On a movie set, an archway is modeled by the equation y = -0.5x^2 + 3x, where y is the height in feet and x is the horizontal distance in feet. a laser is directed at the archway at an angle modeled by the equation -0.5x + 2.42y = 7.65 such that the beam crosses the archway at points a and b. at what height from the ground are the points a and b?
a.) 1.5 feet and 3.5 feet
b.) 1.4 feet and 4 feet
c.) 3.5 feet and 4 feet
d.) 4 feet and 4 feet

David bought a poster for an art project. the poster is 2.7 feet wide and 3.9 feet tall. what is the area of the poster?

Which equation is equivalent to the given expression? -(1/2y+1/4) a. -1/4(1+2y) b. 1/4(2y-1) c. -2(1/4y-1/8) d. 2(1/8-1/4y)

Need to finish my juan wants to build a greenhouse in his back yard. he needs to maximize the ratio of floor area to structure volume in order to provide the most room for plants while minimizing the area to be heated. find the description of the structure that best meets juan’s criteria. a.) a hemisphere with a diameter of 12 feet b.) a cube with a side length of 12 feet c.) a cone with a diameter of 12 feet and a height of 10 feet d.) a square pyramid with a base side length of 12 feet and a height of 9 feet