Answer:
log 3 x +1 = f^-1(x)=[tex]\frac{10^x^-^1}{3}[/tex]
log 3 (x-1) = f^-1(x)=[tex]\frac{x}{log(3)} +1[/tex]
log 3 x - 1 = f^-1=[tex]\frac{10^x^+^1}{3}[/tex]
The inverse of the function f(x) = 3x - 1 is f⁻¹(x) = (x + 1)/3.
What is an inverse function?First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.
We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.
Given, f(x) = 3x - 1.
Or y = 3x - 1.
3x = y + 1.
x = (y + 1 )/3.
f⁻¹(x) = (x + 1)/3.
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Simplify | - 7 - 1 |.
| - 7 - 1| = | - 7 + ( -1 ) |
= | -8|
= 8
= 8
| -7 - 1 | = 8
Answer:
8
Step-by-step explanation:
the letters of the word combine are placed at random in a row in how many ways can an arrangement occur such that all vowels are placed together
==========================================================
Explanation:
The word "combine" has three vowels o, i, and e.
One grouping of the three vowels together leads to oie, which we'll replace with Z for now.
So we have the "word" Zcmbn after taking out the vowels and replacing with Z temporarily. There are 5 letters in Zcmbn making 5! = 5*4*3*2*1 = 120 different permutations.
Within any permutation of Zcmbn, there are 3! = 3*2*1 = 6 ways to arrange the sequence oie
So overall there are 6*120 = 720 different ways to arrange the word "combine" such that all the vowels stick together.
If the tangent line to y = f(x) at (5, 2) passes through the point (0, 1), find f(5) and f '(5).
Answer:
f(5) = 2
f'(5) = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Tangent line to a function y = f(x) on a point (5, 2) passes through two points (5, 2) and (0, 1)
Let the equation of the line is,
y - y' = m(x - x')
Slope of a line passing through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{2-1}{5-0}[/tex]
= [tex]\frac{1}{5}[/tex]
Therefore, equation of the line passing through (0, 1) and slope = [tex]\frac{1}{5}[/tex] will be,
y - 1 = [tex]\frac{1}{5}(x-0)[/tex]
y = [tex]\frac{x}{5}+1[/tex]
Function representing equation will be,
f(x) = [tex]\frac{x}{5}+1[/tex]
At x = 5,
f(5) = [tex]\frac{5}{5}+1[/tex]
= 1 + 1
= 2
f(5) = 2
f'(x) = [tex]\frac{d}{dx}(\frac{x}{5}+1)[/tex]
= [tex]\frac{1}{5}[/tex]
Therefore, f'(5) = [tex]\frac{1}{5}[/tex] will be the answer.
is the following a function? why or why not
Answer:
No
Step-by-step explanation:
Functions can only have 1 range per domain (Only 1 Y output per X). Another method is by using the vertical line test, and in this case it fails because more than 2 points are on the same vertical line (x = 1 and x = 2)
A students regular desk is 30 inches long and 18 inches wide. The teachers desk is similar to the student desk and has a length of 50 inches. What is the width of the teachers desk?
Answer:
Width of Teacher desk = 30 in
Step-by-step explanation:
Given:
Length of student desk = 30 in
Width of student desk = 18 in
Length of teacher desk = 50 in
Find:
Width of Teacher desk
Computation:
Assume,
Width of Teacher desk = x
Teacher desk is similar to student desk
Length of student desk / Width of student desk = Length of teacher desk / Width of Teacher desk
30 / 18 = 50 / x
x = [(50)(18)] / 30
Width of Teacher desk = 30 in
[tex] |7 + 8x| > 5[/tex]
I've tried solving this inequality multiple times and I just can't get it right. I don't know what I'm doing wrong. please help
The absolute value is defined as
[tex]|x|=\begin{cases}x&\text{if }x\ge0\\-x&\text{if }x<0\end{cases}[/tex]
So for example, if x = 3, then |x| = |3| = 3, since 3 is positive. On the other hand, if x = -5, then |x| = |-5| = -(-5) = 5, since -5 is negative. The absolute value is always positive.
For the inequality |7 + 8x| > 5, you consider the two cases where the argument to the absolute value (the expression you find inside the bars) is either positive or negative.
• If 7 + 8x ≥ 0, then |7 + 8x| = 7 + 8x, so that
[tex]|7+8x|>5\implies 7+8x>5 \implies 8x>-2 \implies x>-\dfrac14[/tex]
• Otherwise, if 7 + 8x < 0, then |7 + 8x| = -(7 + 8x), so that
[tex]|7+8x|>5\implies-(7+8x)>5\implies7+8x<-5\implies8x<-12\implies x<-\dfrac32[/tex]
The solution to the inequality is the union of these two intervals.
A taxi company charges $5 to ride in the cab plus an additional $0.35 for each mile driven. If Jose has $45 and he needs to take two taxi rides, how many miles is he able to go without running out of money?
Answer:
100 miles
Step-by-step explanation:
2 rides = 10$
3.5$=10 miles x 10=35$=100 miles
Show all work
14 +18 - 2 x 18 -7
Answer:
-11
Step-by-step explanation:
BIDMAS
(BRACKETS, INDICES, DIVISION, MULTIPLICATION, ADDITION, SUBTRACTION)
14 + 18 - 2 x 18 -7
the first thing we do is the multiplication (since there is no division in this question)
14 +18 − (2)(18) −7
14 + 18 - (36) - 7
32 - 36 - 7 = -11
AC has endpoints
A(3,7) and C(6,11).
Find AB if B is the
midpoint of AC.
Answer:
d=2.5
Step-by-step explanation:
first find the coordinate of B(mid point of AC):A(3,7) C(6,11)
d=√(6-3)²+(11-7)²
d=√3²+4²
d=√9+16=√25=5
since B is the mid point : d/2=5/2=2.5
Another way :B(x1+x2/2 , y1+y2/2) , x1=3 , x2=6, y1=7, y2=11
B(9/2,18/2)
B(9/2,9)
Find AB : the length or distance between 2 points:
d=√(x2-x1)²+(y2-y1)²
d=√(3-9/2)²+(7-9)²
d=√(-3/2)²+(-2)²
d=√1.5²+4
d=√6.25
d=2.5
A cone has a diameter of 7 feet and a height of 4 feet. what is the exact volume of the cone?
Answer:
The answer is 153.86
Step-by-step explanation:
A= 3.14 x12.25>2
A= 38.465 x 4
A= 153.86
The coordinates of point T are (0,3). The midpoint of ST is (2,−2). Find the coordinates of point S. The other endpoint is nothing. (Type an ordered pair.)
Answer:
The coordinates of point S are (4,-7).
Step-by-step explanation:
Given the locations of points S and T, the midpoint coordinates are set by midpoint formulas:
[tex]\bar x = \frac{x_{S}+x_{T}}{2}[/tex] and [tex]\bar y = \frac{y_{S}+y_{T}}{2}[/tex]
Where:
[tex]x_{S}[/tex], [tex]x_{T}[/tex] - x-Components of S and T.
[tex]y_{S}[/tex], [tex]y_{T}[/tex] - y-Components of S and T.
The coordinates of S are cleared:
[tex]x_{S} = 2\cdot \bar x -x_{T}[/tex]
[tex]y_{S} = 2\cdot \bar y - y_{T}[/tex]
If [tex]\bar x = 2[/tex], [tex]\bar y = -2[/tex], [tex]x_{T} = 0[/tex] and [tex]y_{T} = 3[/tex], the equations are now solved:
[tex]x_{S} = 2\cdot (2) -0[/tex]
[tex]x_{S} = 4[/tex]
[tex]y_{S} = 2\cdot (-2)-3[/tex]
[tex]y_{S} = -7[/tex]
The coordinates of point S are (4,-7).
75% as a fraction in simplest form
Answer:
3/4
Step-by-step explanation:
Complete the equation of the line through ( 3 , − 1 ) (3,−1)left parenthesis, 3, comma, minus, 1, right parenthesis and ( 4 , 7 ) (4,7)left parenthesis, 4, comma, 7, right parenthesis.
Answer:
[tex]y=8x-25[/tex]
Step-by-step explanation:
Given the coordinates:
(3,−1) and (4,7)
To find:
The equation of line passing through the given points.
Solution:
Let us have a look at the slope intercept form of a line:
[tex]y=mx+c[/tex]
c is the y intercept.
Where [tex]m[/tex] is the slope of the line passing through the points [tex](x_1,y_1),(x_2,y_2)[/tex]
Formula for slope is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]x_1 = 3\\y_1 = -1\\x_2 = 4\\y_2 = 7[/tex]
[tex]m=\dfrac{7-(-1)}{4-3}\\\Rightarrow m = 8[/tex]
So, equation of line becomes:
[tex]y=8x+c[/tex]
Let us put (4, 7) to find the value of c:
[tex]7=8\times 4 +c\\\Rightarrow c = -25[/tex]
So, the equation is:
[tex]y=8x-25[/tex]
The equation of the line passing through the points (3.-1), and (4,7) is [tex]y=8x-25[/tex].
Given information:
The given line passes through the points (3.-1), and (4,7).
It is required to write the equation of the line.
Use the two-point form of a line to write the equation of the line:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\\y-(-1)=\dfrac{7-(-1)}{4-3}(x-3)\\y+1=8(x-3)\\y+1=8x-24\\y=8x-25[/tex]
From the above equation of the line, the slope is equal to 8.
Therefore, the equation of the line passing through the points (3.-1), and (4,7) is [tex]y=8x-25[/tex].
For more details, refer to the link:
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5
Triangle RST has the vertices R(2, 3), S(-2, 1), and T(-1,5). What are the coordinates after the
two transformations
Translation (x, y) -> (x - 2y - 1)
Rotation: 90 degrees counterclockwise at the origin. *
(2 points)
Enter your answer
Answer:
R(-2,0)
S(0,-4)
T(-4,-3)
Step-by-step explanation:
So first you gotta subtract 2 from each x value and 1 from each y value. After you do that, you get:
R(0,2)
S(-4,0)
T(-3,4)
then i put it all onto a graph, and rotated it 90* counterclockwise, from the origin, which puts it in quadrant 3, with the final coordinates above.
What is the distance between (2,-1) and (2,5)
Answer:
6
Step-by-step explanation:
Since the x coordinates are the same, we are only concerned about the y coordinates
Find the difference between -1 and 5
5 - -1
5+1
6
The distance is 6
Which best expression is the best estimate of the product of 7/8 and 8 1/10
A.0•8
B.1•10
C.7•8
D.1•8
Answer:
D. 1x8
Step-by-step explanation:
7/8 rounded is 1. And 8 and 1/10 rounder is 8, so therefore your answer is 1x8.
hope this helps! :)
124.4 divided by 4, idk they want more characters even tho it’s REALLY SIMPLE
Answer:
31.1
Step-by-step explanation:
Answer:
31.1
Step-by-step explanation:
124.4 / 4
= 0.1 * (1244/4)
= 0.1 * 311
= 31.1.
Can someone please help me with these practice problems? *URGENT*
If the bird is directly above the fish how far apart are they
Answer:
they are parallely far apart
the football team lost 8 years on every play for 5 plays which intergers shows the total number of yards the team has lost
Answer:
-40
Step-by-step explanation:
The team won 16 games and lost 8 games.
What is subtraction?
Subtraction is one of the four basic arithmetic operations that is used to find the difference.
A football team won 8 more games than they lost. They played 24 games in the season. How many games were won and how many were lost?
The team lost n games.
The team won 8 more games than it lost, so it won n + 8.
The total number of games the team played was n + n + 8, or 2n + 8.
The team played a total of 24 games, so
2n + 8 = 24
We now solve for n.
2n + 8 = 24
2n = 16
n = 8 (lost games)
n + 8 = 8 + 8 = 16 (won games)
Hence, The team won 16 games and lost 8 games.
Learn more about subtraction here;
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-3/4 x + 1/2 = 3/4 solve for x please
Answer:
[tex]x = -\frac{1}{3}[/tex]
Step-by-step explanation:
1/2 = 2/4Plug 2/4 in: -3/4x + 2/4 = 3/4Subtract 2/4 from each side, so it now looks like this: -3/4x = 1/4Divide each side by -3/4, so it cancels out the -3/4 next to x. It should now look like this: x = -1/3I hope this helps!
How much would $200 invested at 6% interest compounded annually be worth after 5 years? Round your answer to the nearest cent.m
Answer:
$252.50
Step-by-step explanation:
Furture value$252.50
Total Deposits: $200
Interest Earned: $52.50
distribute and combine √12x(-1+√5
Answer:
-2[tex]\sqrt{3x}[/tex] + 2[tex]\sqrt{15x}[/tex]
Step-by-step explanation:
Which decimal comes between 1/2 and 5/8. A. 0.629 B. 0.07 C. 0.499 D. 0.6
Answer:
D
1/2 is 0.5
5/8 is 0.625
Which one is less than 0.625 and greater than 0.5?
0.6
covert 1.3902 to centiliters
Answer:
`13.902
Step-by-step explanation:
5 3/4
i don't know how to solve this
Answer:
it would be 5.75
Hope this helps! :)
(make brainliest if it helped!!)
solve (8²)³ Simplified and what law did you use?
Answer:
[tex]8^{6}[/tex]
Step-by-step explanation:
power to power rule: multiply the bases
Answer:
262144
Step-by-step explanation:
(8²)³
When there is a power on top of a power, In this case (^2)^3, you DON'T Multiply 2 three times. You multiply two WITH 3.
SO,
(8²)³
= 8^6
Final answer =262144
A train of length 180 m approaches a tunnel of length 620 m.
How long will it take the train to pass completely through the
tunnel at a speed of 54 km/h?
PLEASE HELP QUICK!!!
find the volume of the cone. either enter an exact answer in terms of pi or use 3.14 for pi
The formula for the volume of a cone is [tex]V=\pi r^2\frac{h}{3}[/tex]
Plug in the values we know.
[tex]V=\pi (5)^2\frac{6}{3}[/tex]
[tex]V=\pi*25*2[/tex]
[tex]V=50\pi[/tex]
[tex]V=157[/tex]
^ If 3.14 was used for [tex]\pi[/tex]
Hope this helps.
頑張って!
can someone help me solve this