The difference of the square of two positive consecutive even integers is 52. find the integers. use the fact that, if x represents an even integer, then x + 2 represents the next consecutive even integer.

Integers are 12 and 14

Step-by-step explanation:

Let the given consecutive even integers be X and X+2

Now

Given as the difference of the square of two positive consecutive integers is 52

i.e (X+2)² - x² = 52

or (X²+4x+4) - X² = 52

or X²+4x+4-X² = 52

or 4x+4 = 52

or x+1 =

x= 13 - 1

i.e X = 12

and X+2 = 12+2 = 14

so, positive consecutive integers are 12 and 14     ( Answer )

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!