Michael and Derrick each completed a separate proof to show that corresponding angles AKG and ELK are congruent. Who completed the proof incorrectly? Explain. Line AB is parallel to EF, transversal GJ crosses line AB at K and crosses line EF at L.

Michael's Proof

Statement Justification
1. line AB ∥ line EF with transversal segment GJ 1. Given
2. angle AKG is congruent to angle AKL 2. Vertical Angles Theorem
3. angle BKL is congruent to angle ELK 3. Alternate Interior Angles Theorem
4. angle AKG is congruent to angle ELK 4. Transitive Property

Derrick's Proof

Statement Justification
1. line AB ∥ line EF with transversal segment GJ 1. Given
2. angle AKG is congruent to angle BKL 2. Vertical Angles Theorem
3. angle BKL is congruent to angle ELK 3. Alternate Interior Angles Theorem
4. angle AKG is congruent to angle ELK 4. Transitive Property

Suppose y varies directly with x. write a direct variation equation that relates x and y. then find the value of y when x=12 y=7 when x=3

(01.03 mc) which of the following is a step in simplifying the expression x multiplied by y to the power of 2 over x to the power of negative 3 multiplied by y to the power of 3, the whole to the power of negative 4. select one: a. x to the power of negative 4 multiplied by y to the power of negative 2, the whole over x to the power of negative 7 multiplied by y to the power of negative 1. b. x to the power of negative 4 multiplied by y to the power of negative 8, the whole over x to the power of 12 multiplied by y to the power of negative 12. c. x to the power of negative 4 multiplied by y to the power of negative 8, the whole over x to the power of negative 3 multiplied by y to the power of 3. d. x to the power of negative 4 multiplied by y to the power of negative 2, the whole over x to the power of negative 3 multiplied by y to the power of 3.

Two farmers pay a total rent of $140 for a pasture. the first farmer placed $4 oxen in the pasture, and the second farmer placed $30 sheep in the pasture. the farmers split the rent based on the proportion of the pasture eaten by their own animals that month. how much should the first farmer pay, if 1 ox eats as much as 10 sheep in a month?