X + k y = 1
k x + y = 1 / * ( - k )
----------------
x + k y = 1
- k² x - k y = - k
--------------------
x - k² x = 1 - k
x ( 1 - k² ) = 1 - k
x = ( 1 - k ) / ( 1 - k² ) = ( 1 - k ) / ( 1 - k ) ( 1 + k )
y = 1 - k( 1 - k )/( 1 - k² )
y = ( 1 - k ) / ( 1 - k² ) = ( 1 - k ) / ( 1 - k ) ( 1 + k )
a ) For k = - 1 this system has no solution.
b ) For k ≠ - 1 and k ≠ 1, the system has unique solution:
( x , y ) = ( 1/ (1 + k) , 1/( 1 + k ) ).
c ) For k = 1, there are infinitely many solutions.

3 0

2 years ago

Write the point-slope form of the equation of the line through the given point woth the given slope

Andrej [43]

Answer:

3.) $\displaystyle y - 4 = 4[x - 1]$

2.) $\displaystyle y + 5 = 2[x + 2]$

1.) $\displaystyle y + 3 = 1\frac{1}{5}[x + 5]$

Step-by-step explanation:

In the Point-Slope Formula, $\displaystyle y - y_1 = m[x - x_1],$ all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT SIGNS.

* $\displaystyle 1\frac{1}{5} = \frac{6}{5}$

I am joyous to assist you anytime.

3 0

2 years ago

Use the distance formula to find the distance, to the nearest tenth, from S(7, −1) to V(−1, 3).

34kurt

Answer: 8.9 units (choice C)

Explanation:

We plug $(x_1,y_1) = (7,-1) \text{ and } (x_2,y_2) = (-1,3)\\\\$ into the distance formula to get the following

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(7-(-1))^2 + (-1-3)^2}\\\\d = \sqrt{(7+1)^2 + (-1-3)^2}\\\\d = \sqrt{(8)^2 + (-4)^2}\\\\d = \sqrt{64 + 16}\\\\d = \sqrt{80}\\\\d \approx 8.94427\\\\d \approx 8.9\\\\$

4 0

2 years ago

Mark records his science scores in each monthly assessment over a period of 5 months. In the first assessment he scores 76%. In

katovenus [111]

d. both a relation and a function:

Given:

Mark records his science scores in each monthly assessment over a period of 5 months. In the first assessment he scores 76%. In the second assessment he scores 73%. After that, his scores keep increasing by 2% in every assessment.

x represents the number of assessments since he starts recording and y represents the scores in each assessment.

In order for a relation to be a function the association has to be unambiguous that means that for a given input only one output can exist.If an input can have two or more outputs then you cannot determine which is the correct output for that input.

In the given situation:

x is the input that is number of assessments since mark starts recording the scores so there is only one assessment no repeating.so there is only one output.

Hence the relation is a function.

Learn more about the function here:

brainly.com/question/5975436

#SPJ1

4 0

1 year ago