Answers
Answer:
f⁻¹(x) = [tex]2^{\dfrac{x}{4} }[/tex] + 7
Step-by-step explanation:
The inverse of a function reverses the operations performed by the function in the question such if f(x) = y, then we have, f⁻¹(y) = x, which reverses the operation of the first function.
The inverse of a function f(x) = 4·㏒₂(x - 7) is found as follows;
We have;
y = 4·㏒₂(x - 7)
We substitute x for y to get;
x = 4·㏒₂(y - 7) which gives;
x/4 = ㏒₂(y - 7)
[tex]2^{\dfrac{x}{4} }[/tex] = y - 7
y = [tex]2^{\dfrac{x}{4} }[/tex] + 7
Therefore;
f⁻¹(x) = [tex]2^{\dfrac{x}{4} }[/tex] + 7.
Related Questions
What is the slope of the line through (2,-2) and (9, 3)
Answers
Answer:it is 5/7
Step-by-step explanation: the formula for slope is rise/run divide and you get 5/7
Answer:
slope = [tex]\frac{5}{7}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 2) and (x₂, y₂ ) = (9, 3)
m = [tex]\frac{3+2}{9-2}[/tex] = [tex]\frac{5}{7}[/tex]
Patrick graphed (shown below) the high temperatures (in °C) that he experienced on each day of his trip to
Homer, Alaska
What is the meaning of point A?
Answers
Answer:
(7, -5.5)
Step-by-step explanation:
is seen below on this graph (7, -5.5) shows x = 7 and y = -5.5
Here can somebody help me with this problem
Answers
Answer:
H, 40%
Step-by-step explanation:
We can start out simple by finding out the number of cars in each category.
30 remote-controlled cars
90 non remote-controlled cars.
20% of the remote controlled cars are yellow, meaning that there are 6 yellow remote controlled cars.
Since 50% of the total cars are yellow, there are 60 yellow cars. Subtracting this from the yellow remote controlled cars, there are 54 yellow non remote contolled cars.
What this means is that 54/90 of the non-remote cars are yellow, and 36/90 of the non-remote cars are yellow. 36/90 is just 2/5, which means that our answer is H, 40%.
Place the LETTER in the smallest set that contains that value
Answers
Rational B,D,J,k
Integers G
Whole E,G
IRRATIONAL A,C,F,h,I,L
Step-by-step explaining
Whole number is just numbers but with a zero for example 0,1,2,3,4,5,6,……….
Natural number is just like the whole number but without the zero . For example 1,2,3,4,5,6,…..
Integers, The set of integer is all the whole numbers and their opposite for example -3 -2 -1,0,1,2,
Irrational : non- terminating , non-repeating decimal
Can’t be written as a ratio
For example pie , 3.7685922331
Rational can be written as a ratio like fraction
Including fractions and only terminating and repeating decimals for example 1/5 , 0.33333333333……,1.4
Sam weighed his dog. He rounded the weight to the nearest tenth of a pound to get 18.6 pounds. Which could have been the actual weight of Sam's dog?
Answers
Answer:
18.55 <= wt < 18.65
In other words, the dog could weigh anywhere from 18.55 up to , but not including 18.65 lbs
Step-by-step explanation:
Answer:
every thing that is 18.55 and after it until 18.64
Step-by-step explanation:
so that will be 18.55,18.56,18.57,18.58,18.59,18.6,18.61,18.62,18.63,18.64
those are all numbers that could be sams weight
can somewon help me plz i want help
Answers
Answer:
5 * 10^10.
Step-by-step explanation:
(9 * 10^10) - (4 * 10^10) = (9 - 4) * 10^10 = 5 * 10^10.
Hope this helps!
Answer:
5*10^10
Step-by-step explanation:
9 times ten is 9^10, and 4 Times 10^10 is 4^10 so 9^10 minus 4^10 is 50000000000 which is also called 5^10 which is also 5 x 10^10 I think. pls correct me if im wrong
When purchased, a beach ball is deflated and packaged flat. The package states that when inflated to its maximum capacity, the radius of the inflated ball is 7.6 inches. To the nearest hundredth of a cubic inch, how much air will occupy the space contained by the inflated beach ball? Use 3.14 for [tex]\pi[/tex]. In your final answer, include all of your calculations.
Answers
Step-by-step explanation:
V=(4/3) * πr^3
V=(4/3) * π * 7.6 ^3
V=(4/3) * π * 438.976
V= π * 585.301333
V = 1837.85 inch^3
3.14 for pi btw
Which of the following inequalities is correct?
Answers
Answer:
b
Step-by-step explanation:
The first one is not. Think money. Would you rather be 1 dollar in the hole or 6 dollars in the hole? b = - 1. It is larger than - 6.
The third one is not correct either. -c = - 5
- b = 1
1 is larger than -5
The answer is the middle one
-b becomes 1 which is greater than 0.
Evaluate 3a2 + 4b2 for a =
2 and b = 3.
O
168
48
O
36
Answers
Answer:
48
Step-by-step explanation:
a=2
b=3
3a^2+4b^2
3(2)^2+4(3)^2
3(2)(2)+4(3)(3)
3(4)+4(9)
12+36
48
Hope this helps ;) ❤❤❤
three babies A,B and C cry out at interval time. Baby A cries out at every 20 mins, while B cries out at every 30 mins and C cries out at every 40 mins. if they are observed at the same time, after what time will the three of them cry together?
A. after 20 minutes
B. after 30 minutes
C. after 40 minutes
D. after 120 minutes
Answers
Help me ASAP for this picture
Answers
Solution: Multiple 16 by 3/4.
12
Which of the following statements is true for a function with equation f(x) = 5(3)*?
The graph has y-intercept (0,5) and increases with a constant ratio of 3.
The graph has y-intercept (0, 3) and decreases with a constant ratio of 3.
The graph has y-intercept (0, 3) and increases with a constant ratio of 5.
The graph has y-intercept (0,5) and decreases with a constant ratio of 3.
Answers
Answer:
The graph has y-intercept (0,5) and increases with a constant ratio of 3
Step-by-step explanation:
The value of the function when x=0 is 5·3^0 = 5, so the y-intercept is (0, 5).
Each increase of 1 in x causes the function value to increase by a factor of 3, so the 'constant ratio' is 3. (That is the base of the exponential term.)
PLEASE HELP! It was due 3 days ago lol
Answers
Answer:
Part A:
The ratios in the table are equivalent.
The two quantities in this table represent a proportional relationship.
The graph of the relationship would be straight line through origin
Step-by-step explanation:
Part A
The ratios in the table are equivalent.
Length: Cost
6 : 42 = 1 : 7
15: 105 = 1: 7
24 : 168 = 1:7
30 : 210 = 1 : 7
The two quantities in this table represent a proportional relationship.
If we take length = x, then cost =7x
When length = 6 , Cost = 7 *6 = 42
When length = 15 , Cost = 7 * 15 = 105
When length = 24 , Cost = 7 *24 = 168
The graph of the relationship would be straight line through origin
y = 7x
y -> cost and x -> length
When x = 0 , y= 0. so, this graph go through the origin
Part B:
$ 7 per foot
Find the area of this parallelogram in square units. Each box on the grid represents 1 square unit.
Answers
Answer:
the answer is 16
Step-by-step explanation:
If m(2x−3)+n(x+1)=5x for all real numbers x, where m and n are constants, what is the value of m?
Answers
Answer:
m = 1
Step-by-step explanation:
From the question given,
m(2x − 3) + n(x + 1) = 5x for all real numbers x.
Since x is a real number, we can obtain the value of m as follow:
Let x = 1
m(2x − 3) + n(x + 1) = 5x
m(2×1 − 3) + n(1 + 1) = 5×1
m(2 – 3) + n(2) = 5
m(– 1) + n(2) = 5
– m + 2n = 5 ...... (1)
Let x = 2
m(2x − 3) + n(x + 1) = 5x
m(2×2 − 3) + n(2 + 1) = 5×2
m(4 – 3) + n(3) = 10
m(1) + n(3) = 10
m + 3n = 10 ...... (2)
– m + 2n = 5 ...... (1)
m + 3n = 10 ...... (2)
Solve by elimination method
Add equation 1 and 2
– m + 2n = 5
+ (m + 3n = 10)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
5n = 15
Divide both side by 5
n = 15/5
n = 3
Substitute the value of n into any of the equation to obtain the value of m. Here, we shall substitute n into equation 2.
m + 3n = 10
m + 3(3) = 10
m + 9 = 10
Collect like terms
m = 10 – 9
m = 1
Therefore, the value of m is 1
What is the correct evaluation of x2 - y2 - z2, when x is equal to -2, y is equal to 3 and z is equal to 4?
Answers
Answer:
-18
Step-by-step explanation:
x2 - y2 - z2 if x=-2, y=3, and z=4
x2 - y2 - z2
(-2) 2 - (3)2 - (4)2
(-4) - (6) - (8)
-10 -8
-18
Answer:
18
Step-by-step explanation:
3^(2)+4(2)
4-9(5+1)+3
5^(2)+3^(2)-8
(3+2)^(2)+4(2+3)
8^(2)-9(2)+3
2(5)^(2)
4^(2)+6(2+8)
4+5(3)+2(7)-6
8+3(6)-3^(2)
2+6-5+4(6)
Answers
What is the length of AC
Answers
(156 - x)/12 = x
12x = 156 - x
13x = 156
x = 12
AC = 156 - 12
AC = 144
Answer:
|AC| = 144
Step-by-step explanation:
The larger triangle (on the left) and the smaller one (on the right) are similar.
Therefore the following equation of ratios is correct:
x 7
---------- = ---------
156 - x 84
Then 84x = 7(156) - 7x, or
91x = 1092, or x = 12
Then the length of AC is 156 - x, or 144
write 0.895 with 95 repeating on and on as a simplified fraction
PLZ HELP WILL GIVE BRANLIEST
Answers
Answer:
887/990
Step-by-step explanation:
0.8959595....
895.95 - 8.95 = 887
1000 - 10 = 990
Answer:
[tex]\huge\boxed{x = \frac{887}{990}}[/tex]
Step-by-step explanation:
The number given is 0.895..........
Let x = 0.895........
Then
10x = 8.95....... --------(1)
1000x = 985.95........ --------(2)
Subtracting (1) from (2)
1000x - 10x = 985.95..... - 8.95......
990 x = 887
Dividing both sides by 990
[tex]x = \frac{887}{990}[/tex] (In simplest form)
(NO TROLLS 3 TIMES THE CHARM) In △ABC, AB = BC = 20 and DE ≈ 9.28. Approximate BD.
Answers
Answer:
≈ 5.36
Step-by-step explanation:
If we have a triangle in which the angle measure of it being broken down are the same, that means that the legs in which the angle measures are the same will have the same length.
If we already know that DE ≈ 9.28, then we can subtract this from 20 and divide by two to get BD, which is equal to EC.
[tex]20-9.28=10.72\\10.72\div2=5.36[/tex]
However, I'm not 100% sure about this answer.
Hope this helped (and I hope I'm right)
Answer:
5.3589 or 5.36
Step-by-step explanation:
tan (15) = x / 20
x = 40 - 34.64
x = 5.36
14. You bought shoes for $60. They were on sale for 40% off their original price.
a. Write a proportion to solve for the original price of the shoes.
b. Solve the proportion in part (a).
Answers
Check 100-40=60
Think of it as a pie. The pie is 100% if the pie was $60 aka 60% shaded 100-60=40 and 40 is the discount from the shoes.
The Greenbaum family agreed to pay for 3 months of an online TV service in exchange for a $5 credit on the bill each month. If the Greenbaums spend a total of $11.85 on the service over the 3 months, what is the normal price of one month of online TV service?
$5.00
$6.85
$8.95
$30.55
Answers
divide $11.85 by 3 and you get 3.95 then add the $5
Explain in detail the steps for solving multi-step equations.
i just need the steps no problem is included . Thank you sm !
Answers
Answer:
1) Get rid of grouping symbols like square brackets and parentheses
2) Simplify both sides of the equation. Combine like terms if possible.
3) Choose where you want to keep the variable because that will help you decide where to place the constant.
4) Eliminate numbers or variables by using opposite operations. Remember that addition and subtraction are opposites and so are multiplication and division.
Step-by-step explanation:
HELP PLS HELP HELLLOPPPP
Answers
It can’t be option A. because it equals -23 and that doesn’t much to the expression we are looking for answer. Option B. can’t be correct either because it equals -1 and that isn’t right either and lastly option D. can’t be right because it equals -10.2. I hope I explained it good enough, Goodluck :)
Answer Key
Expression We Are Looking For A Match To = -13.8
Option 1 = -23
Option 2 = -1
Option 3 = -13.8
Option 4 = -10.2
Please someone help me!!!!
Answers
Answer:
4 months
Step-by-step explanation:
The 24% APR corresponds to a monthly rate of 24%/12 = 2%. This finance charge on a balance of $300 is ...
0.02 × $300 = $6.00
To pay off $300 will take more than 3 payments of $100 because of the finance charge. Because the finance charge is not very large, the last month's payment will not need to be $100, but will be somewhat less.
It will take 4 months to pay off the balance.
_____
Additional comment
The actual finance charge will depend on your credit agreement. It may amount to $4 the second month, and $2.08 the third month, if it is charged on the outstanding balance. That is, the 4th month's payment may only be $6.08. If there is a finance charge on the initial $300 balance, that may cause the last payment to be a little more than $12.
Mathematics, probability and chance Can somebody help me, I always thank and vote
Answers
Answer:
A. 0
Step-by-step explanation:
In order for there to be a 1 in 3 chance, there would have to be an equal number of the three chalices. Since four is the smallest number, the other two must have four left as well. That means Donavan drank 1 spoiled milk and 2 flat sodas. Therefore, he drank 0 purified water.
Solve the equation using the multiplication property of equality and the reciprocal of
1
4
.
1
4
( r −
5
2
) =
1
8
Answers
you move left 2 units and right 9 units. you end at (4,5). where did you start?
Answers
Answer:
You started at ( -3,5)
Step-by-step explanation:
You end at (4,5)
You got there by moving right 9 units so move left 9 units
Moving left is subtraction in the x direction
(4-9,5)
( -5,5)
Then move left 2 units so move right 2 units which is adding 2 in the x direction
( -5+2, 5)
( -3,5)
You started at ( -3,5)
What is the area of a regular hexagon with an apothem 16.5 inches long and a side 19 inches long? Round the answer to the nearest tenth. A. 625.3 in.2 B. 940.5 in.2 C. 156.3 in.2 D. 1,875.8 in.2
Answers
==============================================
Explanation:
Any regular hexagon is really the combination of six identical (aka congruent) equilateral triangles glued together. If we can find the area of one triangle, then we multiply by 6 to get our final answer.
The apothem is the height of the equilateral triangle with the triangular base being the side length of the hexagon.
area of triangle = (1/2)*base*height
area of triangle = 0.5*(hexagon side length)*(apothem)
area of triangle = 0.5*19*16.5
area of triangle = 156.75
This is the area of one equilateral triangle. Having 6 triangles leads to a total area of 6*156.75 = 940.5 square inches
The area of a regular hexagon with an apothem of 16.5 inches and a side of 19 inches is Area of hexagon = 1/2(length of apothem)(perimeter of the hexagon) = 940.5 inches. (Option-B)
Apothem:Apothem is a perpendicular line from the center of the regular polygon to one of its sides.
Area of Regular polygon with apothem:Area = 1/2 x (length of apothem) x (perimeter of hexagon)
• Given,
apothem = 16.5 inches and length of a side =19 inches
• Perimeter = 6 x (side of a hexagon)
= 6 x (19)
= 114 inches
• Hence,
Area = 1/2 x (16.5) x (114) = 940.5 inches(rounded to the nearest tenth)
Know more about Regular hexagon :
https://brainly.com/question/10209400?referrer=searchResults
#SPJ2
(will give brainliest) find the value of x
Answers
Answer:
x = 180 - [(180 - 3x) + (180 - 2x)]
Step-by-step explanation:
Start off by finding the angles of the triangle
Angle F = 180 - 3x
The angle across from I (which I will call I) = 180 - 2x
Angle G = 180 - (F + I)
Now that we know what G is, we know what x is because the Alternate Exterior Angles Theorem states that if a pair of parallel lines are cut by a transversal, then the alternate exterior angles are congruent. So pretty much X = G
Therefore x = 180 - (F + I) or otherwise said as:
x = 180 - [(180 - 3x) + (180 - 2x)]
I hope this is helpful :)
Explanation:
(180-2x)+(180-3x)+x=180 (angle sum of triangle)
180-2x+180-3x+x=180
180+180-2x-3x+x=180
360-4x=180
360-4x-360=180-360
-4x=(-180)
(-4x)/(-4)=(-180)/(-4)
x=45
Hope this will help.