Given that current age of Jack = 12 years
Given that current age of Sophia = 16 years
Jack says that the relationship between his age and Sophia‘s is proportional
If Jack's age is represented by y and Sophia's age by x then we can write y=kx as they are in proportion
where k is called constant of proportion
Now let's plug given ages of each that is y=12 and x=16 into y=kx to find the constant of proportionality
12=k*16
12/16=k
Which is same as the given value of constant of proportionality.
Hence Jack is right about his statement.
But if you think about practical life situation then age of both will not be in proportion
For example after 1 year Jack's age will be 13 and Sophiy's age will be 17
then constant of proportionality using new values will be 13/17
Clearly 12/16 and 13/17 are not same.
So in practical life, age of both will not in in proportion.
Given <em>YA</em> = <em>B</em>, you can solve for <em>Y</em> by multiplying by <em>A </em>⁻¹ on the right (on both sides of the equation). So we have
<em>YA</em> = <em>B</em> ==> (<em>YA</em>) <em>A </em>⁻¹ = <em>BA </em>⁻¹ ==> <em>Y</em> (<em>AA </em>⁻¹) = <em>BA </em>⁻¹ ==> <em>Y</em> = <em>BA </em>⁻¹
provided that the inverse of <em>A</em> exists. In this case, det(<em>A</em>) = 5 ≠ 0, so the inverse does exist, and
![A=\begin{bmatrix}-1&-4\\0&-5\end{bmatrix} \implies A^{-1}=\dfrac1{\det(A)}\begin{bmatrix}-5&0\\4&-1\end{bmatrix} = \begin{bmatrix}-1&0\\\frac45&-\frac15\end{bmatrix}](https://tex.z-dn.net/?f=A%3D%5Cbegin%7Bbmatrix%7D-1%26-4%5C%5C0%26-5%5Cend%7Bbmatrix%7D%20%5Cimplies%20A%5E%7B-1%7D%3D%5Cdfrac1%7B%5Cdet%28A%29%7D%5Cbegin%7Bbmatrix%7D-5%260%5C%5C4%26-1%5Cend%7Bbmatrix%7D%20%3D%20%5Cbegin%7Bbmatrix%7D-1%260%5C%5C%5Cfrac45%26-%5Cfrac15%5Cend%7Bbmatrix%7D)
Then
![Y=\begin{bmatrix}5&-5\\8&-8\end{bmatrix}A^{-1} = \begin{bmatrix}-5&5\\-8&\frac{24}5\end{bmatrix}](https://tex.z-dn.net/?f=Y%3D%5Cbegin%7Bbmatrix%7D5%26-5%5C%5C8%26-8%5Cend%7Bbmatrix%7DA%5E%7B-1%7D%20%3D%20%5Cbegin%7Bbmatrix%7D-5%265%5C%5C-8%26%5Cfrac%7B24%7D5%5Cend%7Bbmatrix%7D)
Answer: The equation of the perpendicular line intersects the point (-5,1) is y=x+6[/tex]
Step-by-step explanation:
step1:-
The standard form of slope - intercept form y=m x+c
Here m is called slope of the given line
C is called the y- intercept of the given line
Given equation of the straight line y=-x+1
comparing the slope - intercept form y=m x+c
here m= -1 and c=1
step2:-
The equation of the perpendicular line is
} =\frac{-1}{m} (x-x_{1} )[/tex]
substitute m = -1 and c =1 values in equation
![y-1 =\frac{-1}{-1} (x-(-5 )](https://tex.z-dn.net/?f=y-1%20%3D%5Cfrac%7B-1%7D%7B-1%7D%20%28x-%28-5%20%29)
![y-1 ={1} (x-(-5 )](https://tex.z-dn.net/?f=y-1%20%3D%7B1%7D%20%28x-%28-5%20%29)
![y=1+x+5\\y=x+6](https://tex.z-dn.net/?f=y%3D1%2Bx%2B5%3C%2Fstrong%3E%3C%2Fp%3E%3Cp%3E%3Cstrong%3E%5C%5Cy%3Dx%2B6)
step3:- The equation of the perpendicular line intersects the point (-5,1) is
y=x+6[/tex]
<u>conclusion</u><u>:</u>-
The equation of the perpendicular line is
y=x+6[/tex]
Answer:
I have no clue what I could answer that question with other than (-6,-10)
If it there are two negative #'s you add them because they are on the same side of the number line.