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Rufina
2 months ago
7

Alyssa is jogging near Central Park. She runs along 65th Street for about 0.19 miles, turns right and runs along Central Park We

st for about 0.28 miles. She then turns right again and runs along Broadway until she reaches her starting point. How long is her total run to the nearest hundredth of a mile?

Mathematics
2 answers:
zzz [12.3K]2 months ago
8 0
Approximately 0.81 miles.
AnnZ [12.3K]2 months ago
6 0
Roughly 0.81 miles.
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Answer:

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Step-by-step explanation:

The question is (2x+3)^2+8(2x+3)+11=0

We let u=2x+3, so the equation becomes:

u^2+8u+11=0

Where a=1, b=8, c=11


By applying the quadratic formula, we arrive at:

Quadratic formula: \frac{-b+-\sqrt{b^2-4ac} }{2a}

Substituting yields: \frac{-8+-\sqrt{(8)^2-4(1)(11)} }{2(1)}\\=\frac{-8+-\sqrt{20} }{2}\\=\frac{-8+-2\sqrt{5} }{2}\\=-4+\sqrt{5}, -4-\sqrt{5} }

We let u=2x+3, thus x calculates to:

u=2x+3\\(-4+\sqrt{5})=2x+3\\x=\frac{-7+\sqrt{5}}{2}=-2.38

and

u=2x+3\\(-4-\sqrt{5})=2x+3\\x=\frac{-7-\sqrt{5}}{2}=-4.62


The solutions to the equation are x=-2.38 (rounded to 2 decimal places) and x=-4.62 (rounded to 2 decimal places)

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