Diane, John, and Hans sent a total of 135 text messages during the weekend. John sent 9 more messages than Diane. Hans sent 4 times as many messages as Diane. How many messages did they each send

Diane sent 21messages

John sent 30 messages

Hans sent 84 messages

Step-by-step explanation:

Total messages =135

let messages sent by Diane =x

""". sent by John=x+9

sent by Hans=4x

Now the sum

x+x+9+4x=135

6x+9=135

6x=135-9

6x=126

x=126/6

x=21

Diane's message=x=21

John's message=x+9=21+9=30messages

Hans' messages=4×x=4×21=84

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent