You can think of an inverse function as a function that “unwraps” x from whatever operations are attached to it. In the case of F(x) = √x, we can ”unwrap” x by squaring it. This narrows our options down to either A or D. Keep in mind that since there are no real number solutions to the square root of a negative number, we need to limit our domain to non-negative values. In other words, x ≥ 0. With that restriction, our answer is A.
The answer is:
The inverse of the given function is:
A. [tex]f(x)^{-1}=x^{2}[/tex]
Where,
[tex]x\geq 0[/tex]
Why?Inversing a function involves inversing the function variables. If we want to inverse a function, we need to rewrite the variable "x" with "y" and rewrite the variable "y" with "x", and then, isolate the variable "y".
Also, the domain of the original function will be the range of its inverse function, and the range of the original function, will be the domain of the its inverse function.
We are given the function:
[tex]f(x)=\sqrt{x}[/tex]
[tex]f(x)=y=\sqrt{x}[/tex]
So, inversing we have:
[tex]y=\sqrt{x}[/tex]
[tex]x=\sqrt{y}[/tex]
[tex](x)^{2}=(\sqrt{y})^{2}\\\\x^{2}=(y^{\frac{1}{2}})^{2}\\\\x^{2}=y^{\frac{2}{2} }\\\\x^{2}=y[/tex]
So, we have that the given function is only "part" of its inverse function, since negative square roots does not exist, it means that the domain of the given function starts from the number 0 taking only positive numbers.
Hence, we have that the answer is:
A. [tex]F(x)=x^{2}[/tex]
Where,
[tex]x\geq 0[/tex]
Have a nice day!
I am in urgent need of some help!! So uh....Please help me A quadrilateral has angles that measure 72 degrees, 98 degrees and 65 degrees what is the measure of the fourth angle??
So I could be completely wrong, or I could be completely right, but quadrilaterals interior angles equal 360 degrees.
So, if you ad up 98, 72, and 65 you end up with 235 degrees.
In order to find the fourth angle, you would just subtract 235 from 360 and get 125 degrees.
BUT, maybe see if someone else answers too, because I am not 100% sure.
Given the similarity statement ΔDEF ∼ ΔXYZ, which side corresponds with ED?
A. EF
B. ZY
C. XZ
D. YX
YX is corresponding with ED
Hope it helps.
Please mark me brainliest
what is the explicit formula for the geometric sequence with this recursive formula? a1=-7
an=an-1*(1/3)
A. an=- 1/3*7^(n-1)
B. an=1/3*(-7)*^(n-1)
C. an=7*(- 1/3)^(n-1)
D. an=-7*(1/3)^(n-1)
ANSWER
D. [tex]a_n= - 7( \frac{1}{3} )^{n - 1}[/tex]
EXPLANATION
The given explicit formula is
[tex]a_1= - 7[/tex]
and
[tex]a_n=\frac{1}{3} a_{n-1}[/tex]
This implies that,
[tex]r = \frac{1}{3} [/tex]
The explicit formula is given by:
[tex]a_n=a_{1}( \frac{1}{3} )^{n - 1} [/tex]
We substitute the known values to get;
[tex]a_n= - 7( \frac{1}{3} )^{n - 1}[/tex]
Answer:
D
Step-by-step explanation: A P E X
According to the general equation for conditional probability, if (image attached)
A. [tex]\frac{40}{49}[/tex]
B. [tex]\frac{24}{49}[/tex]
C. [tex]\frac{32}{49}[/tex]
D. [tex]\frac{16}{49}[/tex]
Answer: Option A
[tex]P(A|B) = \frac{40}{49}[/tex]
Step-by-step explanation:
In a probabilistic experiment, when two events A and B are dependent on each other, then the probability of occurrence A since B occurs is:
[tex]P(A|B) = \frac{P(A\ and\ B)}{P(B)}[/tex]
Then if [tex]P(A\ and\ B) = \frac{5}{7}[/tex] and [tex]P(B) = \frac{7}{8}[/tex] then:
[tex]P(A|B) = \frac{\frac{5}{7}}{\frac{7}{8}}\\\\P(A|B) = \frac{40}{49}[/tex]
Answer:
Correct choice is A. [tex]P(A|B)=\frac{40}{49}[/tex].
Step-by-step explanation:
Given that [tex]P(A\cap B)=\frac{5}{7}[/tex], [tex]P(B)=\frac{7}{8}[/tex].
Now using those values , we need to find the value of [tex]P(A|B)[/tex].
So apply the formula of conditional probability:
[tex]P(A\cap B)=P(B) \times P(A|B)[/tex]
Plug the given values into above formula, we get:
[tex]\frac{5}{7}=\frac{7}{8} \times P(A|B)[/tex]
[tex]\frac{7}{8} \times P(A|B)=\frac{5}{7}[/tex]
[tex]P(A|B)=\frac{\frac{5}{7}}{\frac{7}{8}}[/tex]
[tex]P(A|B)=\frac{5}{7}\cdot\frac{8}{7}[/tex]
[tex]P(A|B)=\frac{40}{49}[/tex]
Hence correct choice is A. [tex]P(A|B)=\frac{40}{49}[/tex].
Which sequences are geometric? Check all that apply. 10, 7.5, 5.625, 4.21875, … 160, 40, 10, 2.5, … 20, 70, 245, 857.5, … 13, 16.5, 20, 23.5, … 5, 5.5, 6.05, 6.655, … 16, 17.1, 18.2, 19.3, …
The sequence that shows geometric progression are options A), B), C), and E) and this can be determined by finding the geometric ratio.
Check all the options in order to determine which sequence is the geometric sequence.
A) 10, 7.5, 5.625, 4.21875,...
Check from the geometric ratio whether the above sequence is a geometric sequence or not.
Ratio between first and second term:
[tex]\rm r =\dfrac{7.5}{10}[/tex]
r = 0.75
Ratio between second and third term:
[tex]\rm r =\dfrac{5.625}{7.5}[/tex]
r = 0.75
So, yes this sequence is in geometric progression.
B) 160, 40, 10, 2.5, …
Check from the geometric ratio whether the above sequence is a geometric sequence or not.
Ratio between first and second term:
[tex]\rm r =\dfrac{40}{160}[/tex]
r = 0.25
Ratio between second and third term:
[tex]\rm r =\dfrac{10}{40}[/tex]
r = 0.25
So, yes this sequence is in geometric progression.
C) 20, 70, 245, 857.5, …
Check from the geometric ratio whether the above sequence is a geometric sequence or not.
Ratio between first and second term:
[tex]\rm r =\dfrac{70}{20}[/tex]
r = 3.5
Ratio between third and fourth term:
[tex]\rm r =\dfrac{857.5}{245}[/tex]
r = 3.5
So, yes this sequence is in geometric progression.
D) 13, 16.5, 20, 23.5, …
Check from the geometric ratio whether the above sequence is a geometric sequence or not.
Ratio between first and second term:
[tex]\rm r =\dfrac{16.5}{13}[/tex]
r = 1.27
Ratio between third and fourth term:
[tex]\rm r =\dfrac{23.5}{20}[/tex]
r = 1.175
So, no this sequence is not in geometric progression.
E) 5, 5.5, 6.05, 6.655, …
Check from the geometric ratio whether the above sequence is a geometric sequence or not.
Ratio between first and second term:
[tex]\rm r =\dfrac{5.5}{5}[/tex]
r = 1.1
Ratio between third and fourth term:
[tex]\rm r =\dfrac{6.655}{6.05}[/tex]
r = 1.1
So, yes this sequence is in geometric progression.
F) 16, 17.1, 18.2, 19.3, …
Check from the geometric ratio whether the above sequence is a geometric sequence or not.
Ratio between first and second term:
[tex]\rm r =\dfrac{17.1}{16}[/tex]
r = 1.07
Ratio between third and fourth term:
[tex]\rm r =\dfrac{19.3}{18.2}[/tex]
r = 1.06
So, no this sequence is not in geometric progression.
For more information, refer to the link given below:
https://brainly.com/question/4853032
Answer:
1, 2, 3, 5
Step-by-step explanation:
Can I get an explanation please.
Answer:
The correct option is letter D.
Step-by-step explanation:
We have the following expression:
sqrt(y^3) + sqrt(9y^3) - 3y*sqrt(y)
We now that sqrt(a*b) = sqrt(a)sqrt(b)
Applying this rule, we have:
sqrt(y^3) + sqrt(9y^3) - 3y*sqrt(y)
sqrt(y^3) + 3sqrt(y^3) - 3y*sqrt(y)
Also we know that a*sqrt(b) = sqrt(b*a^2)
Applying this we have:
sqrt(y^3) + 3sqrt(y^3) - 3y*sqrt(y) = sqrt(y^3) + 3sqrt(y^3) - 3sqrt(y^3)
Then the result is:
sqrt(y^3) + 3sqrt(y^3) - 3sqrt(y^3) = sqrt(y^3) = y*sqrt(y)
The correct option is letter D.
Which of the following equations is the formula of f(x) = x^1/3 but shifted 4 units to the left and 4 units up?
A. [tex]f(x) = (x-4)^{1/3} +4[/tex]
B. [tex]f(x) = 4x^{1/3} -4[/tex]
C. [tex]f(x)=(x+4)^{1/3} +4[/tex]
D. [tex]f(x) = 4x^{1/3} +4[/tex]
Answer:
Hence correct chcie is C.
[tex]f\left(x\right)=(x+4)^{\frac{1}{3}}+4[/tex]
Step-by-step explanation:
Given function is [tex]f\left(x\right)=x^{\frac{1}{3}}[/tex]
Now it says that function is shifted 4 units to the left and 4 units up.
We need to find about which of the given choice is correct for the given transformation.
When f(x) is shifted "h" units left then we write f(x+h)
So [tex]f\left(x\right)=x^{\frac{1}{3}}[/tex] will change to
[tex]f\left(x\right)=(x+4)^{\frac{1}{3}}[/tex]
When f(x) is shifted "h" units up then we write f(x)+h
So [tex]f\left(x\right)=(x+4)^{\frac{1}{3}}[/tex] will change to
[tex]f\left(x\right)=(x+4)^{\frac{1}{3}}+4[/tex]
Answer:
C
Step-by-step explanation:
For a function f(x) = [tex]x^{\frac{1}{3}}[/tex], we have:
f(x) = [tex](x-b)^{\frac{1}{3}}[/tex] is original translated b units rightf(x) = [tex](x+b)^{\frac{1}{3}}[/tex] is original translated b units leftf(x) = [tex]x^{\frac{1}{3}}+c[/tex] is original translated c units upf(x) = [tex]x^{\frac{1}{3}}-c[/tex] is original translated c units downKeeping these translation rules in mind, we can clearly say that 4 units shifted left and 4 units up has the equation [tex]f(x)=(x+4)^{\frac{1}{3}}+4[/tex]
correct answer is C
Devon's mom ordered 3 pizzas for the girls slumber party to eat. The girls ate 5/2 of the pizza. How is this amount of pizza written as a mixed number?
A. 2 1/2
b. 2 1/5
C. 3
Answer:
2 1/2
Step-by-step explanation:
you have 2 whole pizzas and 1 half (1/2)
Find the solution set.
x^2 – 5x = 0
Answer:
x=0 and x=5
Step-by-step explanation:
x^2 – 5x = 0
Factor out an x
x(x-5) = 0
Using the zero product property
x=0 and x-5 =0
Solving
x=0 x-5+5 = 0+5
x=0 and x=5
Kevin ate 2 slices of cake. Ben ate 1 slice. If Kevin ate 2/6 of the cake and all the slices are the same size, what fraction of the cake was eaten in total
1/2 of the cake was eaten
1+2=3. 3/6=1/2
All the slices are the same size
Find the area of the composite figure. Round to the nearest hundredth.
**Cracks knuckles** let's do this.
Area of triangle = 31.25 yd^2
10 x 6.25 = 62.5
62.5 / 2 = 31.25
Area of rectangle A = 50 yd^2
10 (length) x 5 (7.5 - 2.5) (width) = 50
Area of rectangle B = 48.75 yd^2
7.5 x 6.5 = 48.75
Total area of composite = 130 yd^2
31.25 + 50 + 48.75 = 130
If the arc on a particular circle has an arc length of 14 inches, and the circumference of the circle is 84 inches, what is the angle measure of the arc?
A.
60°
B.
90°
C.
120°
D.
180°
Answer:
A
Step-by-step explanation:
The arc length formula is:
Arc Length = [tex]\frac{\theta}{360}*2\pi r[/tex]
Where
[tex]\theta[/tex] is the angle measure of the arc, and
2πr is the circumference
Putting 84 in place of circumference and 14 in place of arc length, we can solve for [tex]\theta[/tex]:
Arc Length = [tex]\frac{\theta}{360}*2\pi r[/tex]
14 = [tex]\frac{\theta}{360}*(84)[/tex]
14 = [tex]\frac{84\theta}{360}[/tex]
[tex]14*360=84\theta\\5040=84\theta\\\theta=\frac{5040}{84}=60[/tex]
answer choice A is right.
What is the surface area of the cube below?
A. 150 units^2
B. 75 units^2
C. 300 units^2
D. 50 units^2
ANSWER
A. 150 units^2
EXPLANATION
The surface area of a cube is calculated using the formula:
[tex]SA=6 {l}^{2} [/tex]
where
[tex]l = 5[/tex]
We substitute the length to obtain:
[tex]SA=6 {l}^{2} [/tex]
[tex]SA=6 \times {5}^{2} [/tex]
[tex]SA=150 \: {units}^{2} [/tex]
which element is located at a32?
a=[6, 9, -1]
[0, 2, 4]
[7, 8, 2]
A rectangular prism is 4 meters long, 5 meters wide, and has a height of 7 meters. What is its surface area?
a.140 m2
b.166 m2
c.84 m2
d.70 m2
Answer:
5 by 4 face = 20 * 2 = 40
5 by 7 face = 35 * 2 = 70
4 by 7 face = 28 * 2 = 56
Total surface area = 166 square meters
Answer is "b"
Step-by-step explanation:
Answer:
your answer will be A
Justin packed two suitcases for his trip and compared the weights of the items he packed in each of the suitcases. Which statement is true about the box plots? The data for suitcase 1 have an outlier. The data for suitcase 2 have an outlier. Suitcase 1 contains the lightest and heaviest item. Suitcase 2 contains the lightest and heaviest item.
Answer:
A
Step-by-step explanation:
How much carpet do I need for the Master Bedroom?
Answer:
The carpet needed is [tex]288\ units^{2}[/tex]
Step-by-step explanation:
we know that
The area of the master bedroom is the area of a rectangle
so
The area is equal to
[tex]A=bh[/tex]
we have
[tex]b=16\ units[/tex]
[tex]h=18\ units[/tex]
substitute
[tex]A=(16)(18)=288\ units^{2}[/tex]
therefore
The carpet needed is [tex]288\ units^{2}[/tex]
Eric practiced the piano and guitar for a total of 8 hours this week he practiced the piano for 1/4 of that time how many hours did he practice piano this week
Answer: 2
Step-by-step explanation:
If 8 hours are spent the week, and there is only 1/4 used to play piano then you have to know how much 1/4 is of 8.
To get 1/4 of 8 you need to multiply 8 by 1/4.
The answer is 2.
Which algebraic expression represents the phrase "two times the quantity of a number minus 12"? A. 2y - 12 B. 2(y -12) C. 2(y + 12) D. 2y + 12
Answer:
B
Step-by-step explanation:
Two times the quantity of a number minus 12.
Represent the number with the variable y.
The quantity of a number minus 12 is then: (y-12).
Two times this quantity is 2(y-12).
So the answer is 2(y-12), which is B.
Evaluate the expression −11−(−7−9) by rewriting the subtraction as addition
Answer:
5
Step-by-step explanation:
Let's rewrite this a bit.
[tex]-11-(-7-9)=-11+7+9[/tex]
This is because there is a -1 before the expression inside the parentheses, so every sign is reversed.
Now we can add.
[tex]-11+7+9=5[/tex]
What is the area of the rhombus? The figure is not drawn to scale.
Answer:
126 cm²
Step-by-step explanation:
The area (A) of a rhombus is calculated as
A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ ← diagonals
The diagonals of a rhombus are perpendicular bisectors of each other, thus
d₁ = 7 + 7 = 14 and d₂ = 9 + 9 = 18, hence
A = 0.5 × 14 × 18 = 126 cm²
The area of the rhombus is equal to 126 cm². The correct option is B.
What is an area of the rhombus?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rhombus in a two-dimensional plane is called the area of the rhombus.
The area (A) of a rhombus is calculated as
A = × d₁ × d₂ ← diagonals
The diagonals of a rhombus are perpendicular bisectors of each other,
d₁ = 7 + 7 = 14
d₂ = 9 + 9 = 18, hence
The area of the rhombus will be calculated as,
A = 0.5 × d₁ × d₂
A = 0.5 × 14 × 18
A = 126 cm²
Therefore, the area of the rhombus is equal to 126 cm². The correct option is B.
To know more about an area of rhombus follow
https://brainly.com/question/24344399
#SPJ2
What is the surface area of the rectangular prism below?
A. 700 units^2
B. 1260 units^2
C. 823 units^2
D. 740 units^2
Answer:
The surface area of the rectangular prism is 700 units² ⇒ answer A
Step-by-step explanation:
* Lets revise how to find the surface are of the rectangular prism
- The rectangular prism has 6 rectangular faces
- Each two opposite faces are equal
- It has 4 side faces and 2 bases
* We can find the surface area of it by adding the area of
the 6 faces
- In the problem
# The dimensions of the bases are 12 units and 14 units
# The dimensions of the side faces are 12 units and 7 units,
14 units and 7 units
* Now lets find the area of each 2 equal faces
- In the bases
∵ Area of the rectangle = length × width
∴ The area of one base = 12 × 14 = 168 units²
∴ The area of the two bases = 2 × 168 = 336 units² ⇒ (1)
- In the two opposite faces with dimensions 12 units and 7 units
∵ The area of one face = 12 × 7 = 84 units²
∴ The area of the two faces = 2 × 84 = 168 unit² ⇒ (2)
- In the two opposite faces with dimensions 14 units and 7 units
∵ The area of one face = 14 × 7 = 98 units²
∴ The area of the two faces = 2 × 98 = 196 unit² ⇒ (3)
* To find the surface area of the prism add (1) , (2) , (3)
∴ The surface area of the prism = 336 + 168 + 196 = 700 units²
* The surface area of the rectangular prism is 700 units²
To the nearest hundredth, what is the value of x?
Answer:
1. We already have the measure of the hypotenuse and one out of two acute angle, therefore:
sin53° = x/45 => x = sin53° · 45 ≈35.94
2. We already have one out of two legs of the triangle and one acute angle so we know that:
tan27° = 48/x => x = 48/tan27° ≈ 94.21
The value of x in the first right angle triangle is 27.08.
The value of x in the second right angle triangle is 24.46.
What is the value of x?In order to determine the value of x in the first triangle, cos would be used.
Cos 53 = opposite / hypotenuse
Cos 53 = x / 45
0.7071 = x /45
x = 45 x 0.6018
x = 27.08
In order to determine the value of x in the second triangle, tan would be used.
Tan 27 = opposite / adjacent
Tan 27 = x / 48
x = 0.5095 x 48
x = 24.46
How many liters of pure water should be mixed with 18 liters of a 12% saline solution to make a saline solution that is 3% salt?
Four litres of pure water should be mixed with 18 litres of a 12% saline solution to make a saline solution that is 3% salt.
To find the litres of pure water mixed:
Given:
Pure water is mixed with 18 litres of a 12% saline solution to make a saline solution that is 3% salt.
Amount of pure water mixed =?
Now,
As given in the question, we have
18 litres of 12% saline solution
= 18 × (12/100)
= 2.16 litres
To make a saline solution containing 3% salt
Hence, four litres should be mixed to obtain a saline solution having 3% salt.
To know more about mixtures, refer:
#SPJ2
What kind of geometric transformation is shown in the music?
Will give BRAINLIEST.
Is this glide? I can't really see it. Thank you!
The geometric transformation shown in the figure is reflection.
What is Reflection?Reflection is a type of geometric transformation where the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.
here, we have,
Given is a set of lines in the music note.
Three line are drawn separating from a line.
In the first part, when we find the mirror image of the first part, we will get the second part.
Mirror images are found in the transformation of reflection.
So, here, we can say that reflection is the transformation here.
Hence the kind of geometric transformation shown in the line of music is reflection.
Learn more about Reflection here :
brainly.com/question/12604076
#SPJ3
In a village of 3500 people, 12% are left handed, and 15% of the left hand are blonde hair. How many people in the village are blonde and left-handed?
In the village of 3500 people, 63 individuals are both left-handed and have blonde hair.
Explanation:To find out how many people in the village are both left-handed and have blonde hair, we first need to calculate the number of left-handed people, and then find 15% of that number to determine those who are also blonde.
Calculate the number of left-handed people: 12% of 3500 = 0.12 × 3500 = 420.Calculate the number of left-handed people who are blonde: 15% of 420 = 0.15 × 420 = 63.Therefore, 63 people in the village are both left-handed and blonde-haired.
(08.06 MC) The distances (y), in miles, of two cars from their starting points at certain times (x), in hours, are shown by the equations below: Car A y = 55x + 32 Car B y = 42x + 58 After how many hours will the two cars be at the same distance from their starting point and what will that distance be? (5 points) 2 hours, 142 miles 2 hours, 145 miles 3 hours, 142 miles 3 hours, 145 miles
Answer:
2 hours, 142 miles
Step-by-step explanation:
Write a distance formula for both cars and then equate these formulas:
Car A: y = 55x + 32 = y = 42x + 58: Car B
Then 55x + 32 = y = 42x + 58 → 13x = 26, and so x = 2
That distance will be 55(2) + 32, or 142 miles.
The cars will reach the same point after 2 hours (first possible answer)
An equation is formed when two equal expressions. The correct option is A, 2hours, and 142 miles.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the equation for the distance covered by car A in x hours is y = 55x + 32, similarly, the equation for the distance covered by Car B in x hours is y=42x+58.
Now, to know at what time and at what distance the two cars will meet we need to solve the two equations. Since the car will cover the same distance we can write,
y = y
55x + 32 = 42x + 58
55x - 42x = 58 - 32
13x = 26
x = 2
Substitute the value of x in any one of the equations,
y = 55x + 32
y = 55(2) + 32
y = 110 + 32
y = 142
Thus, the car will meet after 2 hours, and the distance will be 142 miles.
Hence, the correct option is A, 2hours, and 142 miles.
Learn more about Equation:
https://brainly.com/question/2263981
#SPJ2
y varies inversely as x. y = 12 when x = 7. Find y when x = 6.
hope it helps you!!!!!!!!!!!!!
Answer: Y=2 !! ;) XD ;P
There are 1,000 meters in 1 kilometer. Convert 5,000 meters to kilometers. A) 0.5 km B) 5 km C) 50 km D) 500 km
Answer:
5,000 meters * 1 kilometer / 1,000 meters = 5 kilometers answer is B
Step-by-step explanation:
Answer:
the answer is 5k
Step-by-step explanation:
Which ordered pair is a solution of the equation y = 3x?
A. (-8, -18)
B. (-8, -3)
C. (-2, -9)
D. (-10, -30)
I believe it’s b or c... Hope this helps!