Difference between revisions of "1950 AHSME Problems/Problem 17"

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== Problem==
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== Problem ==
  
 
The formula which expresses the relationship between <math>x</math> and <math>y</math> as shown in the accompanying table is:
 
The formula which expresses the relationship between <math>x</math> and <math>y</math> as shown in the accompanying table is:
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<math> \textbf{(A)}\ y=100-10x\qquad\textbf{(B)}\ y=100-5x^{2}\qquad\textbf{(C)}\ y=100-5x-5x^{2}\qquad\\ \textbf{(D)}\ y=20-x-x^{2}\qquad\textbf{(E)}\ \text{None of these} </math>
 
<math> \textbf{(A)}\ y=100-10x\qquad\textbf{(B)}\ y=100-5x^{2}\qquad\textbf{(C)}\ y=100-5x-5x^{2}\qquad\\ \textbf{(D)}\ y=20-x-x^{2}\qquad\textbf{(E)}\ \text{None of these} </math>
  
==Solution==
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== Solution ==
  
Plug in the points <math>(0,100)</math> and <math>(4,0)</math> into each equation. The only one that works for both points is <math>\mathrm{(C)}.</math> Plug in the rest of the points to confirm the answer is indeed <math>\boxed{\mathrm{(C)}\ y=100-5x-5x^2.}</math>
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Plug in the points <math>(0,100)</math> and <math>(4,0)</math> into each equation. The only one that works for both points is <math>\mathrm{(C)}.</math> Plug in the rest of the points to confirm the answer is indeed <math>\boxed{\mathrm{(C)}\ y=100-5x-5x^2}</math>.
  
==See Also==
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== See Also ==
  
{{AHSME box|year=1950|num-b=16|num-a=18}}
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{{AHSME 50p box|year=1950|num-b=16|num-a=18}}
  
 
[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]
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{{MAA Notice}}

Latest revision as of 00:51, 12 October 2020

Problem

The formula which expresses the relationship between $x$ and $y$ as shown in the accompanying table is:

\[\begin{tabular}[t]{|c|c|c|c|c|c|}\hline x&0&1&2&3&4\\\hline y&100&90&70&40&0\\\hline\end{tabular}\]

$\textbf{(A)}\ y=100-10x\qquad\textbf{(B)}\ y=100-5x^{2}\qquad\textbf{(C)}\ y=100-5x-5x^{2}\qquad\\ \textbf{(D)}\ y=20-x-x^{2}\qquad\textbf{(E)}\ \text{None of these}$

Solution

Plug in the points $(0,100)$ and $(4,0)$ into each equation. The only one that works for both points is $\mathrm{(C)}.$ Plug in the rest of the points to confirm the answer is indeed $\boxed{\mathrm{(C)}\ y=100-5x-5x^2}$.

See Also

1950 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 16
Followed by
Problem 18
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All AHSME Problems and Solutions

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