Answer:
[tex]f^{-1}(x)=\dfrac{e^x}{3},\ x\in(-\infty,\infty),\ y>0[/tex]
Step-by-step explanation:
Consider the function [tex]f(x)=\ln 3x.[/tex] the domain of this function is x>0 and the range of this function is all real numbers. The inverse function has the domain all real numbers and the range y>0.
If
[tex]y=\ln 3x,[/tex]
then
[tex]3x=e^y,\\ \\x=\dfrac{e^{y}}{3}.[/tex]
Change x into y and y into x:
[tex]y=\dfrac{e^x}{3}.[/tex]
Thus, the inverse function is
[tex]f^{-1}(x)=\dfrac{e^x}{3}.[/tex]
ANSWER
[tex]{f}^{ - 1} (x) = \frac{ {e}^{x} }{3} [/tex]
EXPLANATION
The given logarithmic function is
[tex]f(x) = ln(3x) [/tex]
Let
[tex]y = ln(3x) [/tex]
Interchange x and y.
[tex]x = ln(3y) [/tex]
Solve for y.
[tex] {e}^{x} = {e}^{ ln(3y) } [/tex]
[tex] {e}^{x} = 3y[/tex]
Divide both sides by 3.
[tex] \frac{ {e}^{x} }{3} = y[/tex]
Therefore
[tex] {f}^{ - 1} (x) = \frac{ {e}^{x} }{3} [/tex]
Which is smaller: an angle showing a turn through 1/8 of a circle or an angle showing a turn through 1/3 of a circle? Explain your answer.
Answer:
An angle showing a turn through 1/8 of a circle is smaller
Step-by-step explanation:
we know that
A complete circle represent 360°
so
An angle showing a turn through 1/8 of a circle is
[tex](360\°)*(\frac{1}{8})=45\°[/tex]
An angle showing a turn through 1/3 of a circle is
[tex](360\°)*(\frac{1}{3})=120\°[/tex]
therefore
An angle showing a turn through 1/8 of a circle is smaller
Answer:
1/8 is smaller because it equals 45 degrees
1/3 is bigger because it equals 120 degees
y = |x| translated half a unit downward Answer:
Answer:
y=|x|-0.5
Step-by-step explanation:
downward is represented outside of the abolsute value.
Answer:
|x|-0.5
Step-by-step explanation:
its correct
need geometry help ASAP please!
Answer:
1. 121 π unit²
2. 143°
3. 151 unit²
Step-by-step explanation:
1.
Area of a circle is given by the formula A = πr²
where
A is the area,
r is the radius of the circle
From the given diagram, we can see that the radius is 11, hence the area will be:
[tex]A=\pi r^2\\A=\pi (11)^2\\A=121\pi[/tex]
The answer is [tex]121\pi[/tex] units^2
2.
The unshaded secctor and the shaded sector equals the circle. We know that circle is 360°. The unshaded sector has an angle of 217°. So the shaded part will be 360 - 217 = 143°
The measure of the central angle of the shaded sector is 143°
3.
Area of a sector is given by the formula [tex]A=\frac{\theta}{360}*\pi r^2[/tex]
Where
[tex]\theta[/tex] is the central angle of the sector (in our case it is 143°)
r is the radius (which is 11)
Plugging in all the info into the formula we have:
[tex]A=\frac{\theta}{360}*\pi r^2\\A=\frac{143}{360}*\pi (11)^2\\A=150.99[/tex]
rounding to the nearest whole number, it is 151 units^2
Identify the vertex of the graph. Tell whether it is whether it is a minimum or maximum.
A. (2,-4); maximum
B. (-4,3); maximum
C. (2,-4); minimum
D. (-4,2); minimum
Answer:
(2,-4)
Step-by-step explanation:
it is a minimum because as you can see the lowest is at the point of (2,-4)
Answer:
(2,-4)
Step-by-step explanation:
Suppose segment PQ has one endpoint at P (0,0). If T (6,3) is a point 3/10 of the way from P to Q, find the coordinates of Q.
Answer:
Q(20,10)
Step-by-step explanation:
If point T (6,3) is a point 3/10 of the way from P(0,0) to Q(x,y), then
[tex]\overrightarrow {PT}=\dfrac{3}{10}\overrightarrow {PQ}.[/tex]
Find the coordinates of the vectors [tex]\overrightarrow {PT},\ \overrightarrow {PQ}:[/tex]
[tex]\overrightarrow {PT}=(6-0,3-0)=(6,3);\\ \\\overrightarrow {PQ}=(x-0,y-0)=(x,y).[/tex]
Thus,
[tex](6,3)=\dfrac{3}{10}(x,y),\\ \\(x,y)=\dfrac{10}{3}(6,3)=(20,10).[/tex]
Is 16 gallons equal, less, or more than 64 quarts?
Answer:
less 13 gallons equals 52 quarts
Step-by-step explanation:
Equal to. There are 4 quarts in 1 gallon. So 16x4=64
A red die is tossed and then a green die is tossed. what is the probability that the red die shows a six or the green die shows a six
Answer:
1/12 or 1/6
Step-by-step explanation:
I need a multiple choice to help but if you get 2 attempts it one of these answers.
1/6 or 1/12
Step-by-step explanation: i cannot help you i need a visual representation
7x=3y+45
4x+5y=19 what’s the answer and show work
Answer:
x = 6, y = -1.
Step-by-step explanation:
7x = 3y + 45
4x + 5y = 19.... (1)
Rearranging the first equation:
7x - 3y = 45-----(2)
Multiply equation (1) by 3 and equation (2) by 5:
12x + 15y = 57
35x - 15y = 225
Adding :
47x + 0 = 282
x = 282 / 47 = 6.
To find the value of y substitute x = 6 into equation (2):
7(6) -3y = 45
-3y = 45 - 42 = 3
y = 3/-3 = -1.
Answer:
x = 6 and y = -1
Step-by-step explanation:
It is given two equations,
7x = 3y + 45
⇒ 7x - 3y = 45 -------(1)
4x + 5y=19
⇒ 4x + 5y = 19 --------(2)
To solve these equations
eq (1) * 4 ⇒ 28x - 12y =180 ----(3)
eq (2) * 7 ⇒ 28x + 35y = 133 ----(4)
eq(3) - eq(4) ⇒ 0x - 47y = 47
y = -47/47 = -1
eq(1) ⇒ = 7x - 3*-1 = 45
7x + 3 = 45
7x = 45 - 3 = 42
x = 42/7 = 6
Therefore x = 6 and y = -1
Rewrite the formula for area of a circle to find the radius of a circle.
The area of a circle (A) is given by the formula where r is the circle's radius. The formula to find r is . If and , r is centimeters.
The formula to find the radius of a circle, given the area, is r = √(A/π). This comes from rearranging the formula for the area of a circle, A = πr², to solve for r.
Explanation:The area of a circle (A) is traditionally calculated with the formula A = πr², where A represents the circle's area, and r represents the circle's radius. If we want to rewrite this formula to solve for the circle's radius (r), we would divide both sides of the equation by π and then take the square root. This gives us the formula r = √(A/π). So, if we know the area of the circle and want to find out its radius, we can use this formula.
Learn more about Area and Radius of Circle here:https://brainly.com/question/31831831
#SPJ12
The formula to find the radius r is: [tex]\[ r = \sqrt{\frac{A}{\pi}} \][/tex]
The area of a circle (A) is given by the formula [tex]A = \pi r^2[/tex], where r is the circle's radius. To find the radius r from the area A, you can rewrite the formula as follows:
Start with the area formula:[tex]\[ A = \pi r^2 \][/tex]
To solve for r, divide both sides by [tex]\pi[/tex]:[tex]\[ \frac{A}{\pi} = r^2 \][/tex]
Finally, take the square root of both sides:[tex]\[ r = \sqrt{\frac{A}{\pi}} \][/tex]
On a map the scale is 1 inch :150 miles. If the map distance is 3 inches, find the actual distance
Answer: 450 miles
Step-by-step explanation:
3 inches / 1 inch = 3 times 150 miles = 450 miles
The third term in a sequence is 11.
The term-to-term rule is “take away 4”.
Write an expression, in terms of n, for the nth term of the sequence
The nth term of the sequence can be expressed as:
[tex]T_n = -4n + 23[/tex]
Given that:The term to term rule is "take away 4"The third term of a sequence = 11Calculations of first term and of nth term:Since term to term rule is to take away 4, thus when we go back in sequence, the rule will be to add 4 term to term.
Thus:
Second term = 4 + third term = 4 + 11 = 15
First term = 4 + second term = 15 + 4 = 19
Since the given sequence has a constant difference of -4 between each adjacent terms, thus it is an arithmetic progression with d = -4
The nth term of an arithmetic progression with difference d is given by:
[tex]T_n = T_1 + (n-1) \times d[/tex]
Since d = -4 and first term is 19, thus we have:
[tex]T_n = 19 + (n-1) \times (-4) = -4n + 23\\T_n = -4n + 23[/tex]
Thus, the nth term of the sequence can be expressed as:
[tex]T_n = -4n + 23[/tex]
Learn more about arithmetic progression here:
https://brainly.com/question/24873057
The expression for the nth term of the given sequence is 23 - 4n. Starting from the third term which is 11, we find the first term and use the common difference to write the formula.
Explanation:The student is dealing with a linear sequence and is asked to write an expression for the nth term of the sequence based on the term-to-term rule 'take away 4'. To find the nth term of this arithmetic sequence, we need to use the structure of arithmetic sequences, which follow the pattern a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference between terms. Because we know that the third term is 11, we can backtrack to find the first term by adding 4 twice (since we have been taking 4 away to move forward in the sequence). Therefore, the first term a_1 is 11 + 4 + 4 = 19. Given the common difference is -4 (since we are taking away 4 each time), our nth term expression is a_n = 19 + (n - 1)(-4) or simplified a_n = 23 - 4n.
Learn more about Arithmetic Sequence here:https://brainly.com/question/34721740
#SPJ3
How far did Eddie travel after his break? (The break is the part with only the straight line!)
The break ended at 4pm when he was at 15 km.
The ride ended at 6pm when he was at 45 km.
From 4 to 6pm he rode 45 - 15 = 30 km.
Answer: it would be 30 kilometer
Step-by-step explanation:
45-15=30
On a line graph, time is usually represented by which of the following?
vertical axis
y-intercept
slope
horizontal axis
Answer:
Horizontal axis
Step-by-step explanation:
we know that
In a line graph, vertical axis usually represented the dependent variable and horizontal axis usually represented the independent variable. The time is usually represented in the horizontal axis because is a independent variable
Answer:
Horazontal Axis
The number of fish in a lake decreased by 25% between last year and this year last year there were 60 fish in the lake what is the population this year? If you get stuck consider drawing a diagram
Answer:
45
Step-by-step explanation:
Decreasing by 25% means that there is 25% less of last years amount or 0.25x less. It also means that this year there is only 75% of what was last year actually in the lake or 0.75x. Since last year, there were 60 fish, this means this year there is 0.75(60) = 45. This year has 45 fish.
Answer:
45
Step-by-step explanation:
Use factoring to solve for all the solutions of the quadratic equation. x^2 + 25=0
x=5i
x=-5i
x=+/-5
x=+/-5i
Answer:
[tex]\large\boxed{x=\pm5i}[/tex]
Step-by-step explanation:
[tex]i=\sqrt{-1}\to i^2=-1\\==========================\\\\x^2+25=0\qquad\text{subtract 25 from both sides}\\\\x^2=-25\to x=\pm\sqrt{-25}\\\\x=\pm\sqrt{(-1)(25)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\x=\pm\sqrt{-1}\cdot\sqrt{25}\\\\x=\pm i\cdot5\\\\x=\pm5i[/tex]
Answer: Answer is D
Find the area and circumference of each circle.
Listed in the Item Bank are some important labels for sections of the image below. To find out more information about labels, some have more details available when you click on them. Drag and drop each label to the corresponding area it identifies in the image.
I don't understand this question can someone please tell me the answer? I attached the picture. I will be giving 50 points for this question. Thank you!
Area = πr^2
Circumference = 2πr
Blue:
Area = 5^2 = 25π
Circumference = 2 * 5 * π = 10π
Pink:
Area = 6^2 = 36π
Circumference = 2 *6*π = 12π
White:
r = 3
Area = 3^2 = 9π
Circumference = 2 *3 = 6π
Red:
Area = 7^2 = 49π
Circumference = 2 *7 = 14π
Blue: Area - 25
Circumference - 10
Pink: Area - 36
Circumference - 12
White: Area - 9
Circumference - 6
Red: Area - 49
Circumference - 14
Hope it helped
The vertices of a rectangle are given in the columns of the matrix (picture 1).
If (picture 2) is found to perform a transformation, what are the coordinates of the transformed rectangle?
(0, 0), (0, 18), (18, 18), (18, 0)
(0, 0), (18, 0), (18, –18), (0, –18)
(0, 0), (–18, 0), (–18, –18), (0, –18)
(0, 0), (18, 0), (18, 18), (0, 18)
Answer:
(0 , 0) , (18 , 0) , (18 , -18) , (0 , -18) ⇒ the second answer
Step-by-step explanation:
∵ The vertices of the rectangles are:
(0 , 0) , (0 , 6) , (6 , 6) , (6 , 0)
∵ 3 × [tex]\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right][/tex] × R
∴ That is mean The rectangle rotate 270° around the origin
(270° anti-clockwise or 90° clockwise)
and enlargement by scale factor 3
Answer:
(0 , 0) , (18 , 0) , (18 , -18) , (0 , -18) ⇒ the second answer
Step-by-step explanation:
Mathhhh
Tasha used the pattern in the table to find the value of
Answer:
Tasha made a mistake in Step 4
Step-by-step explanation:
She made a mistake in step 4
When rewriting the value for 4^(-4)
She needed to write
(1/256) = 4^(-4)
Instead, she wrote
(1/256) = -1/4^(-4)
-1/4^(-4) = -256 ≠ (1/256)
Find the equation of the line with m = 2 and passes through the point ( 4 , − 5 ) . Write your answer in standard form A x + B y = C .
Answer:
2x - y = 13
Step-by-step explanation:
To write the equation of a line use the formula [tex]y - y_1 = m(x-x_1)[/tex].
Substitute m = 2 and (4,-5).
[tex]y --5 = 2(x-4)\\y + 5 = 2(x - 4)\\y + 5 = 2x - 8\\y = 2x -13\\-2x + y = -13\\2x - y = 13[/tex]
give the numerical coefficient of the term -x
the coefficient is the number before x
in this case the coefficient is -1.
Which transformation of Figure A results in Figure A'?
a reflection across the y-axis
a reflection across the x-axis
a clockwise rotation of 270° about the origin
a translation of 4 units right
Answer:
A
Step-by-step explanation:
Since we can see that the figure is congruent but just flipped over x = 0, we are just reflecting it across the y=axis.
Answer:
A
Reflection across the y-axis.
What is the quotient?
Answer:
1/5^9
Step-by-step explanation:
X^n / X^m = (X)^n-m
5^(-6-3)
5^-9
1/5^9
Best regards
For this case we have that by definition of power properties:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
Then, we have the following expression:
[tex]\frac {5 ^ {- 6}} {5 ^ 3}[/tex]
It can be rewritten as:
[tex]\frac {1} {5 ^ 6 * 5 ^ 3}[/tex]
By definition of power properties we have:
[tex]a ^ m * a ^ n = a ^ {m + n}[/tex]
So:
[tex]\frac {1} {5 ^ 6 * 5 ^ 3} = \frac {1} {5 ^ 9}[/tex]
Answer:
Option A
WILL MARK BRAINLIEST!! THANKS!!! 10PT!!
Answer:
line dStep-by-step explanation:
Convert the equation to the slope-intercept form (y = mx + b):
[tex]2x+5y=-10[/tex] subtract 2x from both sides
[tex]5y=-2x-10[/tex] divide both sides by 5
[tex]y=\-\dfrac{2}{5}x-2[/tex]
Put x = 0 to the equation of a line:
[tex]y=-\dfrac{2}{5}(0)-2=-0-2=-2\to(0,\ -2)[/tex]
The lines c and d passes through that's point.
Put x = 5 to the equation of a line:
[tex]y=-\dfrac{2}{5}(5)-2=-2-2=-4\to(5,\ -4)[/tex]
The line d passes through that point.
One fifth of a number is subtracted from four fifth of the same number. If the result is 9, what is the number.
Let x be the unknown number. One fifth of this number is x/5, one fourth of this number is x/4. So, we have
[tex]\dfrac{x}{4}-\dfrac{x}{5} = \dfrac{5x-4x}{20} = \dfrac{x}{20}[/tex]
We know that this difference equals 9, so we have
[tex]\dfrac{x}{20}=9[/tex]
Multiply both sides by 20 to get
[tex]x=180[/tex]
can someone please please help me!!!!!
Answer:
Diameter = 10Step-by-step explanation:
If the side of a triangle inscribed in a circle is a diameter, then it is a right triangle.
Use the Pythagorean theorem:
d - diameter
[tex]d^2=8^2+6^2\\\\d^2=64+36\\\\d^2=100\to d=\sqrt{100}\\\\d=10[/tex]
find the length of AB. leave your answer in terms of pi. Please please help!!!!
Answer:
3 pi
Step-by-step explanation:
The length of the arc AB is equal to the circumference times the fraction of the circle
AB = 2*pi*r * (degrees/360)
AB = 2 * pi* (27) * (20/360)
= 54 * pi * (1/18)
= 3 pi
We are asked to leave the answer in terms of pi
Actually, the answer should be 1/9 π. To convert from degrees to radians, you use the conversion π/180°. This is what you do: 20°/1 times π/180°. This let's you cancel out the degrees so you are left in terms of pi. That gets you 20π/180 which simplifies to 1/9 π or 0.11π if you need it as a rounded decimal.
Please can someone help me? also please explain it step by step:) ty
Answer:
The answer is D
Step-by-step explanation:
We know that a triangle adds up to 180 degrees.
Solve for x:
Combine like terms.
2x + 3x - 10 + 50 = 180
Subtract 40 on both sides.
5x + 40 = 180
-40 -40
Divide both sides by 5.
5x = 140
---- ----
5 5
And you get a solution of:
x = 28
Check:
Substitute 28 into x and multiply 28 by the number outside of the parentheses.
2(28) + 3(28) - 10 + 50 = 180
Add/Subtract from left to right.
56 + 84 - 10 + 50 = 180
Add them together.
140 + 40 = 180
And you get 180!
180 = 180
In a fish tank, the number of orange fish is 1 1/4 times the number of blue fish. Drag blue fish to represent the number of blue fish in the tank for every 5 orange fish
Final answer:
For every 5 orange fish in the fish tank, there are 4 blue fish since the number of orange fish is 1 1/4 times the number of blue fish.
Explanation:
In the fish tank scenario where the number of orange fish is 1 1/4 times the number of blue fish, for every 5 orange fish, we need to determine the corresponding number of blue fish. To find this, we can set up a ratio where the number of blue fish (let's call it B) multiplied by 1 1/4 must equal 5 (since 1 1/4 times B is the number of orange fish). So, B * 1 1/4 = 5. This equation can be simplified to B * 5/4 = 5, and by further simplification, we find B = 5 / (5/4) which is equal to B = 4. Therefore, for every 5 orange fish, there would be 4 blue fish in the tank. Hence, if you drag blue fish to represent the number of blue fish, there should be 4 of them for every 5 orange fish.
PERFORM MULITIPLICATION FFAAAASSSSTTTTT!
(b–2)(b+2)(b^2+4)
Answer: =b^4 -16
Step-by-step explanation:
* Hopefully the work below helps:)!!! Mark me the brainliest:)!!!
∞ 234483279c20∞
what is in (e^A)? A, A+1, ln A + ln e, 1 + ln A
Answer:
[tex]\large\boxed{\ln e^A=A}[/tex]
Step-by-step explanation:
[tex]Use\\\\\log_ab^n=n\log_ab\\\\\log_aa=1\\\\\ln a=\log_e a\to\ln e=1\\====================================\\\\\ln e^A=A\ln e=A(1)=A[/tex][/tex]