3. Consider the straight line x + y = 1 and the family of straight lines that pass through the origin given by y = mx. As m changes the line rotates about the
origin. Solve these two systems of linear equation and find their points of inter-
section. Is there always a solution - If yes, briefly explain why. If not - for what
a
values of m is there no solution.

Step-by-step explanation:

Two distinct lines will always have a point of intersection, provided they are not parallel. That is, the system of equations {x +y = 1, y = mx} will have a unique solution as long as m ≠ -1.

The solution to the system can be found by substitution:

  x +mx = 1

  x(1 +m) = 1 . . . . factor out x

  x = 1/(1+m) . . . . . divide by the coefficient of x; we must have m ≠ -1

  y = m/(1+m) . . . . find the y-coordinate of the solution

The point of intersection is (1/(1+m), m/(1+m)).

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The above solution is undefined when the denominator is zero: m = -1. There is no solution for m = -1.

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

The answer is in the image 

The total nom of  code that can be used is equal to 5+3 = 8

The answer is in the image 

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Approximately it is aqual to 1300kg