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)

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

alright well the answers to your question is

2xy/9 hope this have a nice day : )

step-by-step explanation: