Answer:
f¯¹(x) = 23/ (6x + 3)
Step-by-step explanation:
f(x) = (23 – 3x)/6x
The inverse, f¯¹, for the above function can be obtained as follow:
f(x) = (23 – 3x)/6x
Let y be equal to f(x)
Therefore, f(x) = (23 – 3x)/6x will be written as:
y = (23 – 3x)/6x
Next, interchange x and y.
This is illustrated below:
y = (23 – 3x)/6x
x = (23 – 3y)/6y
Next, make y the subject of the above expression. This is illustrated below:
x = (23 – 3y)/6y
Cross multiply
6xy = 23 – 3y
Collect like terms
6xy + 3y = 23
Factorise
y(6x + 3) = 23
Divide both side by (6x + 3)
y = 23/ (6x + 3)
Finally, replace y with f¯¹(x)
y = 23/ (6x + 3)
f¯¹(x) = 23/ (6x + 3)
Therefore, the inverse, f¯¹, for the function f(x) = (23 – 3x)/6x is
f¯¹(x) = 23/ (6x + 3)
Answer:
74.33
Step-by-step explanation:
We need to figure out the surface area. The formula for surface area is A=2πrh+2πr2
We substitute r with the radius of this cylinder and the h represents the height of this cylinder. The height we can find because we just add the diameters of the tennis balls. So 2.6*3 = 7.8. Then we get the radius, which will just be the radius of a sphere, so 1.3. Then we plug them into the formula, giving us 74.33
it represents the amount of wine cucumber and one apple
Step-by-step explanation:
Hey there!
The points of line AB are; (-1,-4) and (2,11).
Note:
- Use double point formula and simplify it to get two eqaution.
- Use condition of parallel lines, perpendicular lines to know whether the lines are parallel or perpendicular or nothing.
~ Use double point formula.
![(y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1)](https://tex.z-dn.net/?f=%28y%20-%20y1%29%20%3D%20%20%5Cfrac%7By2%20-%20y1%7D%7Bx2%20-%20x1%7D%20%28x%20-%20x1%29)
~ Keep all values.
![(y + 4) = \frac{11 + 4}{2 + 1} (x + 1)](https://tex.z-dn.net/?f=%28y%20%20%2B%204%29%20%3D%20%20%5Cfrac%7B11%20%2B%204%7D%7B2%20%2B%201%7D%20%28x%20%2B%201%29)
~ Simplify it.
![y + 4 = \frac{15}{3} (x + 1)](https://tex.z-dn.net/?f=y%20%2B%204%20%3D%20%20%5Cfrac%7B15%7D%7B3%7D%20%28x%20%2B%201%29)
![y + 4 = 5x + 5](https://tex.z-dn.net/?f=y%20%2B%204%20%3D%205x%20%2B%205)
![5x - y + 1 = 0](https://tex.z-dn.net/?f=5x%20-%20y%20%2B%201%20%3D%200)
Therefore this is the equation of line AB.
Now, Finding the equation of line CD.
Given;
The points of line CD are; (1,1) and (4,10).
~ Using formula.
![(y - y1) = \frac{y2 - y1}{x2 - x1}(x - x1)](https://tex.z-dn.net/?f=%28y%20-%20y1%29%20%3D%20%20%5Cfrac%7By2%20-%20y1%7D%7Bx2%20-%20x1%7D%28x%20-%20x1%29%20)
~ Keep all values.
![(y - 1) = \frac{10 - 1}{4 - 1} (x - 1)](https://tex.z-dn.net/?f=%28y%20-%201%29%20%3D%20%20%5Cfrac%7B10%20-%201%7D%7B4%20-%201%7D%20%28x%20-%201%29)
~ Simplify it.
![y - 1 = 3 x - 3](https://tex.z-dn.net/?f=y%20-%201%20%3D%203%20x%20-%203)
![3x - y - 2 = 0](https://tex.z-dn.net/?f=3x%20-%20y%20-%202%20%3D%200)
Therefore, 3x - y- 2 = 0 is the eqaution of line CD.
Use condition of parallel lines.
m1= m2
Slope of equation (i)
![m1 = \frac{ - coeff. \: of \: x}{coeff \: of \: y}](https://tex.z-dn.net/?f=m1%20%3D%20%20%5Cfrac%7B%20-%20coeff.%20%5C%3A%20of%20%5C%3A%20x%7D%7Bcoeff%20%5C%3A%20of%20%5C%3A%20y%7D%20)
![m1 = \frac{ - 5}{ - 1}](https://tex.z-dn.net/?f=m1%20%3D%20%20%5Cfrac%7B%20-%205%7D%7B%20-%201%7D%20)
Therefore, m1 = 5
Slope of second equation.
![m2 = \frac{ - coeff \: .of \: x}{coeff \: .of \: y}](https://tex.z-dn.net/?f=m2%20%3D%20%20%5Cfrac%7B%20-%20coeff%20%5C%3A%20.of%20%5C%3A%20x%7D%7Bcoeff%20%5C%3A%20.of%20%5C%3A%20y%7D%20)
![m2 = \frac{ - 3}{ - 1}](https://tex.z-dn.net/?f=m2%20%3D%20%20%20%5Cfrac%7B%20-%203%7D%7B%20-%201%7D%20)
Therefore, m2 = 3.
Now, m1≠m2.
So, the lies are not parallel.
Check for perpendicular.
m1*m2= -1
3*5≠-1.
Therefore, they aren't perpendicular too.
So, they are neither.
<em><u>Hope </u></em><em><u>it</u></em><em><u> helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>
Answer:
- 65 couple tickets
- 50 individual tickets
Step-by-step explanation:
The two equations are for the revenue and the number of attendees.
3p +5c = 475 . . . . . . revenue from ticket sales (dollars)
p +2c = 180 . . . . . . . number of attendees (2 persons per couple)
Substituting (180-2c) for p in the first equation, we get ...
3(180 -2c) +5c = 475
540 -c = 475 . . . . . . . . . simplify
540 -475 = c = 65 . . . . . add c-475
p = 180 -2(65) = 50 . . . . find p from c
65 couple tickets and 50 individual tickets were sold.