Answer:
Step-by-step explanation:
First, replace f(x) with y
Replace every x with a y and replace every y with an x .
Solve the equation from Step 2 for y .
Replace y with f−1(x) f − 1 ( x ) .
Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.
Final answer:
To find the inverse of a function, you reverse the original operation, whether it's an exponential with its natural log, a square with a square root, or logarithms with their exponential counterpart. These inverses, like ln(e^x) = x, demonstrate how they 'undo' each other. The inverse log can be used to find the original number from its logarithm.
Explanation:
Understanding Inverse Functions
To find the inverse of a function, you essentially want to reverse the original operation. For example, an exponential function and its inverse, the natural logarithm (ln), undo each other. If you have an equation y = ex, taking the natural logarithm of both sides would give you ln(y) = x, which effectively isolates x. This demonstrates that ln(ex) = x and eln(x) = x, showing how these functions are inverses of each other.
Similarly, other function pairs such as sine and arcsine, or a power function and its corresponding root function, act as inverse operations. For instance, if you have a2 = c2 - b2, as in the Pythagorean Theorem, you would take the square root of both sides to find a. This 'undoes' the square, showing that (√()2) is the inverse function of squaring.
When it comes to logarithms, the process of finding an inverse is similar. If you take a logarithm of a number, you can find the original number by taking the inverse log or calculating 10to the power of the logarithm. If you have log10(x) = y, then 10y = x.
Olivia ate four times as many nachos as Reagan. If Reagan ate r nachos, which equation can be used to find the number of nachos Olivia ate, v?
A. 4r = v
B. r + 4 = v
C. 4v = r
D. v + 4 = r
(as i noramlly say im terrible at math)
Answer:
A. 4r=v
Step-by-step explanation:
It says that she ate 4 times as many as Reagen and r represents the number that Reagen at so it would be 4r. While v represents how many Olivia ate which is 4r so 4r = v.
Answer:
A.4r = v
Step-by-step explanation:
Because is really asking for a ratio so the comparison of two objects
so if Olivia ate four times as much as Reagan then first start off by finding the variables which is R and V .R is how much Reagan ate well we know she at 4 times more than Olivia so 4R and now you gotta figure V how much Olivia ate so 4R = V
if you need any more help let me know ...
A cylinder has a radius of 14 m and a height of 6 m.
What is the exact volume of the cylinder?
84m^3
168m^3
504 m^3 1176m^3
Option D: [tex]1176 \pi \ {m}^{3}[/tex] is the volume of the cylinder
Explanation:
Given that the cylinder has a radius of 14 m and a height of 6 m
We need to find the exact volume of the cylinder.
The formula to determine the volume of the cylinder is given by
[tex]Volume=\pi r^{2} h[/tex]
Let us substitute [tex]r=14[/tex] and [tex]h=6[/tex] in the above formula, we have,
[tex]Volume=\pi (14)^{2} (6)[/tex]
Squaring the terms, we get,
[tex]Volume=\pi (196)(6)[/tex]
Multiplying we have,
[tex]Volume=1176\pi \ m^3[/tex]
Thus, the volume of the cylinder is [tex]1176 \pi \ {m}^{3}[/tex]
Therefore, Option D is the correct answer.
volume of a cone with a diameter of 3.5 and a height of 8.4.
Answer: volume is 26.9
Step-by-step explanation:
Volume of a cone is calculated by V=πr^2h/3
Where π is a constant, with value of 3.14
h is height, given as 8.4
r is radius, radius = diameter ÷ 2
Since Diameter is given as 3.5, radius = 3.5/2 = 1.75
Slot the values into the formula
V= 3.14 x 1.75^2 × 8.4/3
= 3.14 x 3.06 x 2.8
=26.9
I hope this helps.
Answer:
0.416
Step-by-step explanation:
How to get the answer for this?
Answer:
NF = 16 units
Step-by-step explanation:
The in-center of a triangle is a point inside the triangle and equidistant from the three sides of the triangleIt is the center of the circle which touch the three sides of the triangle (each side of a triangle is tangent to the circle and the segments drawn from it to the points of tangent are radii of the circle)∵ N is the in-center of ΔABC
∴ N is equidistant from the sides AB, BC and CA
- That means the perpendicular segments from N to AB, BC
and AC are equal
∴ ND = NE = NF
∵ ND = 6x - 2
∵ NE = 3x + 7
- Equate them to find x
∴ 6x - 2 = 3x + 7
- Subtract 3x from both sides
∴ 3x - 2 = 7
- Add 2 to both sides
∴ 3x = 9
- Divide both sides by 3
∴ x = 3
- Substitute the value of x in ND to find its length
∵ ND = 6(3) - 2 = 18 - 2
∴ ND = 16 units
∵ ND = NE = NF
∴ NF = 16 units
What percent of 32 is 57?
Answer:
56.14%
Step-by-step explanation:
Answer: 56.140350877193%
Step-by-step explanation:covert fraction (ratio) 32/57 that’s how you get your answer.
Which number could the point D represent?????????
Answer:
[tex]\leq[/tex]11
Step-by-step explanation:
Answer:
115
Step-by-step explanation:
Do you know what 2/9 x 3 is?
Answer:
[tex]answer = \frac{2}{3} [/tex]
[tex] \frac{2}{9} \times \frac{3}{1} \\ = \frac{6}{9} = \frac{2}{3} [/tex]
Answer:
it is 2/3
since your multiplying a fraction times 3 you should put it over 1 to make it a fraction and then just multiply across and simplify hope this helps!!
Find the value of each variable. If you answer is not an integer, express it in simplest rauitar
Also find the perimeter of the triangle.
Solve the equation 3^(2x) -4*3^(x+1) + 27 = 0. use rules of exponents to change 3^(x+1)
Answer:
[tex]\huge\boxed{x=1\ \vee\ x=2}[/tex]
Step-by-step explanation:
[tex]3^{2x}-4\cdot3^{x+1}+27=0\\\\\text{use}\ (a^n)^m=a^{nm}\ \text{and}\ a^n\cdot a^m=a^{n+m}\\\\\left(3^x\right)^2-4\cdot3^x\cdot3^1+27=0\\\\\left(3^x\right)^2-12\cdot3^x+27=0\\\\\text{substitute}\ 3^x=t>0\\\\t^2-12t+27=0\\\\t^2-3t-9t+27=0\\\\t(t-3)-9(t-3)=0\\\\(t-3)(t-9)+0\iff t-3=0\ \vee\ t-9=0\\\\t-3=0\qquad\text{add 3 to both sides}\\\boxed{t=3}\\\\t-9=0\qquad\text{add 9 to both sides}\\\boxed{t=9}[/tex]
[tex]\text{We return to substitution:}\\\\3^x=t\\\\3^x=3\ \vee\ 3^x=9\\\\3^x=3^1\ \vee\ 3^x=3^2\\\\\boxed{x=1}\ \vee\ \boxed{x=2}[/tex]
Final answer:
To solve the given equation involving exponents, convert 3^(x+1) and solve as a quadratic equation.
Explanation:
The equation is: 3^(2x) - 4*3^(x+1) + 27 = 0. To solve this, we can use the rules of exponents to change 3^(x+1) into 3*3^x.
Step-by-step solution:
Substitute 3^(x+1) with 3*3^x in the equation.
Now, you have a quadratic equation in terms of 3^x, solve it to find the value of 3^x.
Once you find the value of 3^x, proceed to find the value of x.
Find the least common multiple of the following polynomials: 5y2 -80 and y + 4.
Answer:
[tex]5 {y}^{2} - 80[/tex]
Step-by-step explanation:
The given polynomials are:
[tex]5 {y}^{2} - 80[/tex]
and
[tex]y + 4[/tex]
Let us factor the first polynomial to get:
[tex]5 {y}^{2} - 80 = 5( {y}^{2} - 16)[/tex]
We need to rewrite as difference of two squares:
[tex]5 {y}^{2} - 80 = 5( {y}^{2} - {4}^{2} )[/tex]
We can now factor to get:
[tex]5 {y}^{2} - 80 = 5( {y} - 4)(y + 4)[/tex]
So the least common multiple of
[tex]5( {y} + 4)(y - 4) \: and \: (y + 4) \: is \: 5( {y} + 4)(y - 4) = 5 {y}^{2} - 16[/tex]
l
x^3-10x=100
Use a trial and improvement method to find this solution.
Give your answer to 1 decimal place.
Show working
The value of x is approximately 5.4 when x^3 -10x = 100
How to solve the equation?The equation is given as:
x^3 -10x = 100
Using trial by error, we keep testing for the value of x that is true for x^3 -10x = 100
After several attempts, we have:
x = 5.4 (approximately)
Substitute 5.4 for x in x^3 -10x = 100
5.4^3 -10 * 5.4 = 100
Evaluate
103.5 = 100
Approximate
100 = 100
This means that x is approximately 5.4 when x^3 -10x = 100
Read more about equations at:
https://brainly.com/question/2972832
#SPJ1
A solution to the equation x^3 −10x=100 using the trial and improvement method is approximately x=5.3 (rounded to 1 decimal place).
let's use the trial and improvement method to find a solution for the equation
x^3 −10x=100.
Start with a reasonable guess for x. In this case, it's often helpful to start with small integers.
Substitute the guess into the equation and see if it satisfies the equation.
Let's try
5^3 −10×5=125−50=75
The result is not equal to 100. Since the result is less than 100, we need to increase our guess.
Let's try
6^3 −10×6=216−60=156
The result is still not equal to 100. Since the result is now greater than 100, we need to decrease our guess.
Let's try
5.5^3 −10×5.5=166.375−55=111.375
This result is still greater than 100, so we need to try a smaller value.
5.2^3 −10×5.2=140.608−52=88.608
Now, this result is closer to 100. We can continue to refine our guess.
Let's try
5.3^3 −10×5.3=150.097−53=97.097
This result is getting closer to 100. We can keep refining our guess, but for the sake of brevity, let's stop here.
So, a solution to the equation x^3 −10x=100 using the trial and improvement method is approximately x=5.3 (rounded to 1 decimal place).
for such more question on improvement method
https://brainly.com/question/30182691
#SPJ3
Find the equation of the line that passes through the points (-800, 200) and (-400, 300).
Answer:
y=1/4x+400
Step-by-step explanation:
Slope=Rise/Run=(300-200)/(-400-(-800))=100/400=1/4
Now we have the slope, making our equation:
y=1/4x+b
We need b, the y-intercept, which we can use any ordered pair to plug in:
200=1/4(-800)+b
200=-200+b
400=b
So the equation that passes through the points (-800, 200) and (-400, 300) is: y=1/4x+400
The equation of line that passes through the points P(-800, 200) and Q(-400, 300) is y = x/4 + 400.
What is the general equation of straight line?
The general equation of straight line is -
y = mx + c
Given is a line that passes through the points P(-800, 200) and
Q(-400, 300).
First we will find the slope of the line -
m = (y₂ - y₁)/(x₂ - x₁)
m = (300 - 200)/(-400 + 800)
m = 100/400
m = 1/4
Now, the line passes through the point Q(-400, 300). Therefore -
300 = (1/4) x (- 400) + c
300 = - 100 + c
c = 400
The final equation of the line will be -
y = x/4 + 400
Therefore, the equation of line that passes through the points P(-800, 200) and Q(-400, 300) is y = x/4 + 400.
To solve more questions on Straight lines, visit the link below-
https://brainly.com/question/27730503
#SPJ2
Of the 250 cats in a local cat show, 73 are orange, 11 are white, 80 are black, 27 are calico, 50 are gray, and 9 are tuxedo. To the nearest thousandth, what is the probability a
randomly selected cat from the show will be gray or tuxedo?
Answer:
[tex]0.236[/tex]
Step-by-step explanation:
The total number of cats in a local cat show is 250
Of these, 73 are orange, 11 are white, 80 are black, 27 are calico, 50 are gray, and 9 are tuxedo.
The probability of a
randomly selected cat from the show will be gray or tuxedo is
[tex] = \frac{50}{250} + \frac{9}{250} [/tex]
We simplify to get:
[tex] = \frac{50 + 9}{250} [/tex]
[tex] = \frac{59}{250} [/tex]
[tex] = 0.236[/tex]
To find the probability of selecting a gray or tuxedo cat in a cat show, add the number of gray and tuxedo cats, then divide by the total number of cats.
The probability that a randomly selected cat from the show will be gray or tuxedo is calculated by adding the number of gray cats and tuxedo cats, then dividing by the total number of cats.
Number of gray cats = 50
Number of tuxedo cats = 9
Total number of gray or tuxedo cats = 50 + 9 = 59
Probability = Number of gray or tuxedo cats / Total number of cats
Probability = 59 / 250 ≈ 0.236
what is it ????????????????????
Answer:
B. 1/10 i think c:
Step-by-step explanation:
Answer: 0.65 I think 1/10
Step-by-step explanation: You find 25% of 1, (.25), then add 2/5
Please help I’ve been stuck on it forever. :(
Answer:
$31.37 is the sale price
Step-by-step explanation:
All you need to do to find the discount price (sale price) is multiply the price of the item by the decimal form of the percentage.
1. Store A. 40% off the original price of $159.99
[tex](159.99 * .40) = 63.996[/tex]
63.996 is the discount price we are looking for
2. Store B. 25% off the original price of $130.50
[tex](130.50 * .25) = 32.625[/tex]
32.625 is the discount price we are looking for
3. Now to find their difference you just subtract the two values.
[tex]($63.996 - $32.625) = $31.371[/tex]
The discount price (sale price) is $31.371
Mrs.Kennedy has 1/4 liter of oranges she want to give 3 students in her advisory
2+2 is 4
4+4 is 8
What is 8+8
Answer:
The answer is 16
Step-by-step explanation:
The roots of a quadratic equation depend on the values of the coefficients.
True
False
Answer:
True
Step-by-step explanation:
The nature of roots of a quadratic equation are determined by
[tex] {b}^{2} - 4ac[/tex]
where a, b, and c are the coefficients of the quadratic equation
[tex]a {x}^{2} + bx + c = 0[/tex]
Therefore it is true that, the roots of a quadratic equation depend on the values of the coefficients.
What is the surface area of the cylinder with height 3yd and radius 4yd?Round your answer to the nearest thousandth.
Answer:
175.93cm²
Step-by-step explanation:
Answer: 175.929 yd^2
Step-by-step explanation:
Factor the following polynomial: "4x2−16"
Answer:
Step-by-step explanation:
does it have to be right?
How do I do this table !!!
Answer:
Step-by-step explanation:
just mutiply 120 by 1,2,3,4,5,6,7,8
Which statements are true about the components of a circle? Check all that apply.
The radius is half the length of the diameter.
The circumferences is triple the radius.
The circumference is the perimeter of a circle.
To find the circumference, multiply it by the diameter.
The diameter is triple the length of the radius.
The radius of a circle is half the length of the diameter, and the circumference is the perimeter of the circle. However, the circumference is not triple the radius, and the diameter is not triple the length of the radius.
Explanation:In the context of Mathematics, particularly geometry, the following statements are indeed true about the components of a circle:
The radius is half the length of the diameter. This is because the radius of a circle is defined as the distance from the center of the circle to its edge, while the diameter is the distance across the circle passing through the center. The circumference is the perimeter of the circle. This perimeter is also called the circumference in the context of circles, as it is the length around the edge of the circle.However, the statements that the circumference is triple the radius, to find the circumference multiply it by the diameter, and the diameter is triple the length of the radius, are incorrect. The circumference of a circle is calculated as 2πr (two times the radius times Pi), and the diameter is twice the length of the radius, not triple.
Learn more about Circle Components here:https://brainly.com/question/32128061
#SPJ12
determine the measures of the unknown angles in the figure
PLEASE HELP WILL GIVE MANY POINTS
Answer: You will need to put a protractor over the paper for me to answer the first one because I can only answer with protractors
Step-by-step explanation:
Answer:
apd=115
cpe=25
bpd=65
Step-by-step explanation:
1. Write the rule for finding a reflection of a point across the y-axis. 2. Use this rule to find the coordinates for the reflection of point (−3, −6) across the y-axis.
Answer:
(3,6) if (-3,-6) is reflected off the y-axis
Which expression is equivalent to (3x2-7
(2x - 11)-(x2+4)
(522-6)-(2x2-1)
(10x2-4)-(7x+3)
(15x2 +8)= (18x2 +1)
The equivalent value of the expression is A = ( 10x² - 4 ) - ( 7x² + 3 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = 3x² - 7 be equation (1)
On simplifying , we get
Let the second expression be represented as B
where B = ( 10x² - 4 ) - ( 7x² + 3 )
On simplifying , we get
B = 10x² - 4 - 7x² - 3
B = ( 10x² - 7x² ) - ( 4 + 3 )
B = 3x² - 7
Therefore , the value of B = A
Hence , the expression is B = ( 10x² - 4 ) - ( 7x² + 3 )
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ7
{d(1)=13
{d(n)=d(n−1)+17
Find the 4 term in the sequence
d(4) = 64
Step-by-step explanation:
Step 1:
d(n)=d(n−1)+17
d(2) = d(1) +17
= 13+17
= 30
d(3) = d(2) + 17
= 30+17
=47
Step 2:
d(4) = d(3) + 17
= 47+17
= 64
The bill for dinner was $73.57 you left $11.43 for the tip what percentage of the original bill was the tip ? Round to the nearest whole percent
Answer:
16%
Step-by-step explanation:
Percentage of the tip is the tip divided by the original bill and the result multiplied by 100%
That’s
$11.43/$73.57 x 100%
0.1554 x 100%
15.54
16%
The tip was 16% of the original bill
The tip was about 16% of the total bill. This was calculated by dividing the tip amount by the total bill, multiplying by 100 to get a percentage, and then rounding to the nearest whole percent.
Explanation:To find out what percentage the tip was of the original bill, you would divide the amount of the tip by the total bill before the tip, and then multiply that number by 100 to get a percentage. Here's how you would calculate it in this case:
First, divide $11.43 (the amount of the tip) by $73.57 (the original bill). This will give you the decimal 0.1554285.Multiply this decimal by 100 to convert it to a percentage. This will give you 15.54285. Round this number to the nearest whole percent. The rounded percentage in this case is approximately 16%.So, the tip was about 16% of the total bill.
Learn more about Percentages here:https://brainly.com/question/32197511
#SPJ3
a drawing of a shape that is proportional to another is called
a. scale drawing
b. angle
c. degree
d. polygon
A scale drawing is a drawing made with proportionate scaling. It helps represent objects or spaces accurately and proportionally.
A scale drawing is a drawing that is done with a scale so that specific small units of measure represent larger units of measure. Scale drawings are used to represent objects or spaces proportionally, aiding in visualizing and understanding relationships between different elements.
What is an inequality
Adam got 97, 70, 89, 99, 100, 78, 79, 89, 77, and 72 on his reading test. What is the mean of Adam's reading test?
Answer:
97+70+89+99+100+78+79+77+72=85