Answer:
inifinitely many solutions
Step-by-step explanation:
Answer:
Option 4
Step-by-step explanation:
Given function is,
![f(x)=2\frac{1}{2}-3\frac{1}{3}x](https://tex.z-dn.net/?f=f%28x%29%3D2%5Cfrac%7B1%7D%7B2%7D-3%5Cfrac%7B1%7D%7B3%7Dx)
Steps to get the inverse of the given function,
Step 1,
Convert the function into equation,
![y=2\frac{1}{2}-3\frac{1}{3}x](https://tex.z-dn.net/?f=y%3D2%5Cfrac%7B1%7D%7B2%7D-3%5Cfrac%7B1%7D%7B3%7Dx)
Step 2,
Interchange the variables 'x' and 'y',
![x=2\frac{1}{2}-3\frac{1}{3}y](https://tex.z-dn.net/?f=x%3D2%5Cfrac%7B1%7D%7B2%7D-3%5Cfrac%7B1%7D%7B3%7Dy)
Step 3,
Solve the equation for the value of y,
![x-2\frac{1}{2}=-3\frac{1}{3}y](https://tex.z-dn.net/?f=x-2%5Cfrac%7B1%7D%7B2%7D%3D-3%5Cfrac%7B1%7D%7B3%7Dy)
![x-\frac{5}{2}=-\frac{10}{3}y](https://tex.z-dn.net/?f=x-%5Cfrac%7B5%7D%7B2%7D%3D-%5Cfrac%7B10%7D%7B3%7Dy)
![-x+\frac{5}{2}=\frac{10}{3}y](https://tex.z-dn.net/?f=-x%2B%5Cfrac%7B5%7D%7B2%7D%3D%5Cfrac%7B10%7D%7B3%7Dy)
![-3x+\frac{15}{2}=10y](https://tex.z-dn.net/?f=-3x%2B%5Cfrac%7B15%7D%7B2%7D%3D10y)
![-\frac{3}{10}x+\frac{15}{20}=y](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B10%7Dx%2B%5Cfrac%7B15%7D%7B20%7D%3Dy)
![y=-\frac{3}{10}x+\frac{3}{4}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B3%7D%7B10%7Dx%2B%5Cfrac%7B3%7D%7B4%7D)
Step 4,
Convert the equation into inverse function,
![f^{-1}x=-\frac{3}{10}x+\frac{3}{4}](https://tex.z-dn.net/?f=f%5E%7B-1%7Dx%3D-%5Cfrac%7B3%7D%7B10%7Dx%2B%5Cfrac%7B3%7D%7B4%7D)
For x-intercepts,
Substitute y = 0,
![0=-\frac{3}{10}x+\frac{3}{4}](https://tex.z-dn.net/?f=0%3D-%5Cfrac%7B3%7D%7B10%7Dx%2B%5Cfrac%7B3%7D%7B4%7D)
![\frac{3}{10}x=\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B10%7Dx%3D%5Cfrac%7B3%7D%7B4%7D)
![x=\frac{10}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B10%7D%7B4%7D)
![x=\frac{5}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B5%7D%7B2%7D)
![x=2\frac{1}{2}](https://tex.z-dn.net/?f=x%3D2%5Cfrac%7B1%7D%7B2%7D)
Therefore, x-intercept of the inverse function is
.
Option 4 will be the answer.
Using addition
x-y+1/2x+y=1+5
x+1/2x+0y=6
3/2x=6
![\frac{3}{2}x=6](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B2%7Dx%3D6%20)
3x=12
x=4
Using the value of x
x-y=1
4-y=1
y=3
With x as 4 and y as 3, their product is 12
And can be written as (4,3)
Answer:
The answer to your question is x = 3.356 cm
Step-by-step explanation:
This is a right triangle so we can use the Trigonometric functions to solve this problem.
Data
Ф = 40°
Adjacent side = 4 cm
Opposite side = x
Process
1.- We must know the lenght of the opposite side so we must use the tangent to solve it.
tangent Ф = ![\frac{Opposite side}{Adjacent side}](https://tex.z-dn.net/?f=%5Cfrac%7BOpposite%20side%7D%7BAdjacent%20side%7D)
2.- Solve it for Opposite side
Opposite side = tanФ x Adjacent side
Opposite side = tan 40° x 4
Opposite side = 0.839 x 4
Opposite side = 3.356
Opposite side = x = 3.356 cm
Answer:
Step-by-step explanation:
6j - k = 23
6j + 3k = 11.....multiply by -1
---------------
6j - k = 23
-6j - 3k = -11 (result of multiplying by -1)
---------------
-4k = 12
k = -12/4
k = - 3 <=====
6j - k = 23
6j - (-3) = 23
6j + 3 = 23
6j = 23 - 3
6j = 20
j = 20/6
j = 10/3 <===
solution is : j = 10/3 and k = -3