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? A. (1, 5.5) and (5.25, 6.56) B. (1, 5) and (5.25, 3.94) C. (1.5, 4.87) and (3.5, 4.37) D. (1.5, 5.62) and (3.5, 6.12) E. There is no real solution.

Jackie purchased 3 bottles of water and 2 cups of coffee for the family for $7.35. ryan bought 4 bottles of water and 1 cup of coffee for his family for 7.15. how much does each bottle of water cost? how much does each cup of coffee cost?

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

Evaluate the expression for the given value of the variable. ∣-4b-8∣+∣-1-b^2 ∣+2b^3 ; b=-2