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suter [353]
3 years ago
6

Find x. 6.5 cm x 2.5 cm Y= cm

Mathematics
1 answer:
Talja [164]3 years ago
6 0

9514 1404 393

Answer:

  x = 6.0 cm

Step-by-step explanation:

The ratio of the given dimensions is 2.5/6.5 = 5/13. This should give you a clue that the dimensions here are all half those of the (5, 12, 13) Pythagorean triple. That is, ...

  x = 12/2 = 6 . . . cm

__

In case you haven't memorized a few of the Pythagorean triples commonly used in algebra problems*, you can figure x using the Pythagorean theorem:

  6.5² = 2.5² +x²

  42.25 -6.25 = x²

  x = √36 = 6

  x = 6.0 cm

_____

* most commonly seen are (3, 4, 5), (5, 12, 13), (7, 40, 41) and their multiples.

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\bf ~~~~~~\textit{parabola vertex form}
\\\\
\begin{array}{llll}
\boxed{y=a(x- h)^2+ k}\\\\
x=a(y- k)^2+ h
\end{array}
\qquad\qquad
vertex~~(\stackrel{}{ h},\stackrel{}{ k})\\\\
-------------------------------\\\\
vertex~(5,6)\quad 
\begin{cases}
x=5\\
y=6
\end{cases}\implies y=a(x-5)^2+6
\\\\\\
\textit{we also know that }
\begin{cases}
x=0\\
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\\\\\\
-75=25a\implies \cfrac{-75}{25}=a\implies a=-3
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therefore\qquad \boxed{y=-3(x-5)^2+6}
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Answer:

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Step-by-step explanation:

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