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Maurinko [17]
3 years ago
11

It is given that yvaries directly as x. If y= 5 when x= 4 determine the constant of variation,

Mathematics
1 answer:
aivan3 [116]3 years ago
3 0

Answer:

k=\dfrac{5}{4}

Step-by-step explanation:

Given that,

y varies directly as x. It means,

y = kx

Where

k is the constant of variation

or

k=\dfrac{y}{x}\\\\k=\dfrac{5}{4}

So, the constant of variation is \dfrac{5}{4}.

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A rectangular auditorium seats 1564 people. the number of seats in each row exceeds the number of rows by 1212. find the number
yanalaym [24]
<span>We can safely assume that 1212 is a misprint and the number of seats in a row exceeds the number of rows by 12. Let r = # of rows and s = # of seats in a row. Then, the total # of seats is T = r x s = r x ( r + 12), since s is 12 more than the # of rows. Then r x (r + 12) = 1564 or r**2 + 12*r - 1564 = 0, which is a quadratic equation. The general solution of a quadratic equation is: x = (-b +or- square-root( b**2 - 4ac))/2a In our case, a = 1, b = +12 and c = -1564, so x = (-12 +or- square-root( 12*12 - 4*1*(-1564) ) ) / 2*1 = (-12 +or- square-root( 144 + 6256 ) ) / 2 = (-12 +or- square-root( 6400 ) ) / 2 = (-12 +or- 80) / 2 = 34 or - 46 We ignore -46 since negative rows are not possible, and have: rows = 34 and seats per row = 34 + 12 = 46 as a check 34 x 46 = 1564 = total seats</span>
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3 years ago
Translate the following statement to an inequality.
Irina-Kira [14]

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Step-by-step explanation:

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