Olivia likes to knit hats and mittens for friends and family. Last fall, she knitted 4 hats and 5 pairs of mittens, which took a total of 78 hours. This fall, she knitted 5 hats and 5 pairs of mittens, which took a total of 85 hours. If each hat and each pair of mittens takes the same amount of time to knit, how long does it take Olivia to knit a hat and a pair of mittens?

1234567891011 match the reasons with the statements in the proof. given: j | | k m 1 = m 3 prove: l | | m 1. j||k, m∠3 = m∠1 if lines are ||, then corresponding angles are =. 2. m∠1 = m∠2 if alternate interior angles are =, then lines are ||. 3. m∠2 = m∠3 substitution 4. l||m given

Five dinosaurs go for a walk and come across some lovely chicken wings. their names are rexy, bronto, steggy, paly, and terry. there are exactly 5 dozen wings(equal enough for each dino to have a dozen right? ); however, terry is on a diet and he only eats 6 wings. if paly eats 2 more than terry, steggy eats 4 more than paly, and bronto and rexy eat the same amount because they are really hungry from not eating all day, how many chicken wings did each dino eat?

Sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y. draw a typical approximating rectangle and label its height and width. y= 5x, y=7x^2then find the area s of the region.