To determine the inverse of function f,
change f(x) to y, switch
and y,
and solve for
The resulting function can be written as
f(x) = (x - 3.
Answers
Answer:
To determine the inverse of function f, change f(x) to y, switch x and y, and solve for y.
[tex]\frac{1}{8} (x-4)^3[/tex]
Step-by-step explanation:
f(x) = [tex]\sqrt[3]{8x} +4[/tex]
Change f(x) to y: y = [tex]\sqrt[3]{8x} +4[/tex]
Switch x and y: x = [tex]\sqrt[3]{8y} +4[/tex]
Solving for y: x - 4 = [tex]\sqrt[3]{8y}[/tex]
(x-4)^3 = 8y
y = [tex]\frac{1}{8}[/tex][tex](x-4)^3[/tex]
Therefore: inverse of function f = [tex]\frac{1}{8} (x-4)^3[/tex]
The inverse function of f(x) will be f⁻¹(x) = 1/8(x - 4)³.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The function f(x) is given below.
f(x) = ∛(8x) + 4
Then the inverse function of f(x) will be
Put x = f⁻¹(x) and f(x) = x. Then we have
x = ∛{8f⁻¹(x)} + 4
∛{8f⁻¹(x)} = x - 4
Cube on both sides, then we have
8f⁻¹(x) = (x - 4)³
f⁻¹(x) = 1/8(x - 4)³
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Related Questions
Bethany and Samuel are buying a new house. They have $25,000 saved for a down payment and know that they can afford a monthly payment of $1,500 or less. They also know that the best interest rate they can get is 5.1% annually and they want to sign a 30-year mortgage.
1. This equation is used to find the monthly payment, m, given the monthly interest rate, i, the principal, P, and the number of interest periods, n, in months:
Using the equation, find the largest possible principal P for their situation. In other words, what is the largest amount of money they can borrow? (Hint: To answer the question, you must rearrange the equation.)
Answers
The largest amount of money they can borrow is $$276.268.65
How to calculate the largest amount?The main formula used in this problem is the Present Value of an annuity Formula:
P = R[1-(1+i)⁻ⁿ]/i
Where;
P: present value (the mortgage value)R: periodic paymentt: time (in years)r: annual interest ratem: number of compounding per yeari=r/m (rate per period)n=mt the total number of paymentsThe maximal monthly payment that Bethany and Samuel can afford is $1,500.
The best interest rate is %5.1 annually, and they want to sign a 30-year mortgage.
This implies that
R=1,500
t=30
r=%5.1 = 5.1 /100 = 0.051
m=12, because they make the payments monthly
i=r/m=0.051/12=0.00425
n=mt = 12*30=360
That is,
i) they will make 360 monthly payments,
ii) the largest amount of money they can borrow can be found using the formula:
P = R[1-(1+i)⁻ⁿ]/i
Substituting the known values:
P = 1500[1-(1+0.00425)⁻³⁶⁰]/0.00425
Therefore, $276.268.65 is the largest possible principal for the situation
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The first 4 terms of a 10-term geometric series are listed below. Which expression represents the sum
of the series?
16
25
8 + 4 + 10 +...+ 210
5
Answers
Given:
First 10 term of a geometric series are:
[tex]\dfrac{16}{25}+\dfrac{8}{5}+4+10+...+a_10[/tex]
To find:
The expression that represents the sum of the series.
Solution:
The first term of the given geometric series is:
[tex]a_1=\dfrac{16}{25}[/tex]
The common ratio of the given geometric series is:
[tex]r=\dfrac{a_2}{a_1}[/tex]
[tex]r=\dfrac{\dfrac{8}{5}}{\dfrac{16}{25}}[/tex]
[tex]r=\dfrac{8}{5}\times \dfrac{25}{16}[/tex]
[tex]r=\dfrac{5}{2}[/tex]
The sum of first n terms of a geometric sequence is:
[tex]S_n=\dfrac{a_1(1-r^n}{1-r}[/tex]
Where r is the common ratio.
Putting [tex]a_1=\dfrac{16}{25},r=\dfrac{5}{2},n=10[/tex] in the above formula, we get
[tex]S_{10}=\dfrac{16}{25}\left(\dfrac{(1-(\dfrac{5}{2})^{10}}{1-\dfrac{5}{2}}\right)[/tex]
Therefore, the correct option is C, i.e., [tex]\dfrac{16}{25}\left(\dfrac{(1-(\dfrac{5}{2})^{10}}{1-\dfrac{5}{2}}\right)[/tex].
Answer:
the answer is option c or 16/25 ( 1 - ( 5/2 )^10 / 1 - 5/2)
Step-by-step explanation:
You are part of a school and have to report the results of standardized test scores. Which measure of central tendency would you use? Assume that you don't know how your students will perform; consider the general effects of outliers on the three measures of central tendency. Research and summarize the general effects that outliers have on each of the measures of central tendency. Then, using some real values, provide an example of how the three measures of central tendency vary due to outlier effects.
Answers
Sue ate one sweetie one day, and each afterward she ate one sweetie more than she did the day before. How many sweeties did she eat during her first week?
Answers
on solving the provided question we can say that - by unitary method we have 12 days.
What is unitary method ?
The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
Sue ate one sweetie one day,
Sue ate 12 sweetie 12 day,
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Find the volume of the pyramid. 5 ft 2 ft 2 ft
Answers
Answer:
v=6.6667
Step-by-step explanation:
[tex]V=L*W*H/3[/tex]
[tex]V=20/3[/tex]
[tex]V=6.6667[/tex]
Hope this helps :)
What is the ?
Please help I need it quick
Answers
Explanation
Guacamole = 3
Carrot = 16
Chips = 4
True or False: 10, 8, 6, 4, … is a geometric sequence.
Answers
Answer:
False
Step-by-step explanation:
You want to know if it is true that 10, 8, 6, 4, ... is a geometric sequence.
Geometric sequenceA geometric sequence has a common ratio between adjacent terms. Here the ratios are ...
8/10 = 0.8
6/8 = 0.75
These numbers are different, so there is no common ratio. The sequence is not a geometric sequence. (False)
Center: (2, 8) radius: 3
how do I write the equation of the circle in standard form?
Answers
We are given:
Coordinates of center: (2,8)
Radius of circle: 3 units
Finding equation of the circle:
We know that the general form of a circle is:
(x-h)² + (y-k)² = (radius)²
where h is the x-coordinate of the center and k is the y-coordinate
replacing with the given values, we get:
(x-2)² + (y-8)² = (3)²
Need help finding missing answers
Answers
Check the picture below.
so let's start with 34, well a centroid is the point where all "medians" meet, well a median is half of the segment, the heck does that mean? well, it means that CG = GD, and since CD is 34, that means that GD = 17.
let's keep in mind that a centroid cuts all medians in a 2 : 1 ratio, meaning one cut-side is twice as along as the other, that said
[tex]\stackrel{\textit{keeping in mind that BG=57}}{\cfrac{BH}{HG}=\cfrac{2}{1}\implies \cfrac{BH}{HG}=\cfrac{2\cdot \frac{57}{2+1}}{1\cdot \frac{57}{2+1}}}\hspace{10em} \cfrac{BH=38}{HG=19} \\\\\\ \cfrac{HD}{EH}=\cfrac{2}{1}\implies \cfrac{HD}{15}=\cfrac{2}{1}\implies HD=30\hspace{5em}\stackrel{15~~ + ~~30}{ED=45} \\\\\\ \stackrel{\textit{keeping in mind that CF=39}}{\cfrac{CH}{HF}=\cfrac{2}{1}\implies \cfrac{CH}{HF}=\cfrac{2\cdot \frac{39}{2+1}}{1\cdot \frac{39}{2+1}}}\hspace{10em}\cfrac{CH=26}{HF=13}[/tex]
А
How many degrees must
Figure A be rotated
counterclockwise around
the origin in order to line
up with Figure B?
B
A. 90
B. 180
C. 270
D. 360
Answers
Answer:
figure a must be rotated 180°
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the perimeter of the right triangle shown
O 10 units
O 24 units
O 36 units
O 64 unitsl
Answers
Answer: 24 units.
Step-by-step explanation: To find the perimeter of a triangle, you need to add the length, width, and hypotenuse. The length and width are provided, but we need to find the hypotenuse of the triangle. To do this, we need to use the Pythagorean Theorem.
The Pythagorean Theorem is basically a^2 + b^2 = c^2 where a and b are the legs of the triangle and c is the hypotenuse (also known as the triangle's longest side). However, whatever answer you get needs to be square-rooted, which is your complete answer. Let's say that the side that's 6 units is leg a and the side that's 8 units is leg b.
6^2 + 8^2 = c^2
36 + 64 = 100
√100 = 10.
Now that we know the hypotenuse, we can add it to our other two sides.
6 + 8 + 10 = 24.
Therefore, 24 is your answer.
Let me know if this is right! :)
Solve the equation
4.173 - 10x – 2 = 42
Answers
write a real-life word problem that involves one-variable equation. Discuss how you would go about solving this problem.
help pls
Answers
Answer:
A waiter at a restaurant earns 10 dollars per hour. How much money is earned in 4 hours?
Equation: m = 10h
m = money earned
h = hours worked
Plug in 4 for (h)
m = 10(4)
m = 40 dollars
The waiter earns 40 dollars in 4 hours.
Step-by-step explanation:
Is the relation shown in the table a function?
Input: 4,8,4,8
Output: 1,3,5,4
Answers
keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, Check the picture below.
4 1/2 pt=___c
Help me pleaseeeeeee
Answers
Answer:
9 cups
Step-by-step explanation:
1 pt = 2 c
4 1/2 x 2 = 9 c
Factorize the expression, 10ab (a − 2b)³ +24ab² (3a − 6b)²
Answers
Explanation : Group and factor out the greatest common factor (GCF), then combine.
Answer:
226a³b² - 824ab³ + 984b⁴
Step-by-step explanation:
We can factorize the given expression by expanding the two binomials and then combining like terms.
First, expand the two binomials:
10ab (a − 2b)³ +24ab² (3a − 6b)² = 10ab(a³ - 6a²b + 12ab² - 8b³) + 24ab²(9a² - 36ab + 36b²)
Then, combine like terms:
= 10ab(a³ - 6a²b + 12ab² - 8b³) + 24ab²(9a² - 36ab + 36b²)
= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)
= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)
= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)
= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)
= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)
= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)
= 226a³b² - 824ab³ + 984b⁴
What is the slope for y=-3/4x+7
Answers
Answer:
-3/4
Step-by-step explanation:
y=mx+b is in slope-intercept form, in which m=-3/4 and b=7, describing the slope and y-intercept of a linear equation respectively.
What is the slope of a line that is perpendicular to the graph of the function below.
Y=1/4x-3
Answers
Answer:
The slope of a line that is perpendicular to y=1/4x-3 is -4/1x
Step-by-step explanation:
To get a perpendicular line you need to have a slope that is opposite of the other line and the opposite of 1/4 is -4/1x
If the 3rd term of an arithmetic sequence is 2 and the 17th term is -40, find the 7th term
Answers
Answer:
-10
Step-by-step explanation:
t3 = a1 + (n - 1)*d
t3 = a1 + (3 -1)*d
2 = a1 + 2d
t17 = a1 + (n - 1)*d
-40 = a1 + 16d Put the first condition underneath and subtract
2 = a1 + 2d
-42 = 14 d
d = - 3
2 = a1 + 2*(-3)
2 = a1 - 6 Add 6 to both sides
2 + 6 = a1
a1 = 8
Now you want the 7th term
t7 = a1 + (n - 1)*d
t7 = 8 + (7 - 1)*d
t7 = 8 + 6*(-3)
t7 = 8 - 18
t7 = - 10
What is a b c d and e?
Answers
Answer:
Step-by-step explanation:
5 lbs. of organic red potatoes cost
$6.00. What is the price per lb?
Answers
Answer:
0.83333333333
Step-by-step explanation:
5 lbs. of organic red potatoes cost $6.00. The price per pound of organic red potatoes is $1.20.
To find the price per pound of organic red potatoes, we can divide the total cost by the weight in pounds.
Price refers to the monetary value or amount that is assigned or charged for a product, service, or commodity. It represents the cost or value that a buyer is required to pay in exchange for obtaining or acquiring something.
Given that 5 lbs. of organic red potatoes cost $6.00, we can set up the following equation:
Price per pound = Total cost / Weight in pounds
Price per pound = $6.00 / 5 lbs.
Dividing $6.00 by 5 pounds gives us:
Price per pound = $1.20
Therefore, the price per pound of organic red potatoes is $1.20.
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Write the expression as a number in scientific notation.
the quantity 4.2 times ten to the fifth power end quantity times the quantity 1.5 times ten to the negative eighth power end quantity all divided by the quantity 2.5 times ten to the negative fourth power end quantity
2.52 × 10−1
2.52 × 101
3.2 × 10−7
3.2 × 107
Answers
On solving the provided question, we can say that - the answer of the following equation is = [tex](4.2 X 10^5)(1.5 X 10^3) / 2.5 X 10^4[/tex] = 25.2
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
[tex](4.2 X 10^5)(1.5 X 10^3) / 2.5 X 10^4[/tex]
630000/25000
25.2
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prove that the diagonals of a parallelogram bisect each other
Answers
Answer:
[ See the attached picture ]
The diagonals of a parallelogram bisect each other.
✧ Given : ABCD is a parallelogram. Diagonals AC and BD intersect at O.
✺ To prove : AC and BD bisect each other at O , i.e AO = OC and BO = OD.
Proof :[tex]\begin{array}{ |c| c | c | } \hline \tt{SN}& \tt{STATEMENTS} & \tt{REASONS}\\ \hline 1& \sf{In \: \triangle ^{s} \:AOB \: and \: COD } \\ \sf{(i)}& \sf{ \angle \: OAB = \angle \: OCD\: (A)}& \sf{AB \parallel \: DC \: and \: alternate \: angles} \\ \sf{(ii)} &\sf{AB = DC(S)}& \sf{Opposite \: sides \: of \: a \: parallelogram} \\ \sf{(iii)} &\sf{ \angle \: OBA= \angle \: ODC(A)} &\sf{AB \parallel \:DC \: and \: alternate \: angles} \\ \sf{(iv)}& \sf{ \triangle \:AOB\cong \triangle \: COD}& \sf{A.S.A \: axiom}\\ \hline 2.& \sf{AO = OC \: and \: BO = OD}& \sf{Corresponding \: sides \: of \: congruent \: triangle}\\ \hline 3.& \sf{AC \: and \: BD \: bisect \: each \: other \: at \: O}& \sf{From \: statement \: (2)}\\ \\ \hline\end{array}.
Proved ✔
[/tex]
♕ And we're done! Hurrayyy! ;)
# STUDY HARD! So, Tomorrow you can answer people like this , " Dude , I just bought this expensive mobile phone but it is not that expensive for me" [ - Unknown ] :P
☄ Hope I helped! ♡
☃ Let me know if you have any questions! ♪
[tex] \underbrace{ \overbrace {\mathfrak{Carry \: On \: Learning}}}[/tex] ☂
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
if the length of the basketball court is (x+16) and the width is (x-2). what is the area
Answers
Answer:
[tex]x^{2}[/tex]+14x-32 [tex]units^{2}[/tex]
Step-by-step explanation:
a basketball court is a rectangle, therefore its area is length x width.
the length given is (x+16)
the width given is (x-2)
substitute into the rectangular area equation:
length x width = (x+16)(x-2)= [tex]x^{2}[/tex]+14x-32
specific units (e.g. centimetres, meters, feet, etc) were not given so use the term 'units', and because we are dealing with area, use [tex]units^{2}[/tex].
therefore the answer is, [tex]x^{2}[/tex]+14x-32 [tex]units^{2}[/tex].
i hope that helps :)
Answer:
therefore the answer is, [tex]x^{2} +14x-32units^{2}[/tex].
Step-by-step explanation:
p = 800, r = 6%, t = 9 year; compounded quarterly
Answers
Answer:
The answer is 1367.31 not sure but try it
The amount will be $1367.3 after 9 years.
What is compound interest?Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
Given that, p = 800, r = 6%, t = 9 year, we need to find the amount if the principal is compounded quarterly,
A = P(1+r)ⁿ
Since, the principal is compounding quarterly, the formula will become,
A = P(1+r/4)⁴ⁿ
A = 800(1+0.06/4)³⁶
A = 800(1.015)³⁶
A = 1367.3
Hence, the amount will be $1367.3 after 9 years.
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What are 3 prime numbers that add up to 55?
Answers
Answer and Step-by-step explanation:
Prime numbers are numbered that can't be divided by whole numbers other than itself and 1.
7, 11, and 37 are prime numbers that add up to 55.
7 + 11 + 37 = 55
7 + 48 = 55
55 = 55
#teamtrees #PAW (Plant And Water)
Answer:
37+17+1
Step-by-step explanation:
I think
A prime number always has 2 factors:-)
1 and itself are its factors
I hope it helps
What symbol will you find in every linear equation?
Answers
Answer: y = mx + b
Step-by-step explanation:
PLZ HELP! A book sold 38,700 copies in its first month of release. Suppose this represents 9.8% of the number of copies sold to date. How many copies have been sold to date?
Round your answer to the nearest whole number.
Answers
Answer:
394,898
Step-by-step explanation:
9.8% = 0.098
0.098x = 38700
Divide both sides by 0.098
x = 38700/0.098
x = 394,897.9591836735
Rounding
x = 394,898
State whether the equation represents exponential growth, exponential decay, or neither.
y = 11.1.07%
Answers
Answer:
Neither
Step-by-step explanation:
This questions only states
[tex]y = 11.1.07\%[/tex]
This is not a fucntion because there is no variable.
This is not a valid statement, because 11.1.07% is non-sensical.
bruce purchased an 8 ounce can of dr. pepper, there are approximately 30 milliliters in an ounce, which measurement is closest to the amount of dr. pepper bruce purchased in milliliters?
Answers
………………….