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Illusion [34]
3 years ago
14

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)
EThere is no real solution.
Mathematics
2 answers:
katrin [286]3 years ago
5 0

Basically look for the intersection points of these two functions by setting them equal to each other.

-x^2 + 6x = 21/4 - x/4

-x^2 + (25/4)x - 21/4 = 0

x = 1 and x = 21/4


Plug these points back to any of the two original equations, you will get

(1,5) and (21/4, 63/16)


denpristay [2]3 years ago
4 0

1.5 ........ 5.25..... 3.94

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x = 15.7945

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

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  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Trigonometry</u>

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Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify variables</em>

Angle θ = 33°

Opposite Leg = <em>x</em>

Hypotenuse = 29

<u>Step 2: Find Angle</u>

  1. Substitute in variables [sine]:                                                                           sin33° = x/29
  2. [Multiplication Property of Equality] Multiply 29 on both sides:                    29sin33° = x
  3. Rewrite:                                                                                                             x = 29sin33°
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3 years ago
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