The inverse of the function y = log(x₊1) is f ⁻¹(x) = 10ˣ ₋ 1.
Given the function is :
y = log(x₊1)
we are asked to find the inverse of the function.
steps to find inverse function are:
Change f(x) to y to get y = ax + b for the provided function f(x) = ax + b.To get x = ay + b from the equation y = ax + b, replace x with y and y with x.Here, find y and solve for x = ay + b. Then we get y = (x - b/a).Finally, we can substitute y = f-1(x) with f-1(x) = (x - b)/a.now interchange the positions of x and y in the function.
x = log₁₀ (y ₊ 1)
the next step is to isolate the dependent variables.
f ⁻¹(x) = ₋1 ₊ 10ˣ
f ⁻¹(x) = 10ˣ ₋ 1
hence, we get the inverse of the given function as f ⁻¹(x) = 10ˣ ₋ 1.
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I need help please, I’m a little stuck
Answer:
[tex]\boldsymbol{\boxed{f(-4) = -1}}[/tex]
Step-by-step explanation:
[tex]\displaystyle f(x) = \left \{ {{x + 3, x < -1} \atop {-4x -2,x \geq 1}} \right.[/tex]
[tex]-4 < -1 \Longrightarrow f(-4) = -4 + 3 =-1[/tex]
[tex]\boxed{f(-4) = -1}[/tex]
Questions in the picture
Answer:
198299 - Hundreds
2040949 - Millions
94.542 - Hundredths
5848 = 5800
1.83 = 2
459900 = 460000
0.07234 = 0.07
How is 6×1+5×(110)+2×(1100) written in standard form?
A
652
B
256
C
6.52
D
0.652
Answer:
The answer is C = 0.652 in standard form
Help!! I need help with equations
Answer:
[tex]Y=\frac{1}{2}x +2[/tex]
Step-by-step explanation:
When y=2,X=0
When Y =7,X=10
X coordinates come first
(0,2)(10,7)
(x1,y1)(x2,y2)
To find the slope(M)=y2 -y1/x2 -x1
M=7-2/10-0
M=5/10=1/2 (Simplest form)
The equation of a line is given by Y=Mx + C
Where c is the Y intercept which is 2
- The equation of the line = Y=[tex]\frac{1}{2} x +2[/tex]
George jumps off a tire swing into a circular pond causing circles of waves. One of the waves travels at a rate of 16 ft/sec .
a. The radius of the circle increases with time. Write an equation to represent this relationship.
We get that an equation to represent this relationship the relation of increase in radius with respect to time as R = r + 16 t where t is the time and r is the initial radius.
We are given that, the wave travels at a rate of 16 feet / sec when George jumps off a tire swing in the circular pond.
So, this means that the radius of the wave increases by 16 feet in every second.
Now, let the initial radius be r and the radius after t seconds be R.
So, the equation will become:
R = r + 16 t
where 16 t represents the increase in radius in t seconds.
Therefore, we get that an equation to represent this relationship the relation of increase in radius with respect to time as R = r + 16 t where t is the time and r is the initial radius.
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Leena consumes 400 calories at breakfast and 350 calories at lunch. She consumes StartFraction 2 Over 3 EndFraction. of her daily calories at dinner. If x represents the calories consumed at dinner, which statements describe the situation? Check all that apply.
Leena consumed 1,500 calories at dinner.
The equation StartFraction 2 Over 3 EndFraction left-parenthesis x plus 400 plus 350 right-parenthesis equals x.(x + 400 + 350) = x can be used to model the situation.
Leena consumed 500 calories at dinner.
The equation StartFraction 2 Over 3 EndFraction left-parenthesis x right-parenthesis equals x left-parenthesis 400 plus 300 right-parenthesis.(x) = x(400 + 300) can be used to model the situation.
Leena consumed 1,000 calories at dinner.
The equation StartFraction 2 Over 3 EndFraction x left-parenthesis x plus 400 plus 350 right-parenthesis equals x.x(400 + 300) = x can be used to model the situation
The correct statement regarding the algebra will be:
A. Leena consumed 1,500 calories at dinner.
B. The equation StartFraction 2 Over 3 EndFraction left-parenthesis x plus 400 plus 350 right-parenthesis equals x.(x + 400 + 350) = x can be used to model the situation.
How to illustrate the information?Calories consumed at dinner = x
x = 2/3 of daily calorie
Hence, the fraction of calories consumed during breakfast and lunch can be calculated thus :
1 - 2/3 = 1/3
Let the total amount of calories consumed per day = c
1/3 × c = 750
c/3 = 750
c = 750 × 2 = 2250 calories
Calories consumed at dinner = (2250 - (750)) = 1500 calories
Therefore, the correct options are A and B.
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Please find the perimeter of the following shape (I know the answer, please explain steps)
Step-by-step explanation:
the perimeter is the sum of all sides.
it is clearly a symmetric figure.
I assume the sqrt(36) is the whole baseline (incl. the left and right x).
so, we have
sqrt(8) + 2x = sqrt(36) = 6
1/2 × sqrt(8) + x = 3
sqrt(1/4 × 8) + x = 3
sqrt(2) + x = 3
x = 3 - sqrt(2)
to get the inclined sides we use Pythagoras
c² = a² + b²
c being the Hypotenuse, a and b being the legs of the right-angled triangle.
so,
side² = sqrt(8)² + (3 - sqrt(2))² = 8 + (9 - 6×sqrt(2) + 2) =
= 19 - 6×sqrt(2)
each inclined side is
sqrt(19 - 6×sqrt(2))
so, as perimeter we get
6 + sqrt(8) + 2×sqrt(19 - 6×sqrt(2)) =
= 15.3137085...
Hello, I would really appreciate it if someone would help me out with this problem and explain how they did it if possible. If not that is completely alright. I hope you all have an amazing day. Thank you so much! :) (Even if you don't solve the problem feel free to give it your best guess or even just say "hello" to earn yourself some points. You deserve them.) :D (Will be looking for a brainliest!)
Answer:
1/2,187
1/367
3^-7
Step-by-step explanation:
I hope this helped, have an amazing day! :D
What is f(x)=3 x¹/₃ for x=1/125 ?
(F) 15 (G) 3/5 (H) ∛3/5 (I) 5∛3
The value of the given expression for x=1/1250is 3/5. The correct option is (G).
Given the expression is f(x)=[tex]3x^{\frac{1}{3}}[/tex].
The cube root of a number is the factor that we want multiply by itself three times to get that number. The symbol for the cube origin is 3 cube roots, the last cube root. Finding the cube root of any number is the opposite of cubing a number.
We will simplify the given expression by using substitution method and cube root.
Firstly, we will substitute x=1/125 in the given expression f(x)=[tex]3x^{\frac{1}{3}}[/tex], we get
f(x)=[tex]3\left(\frac{1}{125}\right)^{\frac{1}{3}}[/tex]
As we know that the cube root of √125 is 5.
Now, we want to simplify the above equation, we get
f(x)=3(1/5)
f(x)=3/5
Hence, the value of [tex]f(x)=3x^{\frac{1}{3}}[/tex] for x=1/125 is 3/5.
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yo can somebody help me with this please i really need a good grade ill give crown to
Answer: 3/4
Step-by-step explanation:
You have to find one single number that goes into both the numerator and the denominator. In this case, it was 8.
24/8 = 3
32/8 = 4
Answer:
1st one is 3/4
second one is 32
I cant really see the third one
fourth one is $1.03
Step-by-step explanation:
PLEASE HELP ME ASAP!!!!
Which of these can most easily be found on a frequency chart?
A) The median
B) The mode
C) The mean
D) None of these
Frequency refers to the number of times an event or a value occurs. A frequency table is a table that lists items and shows the number of times the items occur(C)
What is 1/2 to the negative third power as a fraction
Answer:
Dunno
Step-by-step explanation:
HURRY FAST
Which equation applies the associative property of multiplication?
Answer:
8/9×7/4×(-5/8)=8/9×(-5/8)×7/4
Step-by-step explanation:
first equation
Amelia took a taxi from her house to the airport. The taxi company charged a pick-up fee of $4.60 plus $0.50 per mile. The total fare was $13.60, not including the tip. Write and solve an equation which can be used to determine
m
m, the number of miles in the taxi ride.
Solution: the number of miles in the taxi ride.= 180 miles
Miles : A unit of length equal to exactly 1.609344 kilometers.
Also equal to 1,760 yards or 5,280 feet.
The average walking speed is 3 miles per hour (so it takes about 20 minutes to walk 1 mile).
The taxi company charged a pick-up fee of $4.60
The taxi company charged $0.50 per mile.
The total fare was $13.60
The total fare = pick-up charged + traveling charged
the number of miles in the taxi ride = m
$13.60= $4.60 + m x $.50
$13.60-$4.60 = $.50m
9 =.50 m
9 /.50 = m
900/5 = m
180 = m
the number of miles in the taxi ride.= 180 miles
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Domain and range graph helppppppp plssssss
For graph number 13:
We can see that the domain is: {-3, 3} the range is: R: {-4, 2} this is not a function
How to find the domain and range with a graph?
For a relation that maps elements x into elements y, we define the domain as the set of the inputs and the range as the set of the outputs. And we say that the relation is a function if each input is mapped into, at most, one output.
If you look at the graph 13 you can see several points, which are of the form (x, y) and are:(-3, 2), (3, 2), (-3, -4), (4, -4)And it makes a little square.
Then you can see that the inputs are -3 and 3, so the domain is:
{-3, 3}
And the outputs are 2 and -4, then the range is:
R: {-4, 2}
And this is not a function, because for example, output 3 is being mapped into two different values.
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21 increased by twice Gail's height
Use the variable g to represent Gail's height.
The expression represented by 21 increased by twice Gail's height is 21 + 2g
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to translate the algebraic expression?The expression is given as
21 increased by twice Gail's height
Where
g represents Gail's height
So, we have
21 increased by twice Gail's height ⇒ 21 increased by twice g
Twice means 2*
So, we have
21 increased by twice Gail's height ⇒ 21 increased by 2g
increased by means +
So, we have
21 increased by twice Gail's height ⇒ 21 + 2g
Hence, the expression represented by 21 increased by twice Gail's height is 21 + 2g
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Simplify each number. (32)⁻⁴/₅
The result of simplifying each number (32)⁻⁴/₅ using the exponent rules is 1/16
To solve this exercise we have to resolve algebraic operations following the exponent rules.
(32)⁻⁴/₅
Base= 32
Exponent= -4/5
As we have a negative exponent, you have to pass the exponent to the denominator:
1/(32)⁴/₅
As we have a fractional exponent, you must convert the exponent to root:
1/[tex]\sqrt[5]{}[/tex](32)⁴
1/[tex]\sqrt[5]{}[/tex]1048576
1/16
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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Determine whether each function is an example of exponential growth or decay. Then, find the y -intercept. y=5 x
The function y = 5x demonstrates exponential growth.
What do we exactly mean by Exponential Function?An exponential function is indicated when the input variable x appears as an exponent in the formula f(x) = ax.Both the exponential function and the value of x have an effect on the exponential curve.The exponential function is a fundamental mathematical function with the following formula:
f(x) = aˣ
Where a>0 and a does not equal to 1.x can be any genuine number.If the value of the variable is negative, the function for (-1<x<1) is undefined.Here,
The variable is "x".The base of the function, "a," is a constant.An exponential curve may increase or decrease depending on the exponential function.If a quantity regularly increases or decreases by a predetermined percentage, it should have either exponential growth or exponential decay.So,
Given function: y = 5x
If we put x = 1 as follows:
y = 5×1y = 5Then, if we put x = 2 as follows:
y = 5×2y = 10We see that 10 > 5.
So, when x increases, y also increases.Therefore, the function y = 5x demonstrates exponential growth.
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If the variable h represents how many hours samantha works, write an algebraic expression that describes how much
samantha earns if she makes $14. 55 an hour. Create another an real life algebraic expression (or equation). Choose and define your variable
The algebraic expression that describes how much Samantha earns after h hours if she makes $14.55 an hour is x = $14.55h, where x is the amount of money she earns and h is the number of hours she works.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question.
If Samantha makes $14.55 an hour, and h is the number of hours she works, then the algebraic expression to demonstrate how much she earns is:
x = $14.55h
where x = amount of money she earns
h = number of hours she works
Another real life situation:
A piggy bank contains $25, and $1.50 is added each day. The algebraic expression to demonstrate how much money the piggy bank contains is:
m = $25 + $1.50(d)
where m = amount the piggy bank contains after d days
d = number of days
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6n - 12 = 3( 2n- 4 )
Answer:
0 = 0 (this equation is always true)Step-by-step explanation:
6n - 12 = 3( 2n- 4 )
6n - 12 = 6n - 12
0 = 0
this equation is always true
In a sale, normal prices are reduced by 25%. Freddie bought a car in the sale. The sale price of the car was £7500. Work out the normal price of the car.
The normal price of the car on the basis that the sale price of the car was £7500 is £10,000.
What percentage of the normal price is the sales price?The fact that the normal prices are reduced by 25% means that the actual price paid eventually is 75%, which is 100% minus discount of 25%, hence, the actual price of £7500 paid eventually represents 75% of normal price
75% of normal price= £75001% of normal price=£100100% of normal price=£100*100100% of normal price=£10,000Find out more about normal price on: brainly.com/question/20532904
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1 2/3*1 1/5
you must show working
Answer: 2
Step-by-step explanation:
= Convert 1 2/3 to an improper fraction (which is 5/3)
= Convert 1 1/5 to an improper fraction (which is 6/5)
= Proceed to cancel out the common factor of 5 so your answer should start to look like this
1/3 * 6
= Now cancel the common factor which is three
Therefore your answer is 2
Hope it helps ^^
What is an equation of the line that passes through the points (7,-3) and
(-8,-3)?
Answer:
Step-by-step explanation:
m= [ -3-(-3)] ÷ [-8-7} = 0
Therefore, the slope of the line is 0.
Now use the slope and either of the two points to find the y-intercept.
y= mx+b
-3= (0)(7)+b
b=-3
Write the equation in slope intercept form as:
y= mx+b
y= (0)x-3
y= -3
Hence, the equation of the line is y= -3.
Find the value of x.
3x = 2 + 31
Answer:
x=11
Step-by-step explanation:
3x=2+31
3x=33
divide both sides by the coefficient of x
x=11
I need help on this it’s been hours
Answer:Eric cause 5/12 is greater
Step-by-step explanation:
One of the worlds largest crocodiles weighed 38,400 ounces how many tons did the crocodile weigh
Answer: 1.2 tons
Step-by-step explanation:
Answer: 1,777
Step-by-step explanation:
Jake is a factory manager for a company that produces batteries. Occasionally, some are found to be defective. Based on previous results, Jake estimates that 12 batteries will be defective for a certain month. However, 10 were actually defective. What is the percent error of Jake’s estimate?
Based on the estimated number of defective batteries and the number of batteries that were actually defective, the percent error of Jake's estimate is 20%
How to find the percent error?The percent error of a problem can be found by the formula:
= (Expected results - Actual results) / 100%
Expected results = 12 defective batteries
Actual results = 10 defective batteries
Jake's percentage error is therefore:
= (12 - 10) / 100%
= 2 / 10 x 100%
= 0.2 x 100%
= 20%
In conclusion, the percent error of Jake's estimate is 20%.
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Oil flows through a pipe at a rate of 40m^3/s. How long will it take to fill a tank of volume 1.2x10^5m^3?
Volume is a three-dimensional quantity that is used to measure the capacity of a solid shape. If oil flows through a pipe at a rate of 40m³/s then it takes 50mins to fill a tank of volume 1.2x10⁵m³
What is Volume?Volume is a three-dimensional quantity that is used to measure the capacity of a solid shape. It means the amount of three-dimensional space a closed figure can occupy is measured by its volume.
Given that Oil flows through a pipe at a rate of 40m³/s.
Volume of the tank is 1.2x10⁵m³
volume =Rate *time
Time=Volume/ Rate
Time= 1.2*10⁵m³ / 40m³=3000seconds
We need to convert time in seconds to minutes
We know that 1 hr = 60 mins.
So divide 3000 sec by 60
3000/60= 50 minutes.
Therefore 50 min it will take to fill a tank of volume 1.2x10⁵m³.
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What is the least common multiple of 3, 9, and 12?
Answer:
36
Step-by-step explanation:
3=3
9=3*3 = 3^2
12=2*2*3 = 2^2*3
lcm = 2^2*3^3
= 4*9
therefore lcm= 36
Answer:
36
Step-by-step explanation:
[tex]\bold{3} \times \bold{12} = 36\\\bold{9} \times 4 = 36[/tex]
I need help on this percent practice please. Thank you
By solving the percent application, the result is 45% of 120 is 54 and 81 is 75% of 108.
(A) 45% of 120
Multiply 45/100 with 120 =(45/100) x 120 = (45 x120) / 100 = 54.
(B) 81 is 75%
Formula = Number x 100/Percent
= 81 x 100/ 75 = 108
Following shows the steps on how to derive this formula and find out 75% of what number is 81. Then take 100% of that figure. Setup the equation
81/75% = Y/100%
Solve for Y
Using cross multiplication of two fractions, we get
75Y = 81 x 100
75Y = 8100
Y = 8100
100 = 108
Hence, by solving the percent application, the result is 45% of 120 is 54 and 81 is 75% of 108.
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