a. The inverse image of f(x) is f⁻¹(x) = ∛(x/3)
b. The inverse image of g(x) is [tex]g^{-1}(x) = e^{x}[/tex]
c. The inverse image of h(x) is h⁻¹(x) = x + 9
The domain of TSince T = {x ∈ R : 0 ≤ [x^2 − 25} ⇒ x² - 25 ≥ 0
⇒ x² ≥ 25
⇒ x ≥ ±5
⇒ -5 ≤ x ≤ 5.
Inverse image of f(x)
The inverse image of f(x) is f⁻¹(x) = ∛(x/3)
f : R → R defined by f(x) = 3x³
Let f(x) = y.
So, y = 3x³
Dividing through by 3, we have
y/3 = x³
Taking cube root of both sides, we have
x = ∛(y/3)
Replacing y with x we have
y = ∛(x/3)
Replacing y with f⁻¹(x), we have
So, the inverse image of f(x) is f⁻¹(x) = ∛(x/3)
Inverse image of g(x)
The inverse image of g(x) is [tex]g^{-1}(x) = e^{x}[/tex]
g : R+ → R defined by g(x) = ln(x).
Let g(x) = y
y = ln(x)
Taking exponents of both sides, we have
[tex]e^{y} = e^{lnx} \\e^{y} = x[/tex]
Replacing x with y, we have
[tex]y = e^{x}[/tex]
Replacing y with g⁻¹(x), we have
So, the inverse image of g(x) is [tex]g^{-1}(x) = e^{x}[/tex]
Inverse image of h(x)The inverse image of h(x) is h⁻¹(x) = x + 9
h : R → R defined by h(x) = x − 9
Let y = h(x)
y = x - 9
Adding 9 to both sides, we have
y + 9 = x
Replacing x with y, we have
x + 9 = y
Replacing y with h⁻¹(x), we have
So, the inverse image of h(x) is h⁻¹(x) = x + 9
Learn more about inverse image of a function here:
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To solve the equation 3 sin(2x) = 5cosx, you should rewrite it as
O A. cosx(3sinx - 5) = 0
0 B. cosx(6sinx - 5) = 0
O C. 3sinx + 5cosx = 0
Help me out
Answer:
OPTION B
Step-by-step explanation:
3sin(2x)=5cos(x)
3×(2sinxcosx)=5cos(x)
6sin(x)cos(x)=5cos(x)
6sin(x)cos(x)-5cos(x)=0 Factor out a cos(x)
cosx(6sinx-5)=0
help pleaseeeeee
1.) In the number 546,789, what digit indicates the value of "one hundred thousand"?
2.) What is the expanded notation of 8843?
3.) Write the following number in words: 38,403,277
Answer:
1.) 5
2.) 8,000 + 800 + 40 + 3
3.) Thirty-eight million, four-hundred and three thousand, two-hundred and seventy-seven.
Step-by-step explanation:
1.) In the number 546,789, what digit indicates the value of "one hundred thousand"? 5
2.) What is the expanded notation of 8843?
8,000 + 800 + 40 + 3
3.) Write the following number in words: 38,403,277
Thirty-eight million, four-hundred and three thousand, two-hundred and seventy-seven.
Hope this helps!
12.Identify the type of triangle
Answer:
a) acute triangle
b) obtuse triangle
c) right-angled triangle
d) equilateral
e) isosceles, right-angled triangle
Step-by-step explanation:
If all the angles in the triangle are less than 90°, it is an acute triangleIf one angle in the triangle is a right angle, then it is a right-angled triangleIf at least one angle is above 90°, it is an obtuse triangleIf all the sides of the triangle are equal, it is an equilateral triangleIf two sides of the triangle are equal, it is an isosceles triangleIf no sides of the triangle are the same length, it is a scalene triangleHope this helps!
Please can some one help me
Answer: So for Choice A 30% off $25 is $7.50 off or $17.50 which is 70% of the original price and you save 7.50 dollars.
Then for Choice B 25% off $32 is $8 off or $24 which is 75% of the original price and you save 8 dollars.
Therefor the better choice is Choice B.
Step-by-step explanation:
hope it helps
Which product is positive
Answer:
Answer: It is number 4. You are correct.
Step-by-step explanation:
-2/5-8/91/32/7
Help help math math math
Lets see some basics properties of shapes provided in the choices :
⧉ Pαrαllєlσgrαm ↬σppσѕítє ѕídєѕ αrє cσngruєnt αdjαcєnt αnglєѕ αrє ѕupplєmєntαrч ⧉ Rєctαnglє ↬❑ A spєciαl tчpє σf prαllєlσgrαm, with ѕαmє prσpєrtiєѕ
αll αnglєѕ mєαѕurє 90°⧉ Rhσmвuѕ ↬❑ A ѕpєcíαl tчpє σf pαrαllєlσgrαm wíth αll ѕídєѕ єquαl (cσngruєnt) tσ єαch σthєr вut αll αnglєѕ αrє nσt nєcєѕѕαrílч 90°
⧉ Squαrє ↬❑ A ѕpєcíαl kínd σf rhσmвuѕ hαvíng αll ѕídєѕ єquαl αnd єαch αnglє mєαѕuríng 90°
[tex]\rule{20cm}{1 mm}[/tex]
❖ Anѕwєr ~☘ So, what we can conclude from the properties is that square has all required properties asked by the question.
hence, the correct choice is ' D '
[tex]\qquad \qquad\huge \dag\normalsize \sf \boxed{ \underline{ǤríʍɌεαƿєr}} \: \huge \dag[/tex]
Which of the following represents e5 rounded to the nearest thousandth?
Answer:
C. 148.413
Step-by-step explanation:
Hope it helps!!!
Brainliest pls!!!Answer: c
Step-by-step explanation:
(06.03 MC)
An archer shoots an arrow up towards a target located on a hill, which is shown by the graph.
A graph of a line and a parabola intersecting at (48.63, 10.7).
Which set of equations best models the point of intersection of the arrow and the target?
y = –0.004x2 + 0.25x + 8 and y = x
y = 0.004x2 + 0.25x + 8 and y = 0.22x
y = –0.004x2 + 0.25x + 8 and y = 0.22x
y = –0.004x2 + 0.25x + 8 and y = –x
The set of equation that models the point of intersection of the arrow
and the target is the option; y = -0.004·x² + 0.25·x + 8 and y = 0.22·x
How can the given equations be analyzed?The given parameters are;
Point of intersection of the line and the parabola is the point (48.63, 10.7)
Therefore, the point (48.63, 10.7) satisfies both the equation of the
parabola and the equation of the line, which by plugging in the value x =
48.67 in the different parabolas, we have;
The first set;
y = -0.004 × 48.67² + 0.25 × 48.67 + 8 ≈ 10.7, which corresponds with the ordered pair.The linear function in the first set should be excluded, given y ≠ x in the
ordered pair.
In third set, y = -0.004 × 48.67² + 0.25 × 48.67 + 8 ≈ 10.7, while, from the
ordered pair, we have;
y = C·x
10.7 = 48.63·x
[tex]C = \dfrac{10.7}{48.63} \approx \mathbf{0.22}[/tex]
Therefore;
y ≈ 0.22·x
The set of equations that best models the point of intersection of the arrow and target are therefore;
y = -0.004·x² + 0.25·x + 8 and y = 0.22·xLearn more about the equation of a parabola here:
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Aliya has 125 stickers. Amari has twice
as many stickers as Aliya. How many
stickers does Amari have?
Answer:
250 stickers
Step-by-step explanation:
125 plus 125 is 250
Answer:
250 stickers because 125x2=250
Find the missing number 3+=5?
Answer:
2.
Step-by-step explanation:
We can view this problem as 5-3=?.
5-3=2
So the missing number is 2.
which two number does the square root of 61 lie between on a number line?
The square root of 61 is about 7.81, so it lies in between the numbers 7 and 8.
Hope that helps!
2 math questions please help
Answer:
Step-by-step explanation:
2)Cos²x - Sin² x = √2/2
Cos²x - Sin² x = Cos 2x
⇒ Cos 2x = √2/2
General solution for Cos 2x = √2/2 is
[tex]2x = \dfrac{\pi }{4}+2\pi n \ ; 2x=\dfrac{7\pi }{4}+2\pi n\\\\\\x = \dfrac{\pi }{2*4}+\dfrac{2\pi n }{2} \ ; \ x=\dfrac{7\pi }{4*2}+\dfrac{2\pi n}{2}\\\\\\x =\dfrac{\pi }{8}+\pi n ; \ x=\dfrac{7\pi }{8}+\pi n[/tex]
Option A
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
[tex]f(x)=5sin(\frac{x}{12})+14.5\\\\17=5sin(\frac{x}{12})+14.5\\ \\2.5=5sin(\frac{x}{12})\\ \\0.5=sin(\frac{x}{12})\\ \\\frac{x}{12}=\frac{\pi}{6}+2\pi n,\frac{5\pi}{6}+2\pi n\\ \\x=2\pi+24\pi n,10\pi+24\pi n[/tex]
Therefore, the fourth option is correct.
Problem 2
[tex]cos^2x-sin^2x=\frac{\sqrt{2}}{2}\\ \\cos(2x)=\frac{\sqrt{2}}{2}\\\\2x=\frac{\pi}{4}+2\pi n,\frac{7\pi}{4}+2\pi n\\ \\x=\frac{\pi}{8}+\pi n,\frac{7\pi}{8}+\pi n[/tex]
Therefore, the first option is correct.
A group of 180 students is divided into 20 teams for a competition. b. Part way through the competition, the students are gathered together and divided into 15 teams. If there are still 180 students in the competition, how many students are on each team now? (Enter your answer as a whole number. For example, 5)
Answer:
12 people per team
Step-by-step explanation:
180/15=12
using the spinner below, what is the probability that you will land on red or blue?
Answer:
red is 50% blue is 25%
Step-by-step explanation:
red is half the circle so it would be 50% and blue is half of a half so 25%
math help !!! could someone please explain how to find the answer
3 Which ordered pair is in the solution
set of the following inequality?
2x – 4y > 15
A (-8, -2)
B (3,4)
C (-4,0)
D (0,-4)
Answer:
D. (0,-4)
Step-by-step explanation:
When you plug in 0 into the x and -4 into the y variable you get 2(0)-4(-4)>15.
Then you solve and get 0+16>15.
then you at and get 16>15.
16 is greater than 15 which makes D correct
Solve the following equation, answer as a reduced, mixed number. Then place the correct number in the box provided. 4(7 - 3x) = 7(4 - 2x)
Answer:
x = 0
Step-by-step explanation:
4(7 - 3x) = 7(4 - 2x)
28 - 12x = 28 - 14x distributed
28 + 2x = 28 added 14x to both sides
2x = 0 subtracted 28 from both sides
x = 0 divided both sides by 2
Step-by-step explanation:
Which fractions are equivalent to 812?
Answer:
812/1 = 1624/2 = 2436/3
= 3248/4 = 4060/5 = 4872/6
= 5684/7 = 6496/8 = 7308/9
= 8120/10 = 8932/11 = 9744/12
= 10556/13 = 11368/14 = 12180/15
= 12992/16 = 13804/17 = 14616/18
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
The list tends to be much bigger.
Hope this helps!
Answer:
See below.Step-by-step explanation:
Fractions equivalent to 8/12:
2/316/2424/3636/4840/60And on and on.There is an infinite amount, but this is how far I can get.
In ΔUVW, the measure of ∠W=90°, VU = 41, UW = 9, and WV = 40. What is the value of the cosine of ∠V to the nearest hundredth?
Answer:
∠V = 12.68°
Step-by-step explanation:
In this question, we are tasked with calculating the value of the sine of ∠V to the nearest hundredth
Kindly note that since one of the angles in the triangle equals 90°, then we are dealing with a right-angled triangle.
PLEASE VIEW ATTACHMENT TO SEE THE DIAGRAM OF THE SHAPE
Mathematically, to calculate the sine of an angle in a triangle, the ratio to use is
Sine of an angle = length of side facing angle/length of hypotenuse = opposite/Hypotenuse
From the diagram, we can see that the length of the opposite is 9 while the length of the hypotenuse is 41
Sine V = 9/41
V = arcsin (9/41)
V = arcsin (0.2195)
V = 12.68° to the nearest hundredth
The value of the cosine of ∠V is 0.98
How to determine the value of the cosine of ∠V?The given parameters are:
∠W=90°, VU = 41, UW = 9,WV = 40The cosine of V is calculated using:
cos(V) = WV/VU
So, the equation becomes
cos(V) = 40/41
Evaluate
cos(V) = 0.98
Hence, the value of the cosine of ∠V is 0.98
Read more about right triangles at:
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Kai's Kites decided to advertise on billboards around town and track the relationship between the number of billboard advertisements
they posted and the number of kites they sold. This table gives the total number of billboards advertisements they bought compared
to the total number of kites they sold. The data can be modeled by a quadratic function
Billboard advertisements
1
2
3
4
5
Kite sales
6
120
229
344
463
588
717
What function best models the data?
Answer:
y=2.5x^2+102x+15.4
Step-by-step explanation:
Order the fractions from least to greatest 3/5 1/3 and 1/8 and 7/8
Please answer. Thanks! 7-5(2x-9)=-(-6x+10)+4
Answer:
x = 29/8
Step-by-step explanation:
7 - 5(2x - 9) = -(-6x + 10) + 4
7 - 10x + 45 = (6x - 10) + 4
-10x + 52 = 6x - 10 + 4
-10x + 52 = 6x - 6
52 + 6 = 6x + 10x
58 = 16x
x = 58/16 = 29/8
A principal of 4600$ is invested at 9% interest, compounded annually. How much will the investment be worth after 12 years?
Answer:
$12,938.26
Step-by-step explanation:
The equation for solving this is:
A = P(1+r/n)^nt
P = 4600
^ initial amount/principal
R = 0.09
^ rate (9% converted to a decimal)
n = 1
^ how often it is compounded (yearly, so it is 1)
t = 12
^ how long the investment is for (in years)
A = 4600(1.09)^12
A = 12,938.26
^ rounded to the nearest hundred, because when dealing with money it has to be rounded to the nearest hundred. Un-rounded the answer is 12938.2579962.
The investment will be worth $12,938.26 after 12 years.
Your credit card has a limit of $9,500 and you have a current balance of $3,200. Answer the following questions using complete sentences: is the debt ratio more or less than 43%(if you could show work for this i would apricate it )
Answer:
Step-by-step explanation:
9500/3200=296.88% i believe i did it backwards at first sorry
The value of a share of stock decreases in value at a rate of $2.70 per hour during the first 6.5 hours of
trading. Enter and solve an equation to find the decrease in the value of the share of stock during that
time. Let x represent the decrease in value of the share of stock during 6.5 hours.
Answer: the awnser will be 17.55$
Step-by-step explanation: cause you multiply 6.5 x 2.70
Describe a real world problem that you could solve using the volume of spheres
A toy company produces rubber balls that have a radius of 1.7 cm.
What is the volume of one rubber ball? Round to the
nearest hundredth of a centimeter.
20.58 cm3
If the price of the rubber needed to produce a ball is
$0.0045/cm3, what is the cost of producing one ball?
Round to the nearest cent.
If the company sells a ball for $0.50, how much profit
will it make on each ball?
$1.7 cm
20.58 cm^3, $0.09, $0.41
Hope this helps
evaluate 16 + 20/t for t =4
steps please
Answer:
21
Step-by-step explanation:16+20/t, T=4 so its 16 + 20/4, 20/4 is 5, 16+5 = 21.
Please help me I really need it. Please leave how to solve it too thank you.
Step-by-step explanation:
just look at the line.
the distance between 2 whole numbers is split into 1/2, then each 1/2 again into 1/2 = 1/4, and then every 1/4 again into 1/2 = 1/8. so, in total, we are dealing with 8 segments of 1/8 length.
now we count : we have a full 1, and then on the way to 2 we get only 5 units of 1/8 = 5/8.
so, in total the number is
1 5/8
Look at image………………………
Answer:
If I directly give you the answers they won't help you...so I've shown you how to do the questions instead
Step-by-step explanation:
8/9 + 5/6 (make them have the same denominator)
= 48/54 + 45/54
= 93/54 (make it a mixed fraction)
1 and 39/54
(The second and third one are done the same way... make them have the same denominator by using their equivalent fractions (e.g 1/2 = 2/4), add the numerators ONLY... simplify the result)
1 and 6/9 divided by 5/6
(make the first number an improper fraction)
1 x 9 + 6 = 15 (this is the numerator...the denominator remains the same)
15/9 divided by 5/6 (reciprocate the number after the division sign and then change the division sign to a multiplication sign)
15/9 x 6/5
(Then simplify. e.g the 5 in 6/5 can be divided by the 15 in 15/9)
3/9 x 6/1
(The 6 in 6/1 and the 9 in 3/9 have a common factor... 3)
3/3 x 2/1
(3/3 = 1)
1 x 2
=2
(The other questions are done in the same way... Make the mixed fraction an improper fraction(This means the denominator is larger than the numerator)... reciprocate the number after the division sign (This means flipping it (e.g 2/3 becomes 3/2) then change the division sign to a multiplication sign and either directly multiply the result or simplify it first by dividing numerators with denominators (e.g instead of 9/3 x 12/4 = 108/12 = 9, you could say 1 divided 3 = 4 thus 9/1 x 4/4 (which is = 1) thus 9 x 1 = 9). Either way you should get the same answer whichever way you choose.
PS: YOU COULD ALSO USE A CALCULATOR TO CONFIRM YOUR ANSWER
#1
8/9÷5/6=8/9×6/5=16/15#2
7/10÷12/25=7/10×25/12=35/25#3
2/3÷1/5=2/3×5=10/3#4
1-6/9÷5/6=15/9×6/5=2#5
2-3/4÷3/8=11/4×8/3=22/3A dance studio is purchasing tutus for an annual performance. The table represents the number of tutus available for different prices. What is the difference between the unit price of the LEAST EXPENSIVE DEAL and the unit price of the MOST EXPENSIVE DEAL?
Answer: 8
Step-by-step explanation:
420/12 is 35
540/20 is 27
35-27=8