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Crank
4 years ago
7

rish is sorting bolts for her home repair business. She has an 8-pound bag of bolts. If each kitchen her team repairs requires 1

5 pound of bolts, how many kitchen can she repair? Joshua solves the problem by finding 8 ÷ 1 5 = 40 . Melanie solves the problem by finding 8 × 5 = 40
Mathematics
1 answer:
Reptile [31]4 years ago
5 0
I hope you mean 1/5 when you say 1 5. If that's what you mean, then both, Joshua and Melanie, are correct because, both of their equations are the same. 

Joshua's - <span>8 ÷ 1/5 = 40 (Since we can divide a number by fraction, we use this rule: keep, change flip. When we use that Joshua's equation turns into 8 * 5/1 = 8*5 = 40, same as Melanie's.)</span>
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Answer:

The vertex of this parabola, (-2, 3), can be found by completing the square.

Step-by-step explanation:

The goal is to express this parabola in its vertex form:

g(x) = a\, (x - h)^2 + k,

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The vertex form can be expanded to obtain:

\begin{aligned}g(x)&= a\, (x - h)^2 + k \\ &= a\, \left(x^2 - 2\, x\, h + h^2\right) + k = a\, x^2 - 2\, a\, h\, x + \left(a\,h^2 + k\right)\end{aligned}.

Compare that expression with the given equation of this parabola. The constant term, the coefficient for x, and the coefficient for x^2 should all match accordingly. That is:

\left\lbrace\begin{aligned}& a = 3 \\ & -2\,a\, h = 12 \\& a\, h^2 + k = 15\end{aligned}\right..

The first equation implies that a is equal to 3. Hence, replace the "a\!" in the second equation with 3\! to eliminate \! a:

(-2\times 3)\, h = 12.

h = -2.

Similarly, replace the "a" and the "h" in the third equation with 3 and (-2), respectively:

3 \times (-2)^2 + k = 15.

k = 3.

Therefore, g(x) = 3\, x^2 + 12\, x + 15 would be equivalent to g(x) = 3\, (x - (-2))^2 + 3. The vertex of this parabola would thus be:

\begin{aligned}&(-2, \, 3)\\ &\phantom{(}\uparrow \phantom{,\,} \uparrow \phantom{)} \\ &\phantom{(}\; h \phantom{,\,} \;\;k\end{aligned}.

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