we get point (m,m), which I will call C.
The coordinate of point C is (m,m) and the coordinate of point D is (m,0).
A rectangular tank 60 cm long and 50 cm wide is /5 full of water. When 24 liters of water are added, the water level rises to the brim of the tank. Find the height of the tank. (1 liter is 1000cm3 )
Answers
Answer:
The tank is 10cm high
Step-by-step explanation:
Given
[tex]L=60cm[/tex] -- length
[tex]W=60cm[/tex] -- width
[tex]x = \frac{1}{5}[/tex] --- water lever
[tex]Addition = 24L[/tex]
Required
The height of the tank
Let y represents the remaining fraction before water is added.
So:
[tex]y + x = 1[/tex]
Make y the subject
[tex]y = 1 - x[/tex]
[tex]y = 1 - \frac{1}{5}[/tex]
Solve
[tex]y = \frac{5 - 1}{5}[/tex]
[tex]y = \frac{4}{5}[/tex]
Represent the volume of the tank with v
So:
[tex]y * v = 24L[/tex]
Make v the subject
[tex]v = \frac{24L}{y}[/tex]
Substitute: [tex]y = \frac{4}{5}[/tex]
[tex]v = \frac{24L}{4/5}[/tex]
[tex]v = 30L[/tex]
Represent the height of the tank with h;
So, the volume of the tank is:
[tex]v = lwh[/tex]
Make h the subject
[tex]h = \frac{v}{lw}[/tex]
Substitute values for v, l and w
[tex]h = \frac{30L}{60cm * 50cm}[/tex]
Convert 30L to cm^3
[tex]h = \frac{30*1000cm^3}{60cm * 50cm}[/tex]
[tex]h = \frac{30000cm^3}{3000cm^2}[/tex]
[tex]h = 10cm[/tex]
C-x:x is a two-digit natural number such that the sum of its digits is is 89
Answers
If 2x+4=8, what is 9x?
Answers
Answer:
hope it will be helpful to you
Answer:
..have a great day ahahahahah
please help me for 5 points
Answers
Answer:
275 adults
130 children
Step-by-step explanation:
Answer:
275 adults, 130 children
Step-by-step explanation:
Question 4 of 10
Which describes the graph of y=-(x - 3)^2 + 2?
O A. Vertex at (-3,2)
O B. Vertex at (3,-2)
C. Vertex at (3,2)
O D. Vertex at (-3,-2)
Answers
Answer:Vertex at (3, -2)
Step-by-step explanation:
Find angle m
A. 69
B. 23
C. 46
D. 167
Answers
Answer:
a
Step-by-step explanation:
∠DAF - ∠CFA=∠DFC
118-49 =69
10
What are the x- and y-coordinates of point E, which
partitions the directed line segment from A to B into a
ratio of 1:2?
B(-4,9)
9
8
X E
(
mn)(x2 – xı) + x
7-
6
5
4
mm. )(x2 - y) + y
3
-7 -6 -5 4 -3 -2 -14
2 3 4 5 6 7
0 (0, 1)
0 (-1,3)
O(-2,5)
(1,0)
X
-2.
3
A(2,-3)
19
Answers
Answer:
Step-by-step explanation:
The formulas to find the x and y coordinates of E are:
[tex]x=\frac{bx_1+ax_2}{a+b}[/tex] and [tex]y=\frac{by_1+ay_2}{a+b}[/tex] where x1, x2, y1, and y2 are from the coordinates of A and B, and a = 1 (from the ratio) and b = 2 (from the ratio). Filling in to find x first:
[tex]x=\frac{2(2)+1(-4)}{1+2}=\frac{4-4}{3}=0[/tex] and now for y:
[tex]y=\frac{2(-3)+1(9)}{1+2}=\frac{-6+9}{3}=\frac{3}{3}=1[/tex]
The coordinates of E are (0, 1).
Given:
The points are A(2,-3) and B(-4,9).
The point E divides the segment AB in 1:2.
To find:
The coordinates of point E.
Solution:
Section formula: If a point divides a line segment in m:n, then the coordinates of the point is:
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Using the section formula, the coordinates of point E are:
[tex]E=\left(\dfrac{1(-4)+2(2)}{1+2},\dfrac{1(9)+2(-3)}{1+2}\right)[/tex]
[tex]E=\left(\dfrac{-4+4)}{3},\dfrac{9-6}{3}\right)[/tex]
[tex]E=\left(\dfrac{0)}{3},\dfrac{3}{3}\right)[/tex]
[tex]E=\left(0,1\right)[/tex]
Therefore, the coordinates of the point E are (0,1).
PLEASE HELP!!! Find the equation of the line passing through the point that (4,-1)that is parallel to the line 2x-3y=9
Answers
Answer:
y=2/3x-11/3
Step-by-step explanation:
line is parallel so the gradient will be the same ( m=2/3)
using the point (4,-1)
y=2/3x+c
-1=2/3*4+c
-1=8/3+c
c= -11/3
equation ---> y=2/3x-11/3
Solve each equation. Round to four decimal places.
e^x=8
Answers
Answer:
x ≈ 2.0794
Step-by-step explanation:
Given
[tex]e^{x}[/tex] = 8 ( take ln of both sides )
ln [tex]e^{x}[/tex] = ln 8
x lne = ln 8 [ lne = 1 ]
x = ln 8 ≈ 2.0794 ( to 4 dec. places )
Answer:
x ≈ 2.0794
Step-by-step explanation:
[tex] \small \sf \: e {}^{x} = 8[/tex]
Take the natural logarithm of both side of equation
[tex]\small \sf \: In ( e {}^{x} ) = In ( 8 )[/tex][tex] \small \sf \: Use \: In(e {}^{x} ) = x \: to \: simplify \: the \: expression.[/tex]
x = In( 8 )Write the number in exponential form.
x = In(2³)Use In(aⁿ) = n × In ( a ) to transform the expression.
x = 3In( 2 ) ≈ 2.07944Round to four decimal places = 2.0794
Can someone help me with this math homework please!
Answers
PLS HELP(algebra 1)
solve -7 + 18(17h + 19)
Answers
Answer:
335+306h
Step-by-step explanation:
solve the brackets first by distributing 18 to 17h and 19
-7+306h+342
then group the like terms
-7+342+306h
335+306h
i need help ASAP. PLEASE.
Answers
Answer:
1st one
Step-by-step explanation:
If a set of scores for a variable is displayed in a frequency distribution polygon, which scale of measurement was used to measure the variable
Answers
Given: The set of scores for a variable is displayed in a frequency distribution polygon.
To find: We need to find which scale of measurement was used to measure the variable
Solution: A frequency distribution table is always either in interval or in ration scale.
