Answer:
1. f⁻¹(x) = ±²√(-⅓(x + 6)) + 4
2. y = ²√(x–3) + 4
3. y = (x/4)³
9514 1404 393
Answer:
f⁻¹(x) = 4 ±(1/3)√(-3x-18)y = (x -3)² +4y = x³/64Step-by-step explanation:
To find the inverse function, solve for y the equation ...
x = f(y)
__
1.
[tex]x=f(y)\\\\x=-3(y-4)^2-6\\\\x+6=-3(y-4)^2\qquad\text{add 6}\\\\\pm\sqrt{\dfrac{x+6}{-3}}=y-4\qquad\text{divide by -3, square root}\\\\4\pm\dfrac{1}{3}\sqrt{-3(x+6)}=y\qquad\text{add 4, rationalize the denominator}\\\\\boxed{f^{-1}(x)=4\pm\dfrac{1}{3}\sqrt{-3x-18}}\qquad\text{simplify the radical}[/tex]
__
2.
[tex]x=\sqrt{y-4}+3\\\\x-3=\sqrt{y-4}\qquad\text{subtract 3}\\\\(x-3)^2=y-4\qquad\text{square both sides}\\\\\boxed{y=(x-3)^2+4}\qquad\text{add 4}[/tex]
__
3.
[tex]\displaystyle x=4\sqrt[3]{y}\\\\\frac{x}{4}=\sqrt[3]{y}\\\\\left(\dfrac{x}{4}\right)^3=y\qquad\text{cube both sides}\\\\\boxed{y=\dfrac{x^3}{64}}[/tex]
f(x) = 3x + 7. What is f(4) ?
Answer:
I believe the answer is 19.
Cómo se formaron los conjuntos numéricos?
Answer:
Step-by-step explanation:
Los conjuntos numéricos son agrupaciones de números que guardan una serie de propiedades estructurales. Por ejemplo el sistema más usual en aritmética natural está formado por el conjunto de los números naturales, con la suma, la multiplicación y las relaciones usuales de orden aditivo.
What is m∠G to the nearest tenth?
Answer:
Step-by-step explanation:
tan(G) = 28.2/45.8
G = arctan(28.2/45.8) = 31.6°
Answer please and explain
Find missing side lengths
Answer:
[tex]y=30\sqrt{2}[/tex]
Step-by-step explanation:
[tex]In[/tex]Δ[tex]ABC[/tex]
[tex]tan45=AB/BC[/tex]
[tex]1=30/BC[/tex] [tex][tan45=1][/tex]
[tex]-------\\BC=30 \\-------[/tex] ⇒ [tex]OC=30\\[/tex]
[tex]and[/tex] [tex]In[/tex] Δ[tex]ABC[/tex]
[tex]Cos45=Bc/AC[/tex]
[tex]1/\sqrt{2} =x/y[/tex]
[tex]y=\sqrt{2}*x[/tex]
[tex]y=30\sqrt{2}[/tex]
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hope it helps....
have a great day!!
Don uses a funnel to pour oil into his car engine. The funnel has a radius of 6 cm and a slant height of 10 cm. How much oil, to the nearest cubic centimeter, will the funnel hold.
In a sequence of numbers, a4=12, a5=14, a6=16, a7=18, and a8=20.
Which equation can be used to find the nth term of the sequence, an?
a) an=2n+4
b) an=2n+12
c) an=3n
d) an=3n+12
I'm pretty sure it's a, but I just wanna check if I did the work right!
Answer:
you are right, it's a)❤
Step-by-step explanation:
a4=12---> put the formula in it
2×4+4=12
a5=14---> 2×5+4=14
a6=16---> 2×6+4=16
.
.
.
hope it helps❤
How do I Solve 6=18x
Answer:
1/3
Step-by-step explanation:
6=18x
for x
x=6/18
x=1/3
Formulate the null and alternative hypotheses that can be used to determine whether the school is losing money out of the raffle. Note that the issue is whether the school is losing money, not whether the school is breaking even. Please think about what the implication is when formulating the null and alternative hypotheses.
Answer:
https://brainly.com/question/23195326
Step-by-step explanation:
7a +5+2b
Select all of the true statements below.
- 2b and 5 are like terms.
- 5 is a constant.
- 2 is a coefficient.
- 7a+5+2b is written as a product of three factors.
- 7a +5+2b is written as a sum of three terms.
- None of these are true.
Answer:
5 is a constant
2 is a coefficient
7a + 5 + 2b is written as a sum of three terms
Maxwell buys a bag of dog food that contains 18 cups of food, Maxwell feeds his dog 1 cups each day. Maxwell says he will be able to feed his dog for 27 days.
correct?
Answer:
Incorrect
Step-by-step explanation:
Well since there is only 18 cups of dog food he will only be able to feed his dog for 18 days since he feeds his dog 1 cup a day.
Answer:
Incorrect
Explanation:
Maxwell's dog eats one cup of food a day. The bag contains only eighteen cups, so it will feed the dog for eighteen days. There will not be enough food to last Maxwell for 27 days. So, the answer is incorrect.
Please help, test due in 2 hours! Will give good review and brainliest.
Answer:
B. Ellipse
...............................................
how many oz do you think this cup is
Answer:
I'm gonna say 12??
Step-by-step explanation:
Am I close?
Have a nice day! <3
Please help fast!!! Thank you:)
Answer:
Step-by-step explanation:
1. 1.325 x 10^7 = 13,250,000
2. 1.02 x 10^-6 = 0.00000102
Answer:
1 one is correct
3 one is correct
5 one is correct
Step-by-step explanation:
Alice earns M dollars for working 40 hours in a week.Which expression represents the amount of money alice earns each hour?
A.40M
B.40+M
C.40/M
D.M/40
Answer:
m/40
Step-by-step explanation:
$500 at 12% for 6 months (0.5 years) Find the interest
Answer:
Step-by-step explanation:
500(.12)(.5)= $30 interest
Which is the graph of y= 2 8x - 3?
Graph B.
Graph C
Graph A
Please help!
Answer:
Graph C
Step-by-step explanation:
We can tell because the equation states that the y intercept is -3 and has a steep slope
An online retailer wants to study whether more lenient return policies increase purchasing behaviors. They
select a random sample of 2000 customers who have made purchases in the past year.
They use a random number generator to select 1000 customer account numbers to assign to the treatment
group. The remaining 1000 customers are assigned to the control group.
What type of experiment design is this?
A) randomized block
B) stratified
C) completely randomized
D) marched pairs
E) cluster
Answer: Completely Randomized
Step-by-step explanation:
effect of one primary factor rather than many different variables
As per the question the retailer wants to study the return policy that can increase the buying behavior and selects a random sample of 2000.
He uses matched pair of designs in his experiment design in which participants of the same traits get grouped in pairs. After which within each pair, one participant gets randomly allotted to either the treatment, and the other is assigned to the other part.Hence the option D is correct.
Learn more about the study whether more.
brainly.com/question/14894261.
Write a quadratic function f whose only zeros are -3 and -12
Answer:
Step-by-step explanation:
f(x) = (x + 3)(x + 12)
f(x) = x^2 + 3x + 12x + 36
f(x) = x^2 + 15x + 36
Tasha purchased an iPad for $625. A year later, it was selling for $500. What was the percent of change?
Answer:
-20
Step-by-step explanation:
i used a percentage calculator
(X-1)(-5X+1)=0
lesser X=
Greater X=
Answer:
lesser x is -5x+1
Greater x is x-1
Plz help this is due today i would have done it myself but i totally forgot about these so PLZ HELP AND NO LINKS AND NO GROSS PICTURES OR I REPORT.
Answer:
Equal sides and Equal angles
Step-by-step explanation:
Solve the inequality write the answer in interval notation 5x<10 or 15-x<7
Answer:
[tex]\left \{ {{x<2} \atop {y>8}} \right.[/tex]
Step-by-step explanation:
WILL MARK BRAINLIEST PLEASE HELP!!!
A right circular cone is intersected by a plane that passes through the cone's vertex and is parallel to its base, as in the picture below. What is produced from this intersection?
A. A Pair of intersecting lines
B. A Parabola
C. A Point
D. A Pair of parallel lines
Answer:its D. A pair of parallel lines
Step-by-step explanation:
Answer: parallel lines
Step-by-step explanation:
Round two decimal places
729015430.40641995
Answer:
729015430.40641995 = 729015430.41
Step-by-step explanation:
Since the 3 decimal place is 6, you round up. If you round up for 0 you get 1. Therefore your answer is 729015430.41.
____________________
Answer:
the equation for that line would be y=0
Step-by-step explanation:
The slope is 0 so if one were to plug in 0 as a slope to y=mx+b you would get y=0x which can be simplified to y=0. Hope this helped. :)
Fast Auto Service provides oil and lube service for cars. It is known that the mean time taken for oil and lube service at this garage is 15 minutes per car and the standard deviation is 2.4 minutes. The management wants to promote the business by guaranteeing a maximum waiting time for its customers. If a customer's car is not serviced within that period, the customer will receive a 50% discount on the charges. The company wants to limit this discount to at most 8% of the customers. What should the maximum guaranteed waiting time be
Answer:
The maximum guaranteed waiting time should be of 18.37 minutes.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
It is known that the mean time taken for oil and lube service at this garage is 15 minutes per car and the standard deviation is 2.4 minutes.
This means that [tex]\mu = 15, \sigma = 2.4[/tex]
The company wants to limit this discount to at most 8% of the customers. What should the maximum guaranteed waiting time be?
The 100 - 8 = 92th percentile, which is X when Z has a pvalue of 0.92. So X when Z = 1.405.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.405 = \frac{X - 15}{2.4}[/tex]
[tex]X - 15 = 1.405*2.4[/tex]
[tex]X = 18.37[/tex]
The maximum guaranteed waiting time should be of 18.37 minutes.
Angle Relationship: Complementary OR Supplementary
Answer:
supplementary because this is not a 90 degree angle
also i know this person, if anyone want someone to do there homework they can text yktv.sham on insta gram and you can pay her
helpppppppppppp meee
Answer:
-8
Step-by-step explanation:
Plz give brainliest
i dont have any
Quinn and Alexander are painting their bedroom. Quinn has painted 2/5 of his room. Alexander has painted 2/3 of his room. Who has the more left to paint? Explain in a sentence and solve?
Answer:
Alexander
Step-by-step explanation:
Alexander has painted 2/3 of his room. Quinn has painted 2/5 of his. To find who has painted more, convert both fractions to have the same denominators. An easy way to do this is to multiply the numerator and denominator of one fraction by the denominator of the other, then do the same for the other fraction. So, [tex]\frac{2}{3}[/tex] · 5 = [tex]\frac{10}{15}[/tex] and [tex]\frac{2}{5}[/tex] · 3 = [tex]\frac{6}{15}[/tex].
[tex]\frac{10}{15}[/tex] > [tex]\frac{6}{15}[/tex]. So, Alexander has painted more of his room than Quinn has.
