Answer:
EF = 11
Step-by-step explanation:
AD/DE = 3
Therefore, DC/3 = EF
33/3 = 11
7. Find the inverse of f(x) = 4x^3 + 8.
Answer:
The inverse of [tex]\displaystyle{f(x)=4x^3+8}[/tex] is determined to be [tex]{f^{-1}(x)=\sqrt[3]{\frac{1}{4}x-8}[/tex].
Step-by-step explanation:
In order to find the inverse of a function, we need to know a couple of rules about functions.
f(x) = yTo find the inverse, we flip the y-variable with the x-variables and solve for y.Following these rules, our function now becomes [tex]\displaystyle{x=4y^3+8}[/tex].
We now can simplify it further in order to find the value of x.
[tex]\displaystyle{x=4y^3+8}\\\\4y^3=x-8\\\\y^3=\frac{x}{4}-8\\\\\sqrt[3]{y^3}=\sqrt[3]{\frac{x}{4}-8} \\\\y = \sqrt[3]{\frac{1}{4}x-8}\\\\f^{-1}(x)= \sqrt[3]{\frac{1}{4}x-8}[/tex]
Therefore, the inverse of [tex]\displaystyle{f(x)=4x^3+8}[/tex] is [tex]\displaystyle{f^{-1}(x)=\sqrt[3]{\frac{1}{4}x-8}[/tex].
Answer:
[tex]\huge\boxed{f^{-1}(x) = \sqrt[3]{\frac{x-8}{4}}}[/tex]
Step-by-step explanation:
In order to find the inverse of a function, we need to follow a series of steps.
1. Write the function in the form [tex]y=ax^b+c[/tex]
2. Swap where the x and y values are
3. Solve for y
4. Convert into [tex]f^{-1}(x)[/tex] form
So first, we can write [tex]f(x)=4x^3+8[/tex] as [tex]y=4x^3+8[/tex].
Now we need to swap where the x and y variables are. This makes our equation [tex]x=4y^3+8[/tex].
To find the inverse, we now need to solve for y in this equation.
[tex]x=4y^3+8[/tex] Subtract 8 from both sides:[tex]x-8 = 4y^3[/tex] [tex]4y^3 = x-8[/tex] Divide both sides by 4:[tex]y^3 = \frac{x-8}{4}[/tex] Take the cube root of each side: [tex]y = \sqrt[3]{\frac{x-8}{4}}[/tex] Convert into [tex]f^{-1}(x)[/tex] form [tex]f^{-1}(x) = \sqrt[3]{\frac{x-8}{4}}[/tex]Therefore, the inverse of this function is [tex]f^{-1}(x) = \sqrt[3]{\frac{x-8}{4}}[/tex].
Hope this helped!
Aubrey’s monthly bank statement shows a total of $51 in fees for ATM withdrawals. If Audrey made 17 withdraws, what is Audrey charged for each withdrawal?
Answer:
Audrey was charged $3 for each withdrawal.
Step-by-step explanation:
We have to calculate the amount of money charged on one transaction.
In order to find the amount for one ATM withdrawal, the total amount for ATM withdrawals will be divided by number of withdrawals.
Given
[tex]Total\ ATM\ withdrawal\ fees = \$51\\Total\ withdrawals = 17\\Amount\ for\ one\ withdrawal = \frac{Total\ fees}{No.\ of\ withdrawals}\\= \frac{51}{17}\\= \$3[/tex]
Hence,
Audrey was charged $3 for each withdrawal.
work out (-5)2
I will mark brainest but the answer has to be right
the cost of a family membership at a health club $58 per month plus a one time 129 start up fee . if a family spent 651 , how many months is their membership?
Answer:
9 months
Step-by-step explanation:
651=58x+129
-129 -129
522=58x divide 522 by 58
=9
An internet analytics company measured the number of people watching a video posted on a social media platform. The company found 129 people had watched the video and that the number of people who had watched it was increasing by 30% every 3 hours.
(a)
Write an exponential function for the number of people A who had watched the video n hours after the initial observation. (Enter a mathematical expression.)
Answer:
(a) The exponential function representing the number of people who had watched the video [tex]t[/tex] hours after the initial observation is [tex]n(t) = 129\cdot 1.3^{\frac{t}{3} }[/tex].
(b) As [tex]n(120) < 5\times 10^{6}[/tex], we conclude that this video is not going "viral".
Step-by-step explanation:
Statement is incomplete. The complete statement is:
An internet analytics company measured the number of people watching a video posted on a social media platform. The company found 129 people had watched the video and that the number of people who had watched it was increasing by 30% every 3 hours.
(a) Write an exponential function for the number of people A who had watched the video n hours after the initial observation.
(b) A video is said to go "viral" if the number of people who have watched the video exceeds 5 million within 5 days (120 hours). Would this video be considered to have gone viral?
(a) From the statement of the problem we get the following relationship:
[tex]\frac{n_{i+1}}{n_{i}}= r^{[(i+1)-i]}[/tex] (Eq. 1)
Where:
[tex]n_{i}[/tex] - i-th number of people watching a video, dimensionless.
[tex]n_{i+1}[/tex] - (i+1)-th number of people watching a video, dimensionless.
[tex]r[/tex] - Increase ratio, dimensionless.
For Induction Theorem, we get the following relatioship for [tex]i = 0[/tex]:
[tex]\frac{n_{1}}{n_{o}} = r^{1-0}[/tex] (Eq. 2)
For [tex]i = m[/tex], the following relationship is constructed:
[tex]\left(\frac{n_{1}}{n_{o}} \right)\cdot \left(\frac{n_{2}}{n_{1}} \right)\cdot ...\cdot \left(\frac{n_{m+1}}{n_{m}} \right) = r^{m}[/tex]
[tex]\frac{n_{m+1}}{n_{o}} = r^{m}[/tex](Eq. 3)
And for [tex]i = m+1[/tex], we have the following expression:
[tex]\left(\frac{n_{1}}{n_{0}} \right)\cdot \left(\frac{n_{2}}{n_{1}} \right)\cdot ...\cdot \left(\frac{n_{m+2}}{n_{m}} \right) = r^{m+1}[/tex]
[tex]\frac{n_{m+2}}{n_{0}} = r^{m+1}[/tex](Eq. 4)
If we multiply (Eq. 3) by the (m+1)-th ratio based on (Eq. 1):
[tex]\left(\frac{n_{m+1}}{n_{o}}\right)\cdot \left(\frac{n_{m+2}}{n_{m+1}} \right) = r^{m} \cdot r[/tex]
[tex]\frac{n_{m+2}}{n_{o}} = r^{m+1}[/tex]
Which is (Eq. 4) and the exponential function is represented by:
[tex]n_{i+1} = n_{o}\cdot r^{i}[/tex], [tex]i\in \mathbb{N}_{O}[/tex] (Eq. 5)
As the number of people is increased at constant rate every 3 hours, we get that [tex]i[/tex] is:
[tex]i = \frac{t}{3}[/tex], [tex]t \in \mathbb{R}[/tex], [tex]t \geq 0[/tex] (Eq. 6)
Where [tex]t[/tex] is the time, measured in hours.
Then, the exponential function is:
[tex]n(t) = n_{o}\cdot r^{\frac{t}{3} }[/tex] (Eq. 7)
Where [tex]n_{o}[/tex] is the initial number of people watching the video, dimensionless.
If we know that [tex]n_{o} = 129[/tex] and [tex]r = 1.3[/tex], then the exponential function representing the number of people who had watched the video [tex]t[/tex] hours after the initial observation is:
[tex]n(t) = 129\cdot 1.3^{\frac{t}{3} }[/tex]
(b) If we know that [tex]t = 120\,h[/tex], then we evaluate the exponential function:
[tex]n (120) = 129\cdot 1.3^{\frac{120}{3} }[/tex]
[tex]n(120) = 4.659\times 10^{6}[/tex]
As [tex]n(120) < 5\times 10^{6}[/tex], we conclude that this video is not going "viral".
Find the value of in the triangle shown below
9, 7, and x around the triangle
Answer:
Step-by-step explanation: 56
Answer:
130 is correct
Step-by-step explanation:
Simplify (three^six)^eigthteen
Answer:
[tex](3^6)^{18}=3^{108}=3.38139191\times10^{51}[/tex]
Write the equation of the line through (3,9) and (-2,9)
Answer:
y = 9
Step-by-step explanation:
y-y1 = m(x-x1)
m is the slope =y2-y1/x2-x1=9-9/-2-3=0
pick any number out of the given two for (x1, x2)
y-9 = 0*(x-3) so
y-9 = 0 add 9 to both sides
y = 9
Which of these graphs represents a function?
Answer:
C
Step-by-step explanation:
Each x value only corresponds with 1 y value
Fred has $200. He wants to purchase a gym bag for $26 and as many pair of shoes as he can. Each pair of shoes is $45. What is the maximum number of pairs of shoes he can
purchase in addition to the gym bag?
Answer:
3 shoes
Step-by-step explanation:
You can set up an equation to solve this question like this:
200=45s+26
174=45s
174/45=s
s=3.867
You can't have a part of a shoe, so you have to round down to get 3 shoes
Answer:
3
Step-by-step explanation:
In order to get the answer to this question you subtract in till you can no longer subtract after subtracting the cost of the bag.
What we do know:
[tex]M=200[/tex]
[tex]B=26[/tex]
[tex]S=45[/tex]
[tex]200-26=174[/tex]
[tex]174-45=129[/tex]
[tex]129-45=84[/tex]
[tex]84-45=39[/tex]
[tex]S=3[/tex]
Hope this helps
Omar has a gift card for $25 at a clothing store. He wants to buy socks that cost $4 per pair. He also has a coupon for $5 off his entire purchase. Omar wants to know how many pairs of socks he can buy. Write and inequality that represents the situation.
Answer:
4x ≤ 30
Step-by-step explanation:
Omar gets 30 dollars off because $25 + $5 = 30. Let x = pairs of socks
We know each pair costs $4, so the cost would be 4x. Omar has to buy as many pairs as he can with only the coupon and gift card. Omar has to spend $30 (the full discount) or less than $30. Therefore, the inequality would be: 4x ≤ 30 or 4x is less than or equal to 30 ($30).
Answer: 4p-5_<25
Step-by-step explanation:
i got i right
help me with this plzz i need answer asap
Answer:
oof this is easy
Step-by-step explanation:
Straight angles consists with
two right angles
2
Straight angles consists with
one obtuse angle and one acute angle
RESULT
My friend is wrong because a straight angle either consists with two right angles or one obtuse angle and one acute angle.
A class has 17 girls and 4 boys. A teacher needs something from the front office, so selects a student at random to go. Before that student comes back, another teacher drops in and selects another student at random for another task. What is the probability that a girl was selected both times?
Answer:
I think it's like 81%
Step-by-step explanation:
17 /21=.809
Please I need a answer fast
solution
X + k
X - 2k
=X+k-x-2k
=x-x+k-x-2k
=0-k
=-k
or,
1
k
an item is regularly priced at $55 it is priced at a discount of 40 off regular price what is a percent now
Answer:
Thus, a product that normally costs $55 with a 40 percent discount will cost you $33.00, and you saved $22.00. You can also calculate how much you save by simply moving the period in 40.00 percent two spaces to the left, and then multiply the result by $55 as follows: $55 x . 40 = $22.00 savings.
Step-by-step explanation:
The 7th grade class took a survey on their faviorte ice cream. 58 people said they perfer vanilla, while 28 people said they pefer chocolate. Write a ratio comparing chocolate to vanilla. (Write it in the a:b form)
Answer:
58:28
Step-by-step explanation:
simplified its 29:14!
PLEASE HELPP THIS IS IN A DIFFERENT language TO MY BRAin I swear My brain is LagGiNg RN
Answer:
A
Step-by-step explanation:
the first number in slope intercept is the slope and the second number is the y-intercept
Answer:
The answer is Choice a
Step-by-step explanation:
What is the best of these four methods to estimate of the total cost of four items priced at $5.65, $7.80, $3.25, and $4.99?
Answer:
use a calculator that should help u so much
h+ j(j – h); use h = 2, and j = 6
Answer: 32
2+6(6-2)
8(4)
32
PLEASE HELP
Given: AABC with vertices A(5,-2), B(5, -7), and C(1, -2). Which set of
coordinates best repositions the triangle to make a coordinate proof easier?
o (0,0),(4,0), and (4.-5)
O (0,0).(-4,0), and (0, -5)
O(0,0). (0,4), and (5,0)
O (0,0),(4,0), and (0, -5)
None of the other answers are correct
Answer: (0,0),(0,4), and (5,0)
Step-by-step explanation:
It is easy to find lengths of horizontal and vertical segments and distances from (0,0) so always place one vertex at the origin and one or more sides on an axis.
This answer has an x intercept and y intercept.
Tylers brother earns a commission. He makes 3.4% of the amount he sells. Last week, he sold $760 worth of shoes. How much was his commission?
Answer:
Step-by-step explanation:
760*3.4%=25.84 in commission.
Answer:
25.84
Step-by-step explanation:
760*3.4%=25.84 in commission.
Write three expressions equivalent to 3^2 9^2
Answer:
0-^
Step-by-step explanation:
. Are the expressions 3(m - 2) + 2(m - 2) and 5(m - 2) equivalent expressions?
PLEASE ANSWER THIS IS REALLY IMPORTANT!!!
Can someone help me with this question thx
Answer:
D. 3
Step-by-step explanation:
3x−2y=−6
solve for y
-2y=-3x-6
y= 3/2x+3
y=mx+b
b= y intercept --> b = 3
HELP PLZ FIRST TO ANSWE GETS BRAINLIEST
Anna works in sales and earns $100 each week plus $15 per sale. This week, she wants
to be paid at least $500. Which inequality can be used to find the number of sales she
needs to make?
O A. 100 - 15x < 500
OB. 100 + 15x < 500
O C. 100 - 15x 2 500
OD. 100 + 15x 2 500
Hey there!
I think the answer is B.
An orthocenter is the intersection of three
angle bisectors in a triangle.
altitudes in a triangle.
medians in a triangle.
perpendicular bisectors in a triangle.
Answer:
Altitudes in a triangle
option 2
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Find the rate of change given the following
points.
(-1, 3) and (1,7)
A gallon of gas costs $2.73. Walter pays for 24 gallons of gas. He gives the clerk $80.00. How much change should Walter receive after paying for the gas?
He would pay $14.48
To get this answer you would need to multiply $2.73 by 24 and subtract by $80.
Someone help please I can give brainlist?
Answer:
-2.4f - 21
Step-by-step explanation: