Randy has to raise $50.00 to repair his bicycle. He is only $1.00 short. He has only $1 and $5 bills. If he has one more $1 bills than $5 bills, how many does he have of each?

Randy has eight $5 bills and nine $1 bills

Step-by-step explanation:

Randy needs $50.00

And we know that he his only $1.00 short, so he has $49.00

let's define:

x = number of $1 bills that he has

y = number of $5 bills that he has.

then:

x*$1 + y*$5 = $49

We know that he has one more $1 bills than $5 bills.

we can write this as

x = y + 1

So we have a system of two equations and two variables:

x*$1 + y*$5 = $49

x = y + 1

First we can see that the variable "x" is isolated in the second equation, now we can replace that in the other equation:

x*$1 + y*$5 = $49

(y + 1)*$1 + y*$5 = $49

now we can solve this for y.

y*$1 + $1 + y*$5 = $49

y*($1 + $5) = $49 - $1 = $48

y*$6 = $48

y = $48/$6 = 8

He has 8 $5 bills

and we know that:

x = y + 1

x = 8 + 1 = 9

he has 9 $1 bills.

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation:

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47