Fine two integers that have a sum of -17 and a product of 52. What are the integers?

-4 x -13 are the two integers that have a product of 52 and a sum of -17!

Have a great day/night! ^^

{4, 13}

Step-by-step explanation:

Represent the integers by I and J.  Then I + J = -17 and I*J = 52.

Let's solve this system using substitution.  Solve the first equation for I as follows:  

I + J = -17 becomes I = -J - 17

Substitute -J -17 for   I   in the second equation:

(-J - 17)*J = 52

Performing the indicated multiplication, we get:

-J^2 - 17J - 52 = 0

Let's solve this using the quadratic formula.  The quadratic coefficients here are {-1, -17, -52}, and so the discriminant, b^2 - 4ac, is

(-17)^2 - 4(-1)(-52), or 289 - 208, or 81.  This result is positive, so we know that the quadratic equation has two real, unequal roots.  They are:

      17 ± √81         17 ± 9

J =   =

         2(-1)                  -2

Evaluating this last result, we get J = (17 + 9)/2, or J = 13, and

J = (17 - 9)/2 = 8/2, or J = 4

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign

answer: first option i.e. 'a' is correct.

step-by-step explanation:

since we have given that

number of minutes to wrap a small gift box = 4 minutes

we need to find the number of gifts to be wrapped in 5 minutes

since there is a direct variation, as the number of minutes will increase with   number of gifts to be wrapped.

so, let the number of gifts to be wrapped in 5 minutes be x.

so, it becomes,

hence, first option 'a'   is correct.