Difference between revisions of "1950 AHSME Problems/Problem 17"
m (small latex fix) |
|||
| Line 1: | Line 1: | ||
| − | == Problem== | + | == 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: | ||
| Line 7: | Line 7: | ||
<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== | + | == 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 | + | 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== | + | == See Also == |
{{AHSME 50p box|year=1950|num-b=16|num-a=18}} | {{AHSME 50p box|year=1950|num-b=16|num-a=18}} | ||
Latest revision as of 23:51, 11 October 2020
Problem
The formula which expresses the relationship between 
and 
as shown in the accompanying table is:
![\[\begin{tabular}[t]{|c|c|c|c|c|c|}\hline x&0&1&2&3&4\\\hline y&100&90&70&40&0\\\hline\end{tabular}\]](http://latex.artofproblemsolving.com/4/e/d/4ed7c1eaa2515e47df2f96e491ca3fb4eba26556.png)
Solution
Plug in the points 
and 
into each equation. The only one that works for both points is 
Plug in the rest of the points to confirm the answer is indeed 
.
See Also
| 1950 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 16 |
Followed by Problem 18 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
