Given: p: student achieves 90 percent on the geometry final.
q: student will receive a passing grade in geometry class.

Which statement is logically equivalent to q - p?

O If a student achieves 90 percent on the geometry final, then the student will pass geometry class.
O If a student passes geometry class, then the student achieved 90 percent on the geometry final.
O If a student did not achieve 90 percent on the geometry final, then the student did not pass geometry class.
O If a student did not pass geometry class, then the student did not achieve 90 percent on the geometry final.

Paula makes stained-glass windows and sells them to boutique stores. if her costs total $12,000 per year plus $4 per window for the frame. how many windows must she produce to earn a profit of at least $48,000 in one year if she sells the windows for $28 each? 1. define a variable for the situation. 2. write an inequality that represents her profit. note: revenue is money coming in. cost is money going out. profit is the difference between the revenue and the cost. in other words: revenue - costs profit 3.using words, describe how many windows she must sell to have a profit of at least $48,000.

Which of the following is equal to the rational expression when x is not equal to -2 or -6?

Algebraically prove that a clockwise and counterclockwise rotation of 180° about the origin for triangle abc are equivalent rotations.