The archway of the main entrance of a university is modeled by the quadratic equation y = -x2 + 6x. the university is hanging a banner at the main entrance at an angle defined by the equation 4y = 21 − x. at what points should the banner be attached to the archway?

(1,5) and (5.25,3.94)

Step-by-step explanation:

We are given that

The equation of archway

.....(1)

The equation of an angle at  which a banner is hanging is given by

.....(2)

We have to find the points at which the banner should attached to the archway.

Substitute x=0 in equation (1)

Substitute y=0 in equation (1)

The equation (1) is passing through the points (0,0) and (6,0).

Substitute x=0 in equation (2)

Substitute y=0

The equation (2) is passing through the points (0,5.25) and (21,0).

When draw the graph then we can see that the two equation intersects at the point (1,5) and (5.25,3.94).

Hence,the banner should be attached to the archway at points (1,5) and (5.25,3.94)

sorry not sure

step-by-step explanation:

is means division by fractions

step-by-step explanation: