An empty sum is a sum with zero terms and is equal to 0 (the additive identity). We can see this algebraically using repeated addition. For example, adding up 5 three times is equal to 5 + 5 + 5 = 5 · 3 = 15. Following this same reasoning, adding up 5 zero times is equal to 5 · 0 = 0. An empty product is a product with zero terms. Apply a similar process as above to show that an empty product is equal to 1 (the multiplicative identity).

What is the next step in the given proof? choose the most logical approach. a. statement: m 1 + m 2 + 2(m 3) = 180° reason: angle addition b. statement: m 1 + m 3 = m 2 + m 3 reason: transitive property of equality c. statement: m 1 = m 2 reason: subtraction property of equality d. statement: m 1 + m 2 = m 2 + m 3 reason: substitution property of equality e. statement: 2(m 1) = m 2 + m 3 reason: substitution property of equality

There are 40 girls and 32 boys who want to participate in 6th grade intramurals. if each team must have the same number of girls and the same number of boys, what is the greatest number of teams that can participate in intramurals? how many girls and boys will be on each team?

If the equation of a perpendicular bisector of a triangle is y = 2x + 7, what is the slope of the side that it is bisecting? explain how you know.