Let y be the difference of two numbers such that one number varies directly as x while the other number varies inversely as x. if y = –7 when x = –2, and y = 5 when x = 1, express y in terms of x. show your work.

Let a and b the two numbers. So y = a – b. one number varies directly as x , a= k1x. while the other number varies inversely as x, b = k2/x. so the equation y = k1x – k2/x

At y = -7, x =2 then -7 = -2k1 + k2/2

At  y = 5, x =1 then 5 = k1 – k2

Solving k1 and k2, 3 and -2 respectively

So y = 3x+2/x

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!