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Maurinko [17]
2 years ago
16

mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Each problem is worth either

5 points or 2 points. Write a system of equations that can be used to find how many problems of each point value are on the test. Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points. x + y = 29, 5x + 2y = 100 x + y = 100, 5x + 2y = 29 5x + y = 29, 2y + x = 100 2x + y = 100, 5y + x = 29
Mathematics
2 answers:
MakcuM [25]2 years ago
8 0

its the first answer x + y = 29, 5x + 2y = 100

bija089 [108]2 years ago
6 0

Answer:

x + y = 29, 5x + 2y = 100

Step-by-step explanation:

u lied about 100 points

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\bf \textit{hyperbolas, vertical traverse axis }\\\\
\cfrac{(y-{{ k}})^2}{{{ a}}^2}-\cfrac{(x-{{ h}})^2}{{{ b}}^2}=1
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\end{cases}\\\\
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\cfrac{(y+11)^2}{15^2}-\cfrac{(x-7)^2}{8^2}=1\implies \cfrac{(y-(-11))^2}{15^2}-\cfrac{(x-7)^2}{8^2}=1\\\\
-------------------------------\\\\
c=\textit{distance from the center to either foci}\\\\
c=\sqrt{a^2+b^2}\implies c=\sqrt{15^2+8^2}\implies \boxed{c=17}

now, if you notice, the positive fraction, is the one with the "y" variable, and that simply means, the hyperbola traverse axis is over the y-axis, so it more or less looks like the picture below.

now, from the hyperbola form, we can see the center is at (7, -11), and that the "c" distance is 17.

so, from -11 over the y-axis, we move Up and Down 17 units to get the foci, which will put them at (7, -11-17) or (7, -28) and (7 , -11+17) or (7, 6)

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