An airplane has room for 300 coach- fair seats. it can replace any 3 coach seats with 2 first class seats. suppose the airplane is configured with x coach seats and y first class seats. (assume no space is wasted) a) if y=0, what is the value of x? explain the significance in terms of the airplane’s seat configuration. b)if x=0 ,what is the value of y? explain the significance in terms of the airplane’s seat configuration. c)it can be shown that y is a linear function of x. sketch a graph y versus x, labeling both axis-intercepts. d) find a formula for y in terms of x

Given

An airplane has room for 300 coach- fair seats.

It can replace any 3 coach seats with 2 first class seats.

To proof

let  coach seats = x

first class seats =y

As given in the question  airplane has room for 300 coach- fair seats

i.e their is no first class seat.

First point becomes (300,0 )

replace 3 coach seats with 2 first class seats   (Given in question )

second  point becomes (297,2 )

we get two points  (300,0 ) and (297,2 ) .

FORMULA

Equation of line with two point

put the points value in the above equation

sloving the above equation

we get the equation

Proof of (A)

Given : y=0

find the value of x

put this value in

we get

x = 300

Proof of (B)

Given : x =0

find out the value of y

put these value in the equation

y = 200

Proof of (C)

Show that y is a linear function of x.    

y is a linear function of x this is shown in the table and graph given below.

Proof of (D)

find a formula for y in terms of x

the equation

Hence proved

3x + 4y -25 =0 represents the amount of change sianna should recieve

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.