A Chinese restaurant offers 10 different lunch specials. Each weekday for one week, Fiona goes to the restaurant and selects a lunch special. How many different ways are there for her to select her lunches for the week

10⁵

Step-by-step explanation:

10×10×10×10×10

= 10⁵ or 100,000

  x = 4 ± (1/7)√721

Step-by-step explanation:

7x – 9 = 7x^2 – 49

-9 = 7x^2 -56x . . . . . . . . subtract 7x

-9 = 7(x^2 -8x) . . . . . . . . factor out leading coefficient

-9 +7(16) = 7(x^2 -8x +16) . . . . . add the square of (-8/2) inside parentheses

103 = 7(x -4)^2 . . . . . collect terms, write as a square

103/7 = (x -4)^2 . . . . divide by the leading coefficient

±√(103/7) = x -4 . . . . . take the square root

x = 4 ± (1/7)√721 . . . . add 4, rationalize the denominator

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You "complete the square" by making sure the constant in the quadratic is the square of half the x-term coefficient. If changes are made on one side of the equation, the same changes need to be made on the other side of the equation. Here, we added 7(16) to complete the square.