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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distribute and combine √12x(-1+√5
Answer:
-2[tex]\sqrt{3x}[/tex] + 2[tex]\sqrt{15x}[/tex]
Step-by-step explanation:
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
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).
Can someone please help me with these practice problems? *URGENT*
can someone help me solve this
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
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
Simplify | - 7 - 1 |.
| - 7 - 1| = | - 7 + ( -1 ) |
= | -8|
= 8
= 8
| -7 - 1 | = 8
Answer:
8
Step-by-step explanation:
[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.
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.
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?
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
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.
covert 1.3902 to centiliters
Answer:
`13.902
Step-by-step explanation:
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
If the bird is directly above the fish how far apart are they
Answer:
they are parallely far apart
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)
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
75% as a fraction in simplest form
Answer:
3/4
Step-by-step explanation:
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
-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!
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!!)
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!
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.
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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
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.
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
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.
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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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! :)