When a projector is placed 10 meters from a screen as shown, it produces an image 3 meters high. if the tallest image that the projector can produce without distortion is 4.5 meters high, what is the maximum distance the projector can be placed from the screen?

Elena and her husband marc both drive to work. elena's car has a current mileage (total distance driven) of 15,000 and she drives 23,000 miles more each year. marc's car has a current mileage of 46,000 and he drives 9,000 miles more each year. will the mileages for the two cars ever be equal? explain.

Gabriel determined that his total cost would be represented by 2.5x + 2y – 2. his sister states that the expression should be x + x + 0.5x + y + y – 2. who is correct? explain.

Is there a direction u in which the rate of change of f(x, y)equals=x squared minus 3 xy plus 4 y squaredx2−3xy+4y2 at p(1,2) equals 14? give reasons for your answer. choose the correct answer below. a. no. the given rate of change is smaller than the minimum rate of change. b. no. the given rate of change is larger than the maximum rate of change. c. yes. the given rate of change is larger than the minimum rate of change and smaller than the maximum rate of change.