Agroup of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. what is the sum of the two smallest possible values of n?

  46

Step-by-step explanation:

The smallest value of n (found by trial and error) is 13. The next larger value is 4·5 = 20 more than that, 33.

The sum of these values is 13 +33 = 46.

Actually, we looked for solutions to ...

  n = 4k +1 = 5m +3

  4k -5m = 2 . . . . . . subtract 5m+1

We found the smallest solution to be k=3, m=2 giving 12 -10 = 2. Then further solutions are of the form ...

  k = 5p+3, m = 4p+2 . . . . . for any integer p

The corresponding values of n are ...

  n = 4(5p+3)+1 = 20p+13

The two smallest values correspond to p=0 and p=1, so are 13, 33.

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)

the answer is 24

step-by-step explanation: