Final answer:
The two numbers that multiply to 36 and add to -15 are -3 and -12. This is because the multiplication of two negative numbers yields a positive product, and their sum is negative.
Step-by-step explanation:
The student is asking for two numbers that multiply to 36 and add to -15. To solve this, we can set up a system of equations based on the given facts. Let the two numbers be x and y:
Since both numbers multiply to a positive number (36), and their sum is negative (-15), both numbers must be negative according to the rules of multiplication and addition of signed numbers. Remember that when two negative numbers multiply (negative times negative), the result is positive, whereas the addition of two negative numbers (negative plus negative) is also negative.
To find the two numbers, we can factor the product 36 into pairs of factors and look for a pair that sums to -15. The factors of 36 that also add up to -15 are -3 and -12:
- (-3) * (-12) = 36
- (-3) + (-12) = -15
Thus, the two numbers that meet the criteria are -3 and -12.