COPY: Chemical Reactions and Equations

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Questions and Answers

If $y$ varies jointly as $x$ and $z$, and $y = 150$ when $x = 10$ and $z = -6$, what is the constant of variation, $k$?

  • $k = 8400$
  • $k = -2.5$ (correct)
  • $k = -8400$
  • $k = 25$

Given that $y$ varies jointly as $x$ and $z$ and inversely as $w$, and $y = 3$ when $x = -2$, $z = 6$, and $w = 12$, what is the constant of variation $k$?

  • $k = -1$ (correct)
  • $k = -36$
  • $k = 12$
  • $k = -18$

If $y$ varies jointly as $x$ and $z$, with a constant of variation $k = -2.5$, what is the equation that represents this relationship?

  • $y = -2.5xz$ (correct)
  • $y = -2.5z/x$
  • $y = -2.5x/z$
  • $y = -2.5x + z$

Given that $y$ varies jointly as $x$ and $z$ and inversely as $w$, with a constant of variation $k = -3$, which equation represents this relationship?

<p>$y = -3xz/w$ (B)</p> Signup and view all the answers

If $y$ varies jointly as $x$ and $z$, and $y = 150$ when $x = 10$ and $z = -6$, find the value of $y$ when $x = 0.75$ and $z = 0.4$.

<p>$y = -0.75$ (D)</p> Signup and view all the answers

If $y$ varies jointly as $x$ and $z$ and inversely as $w$, and $y = 3$ when $x = -2$, $z = 6$, and $w = 12$, find the value of $y$ when $x = 5$, $z = -4$, and $w = 0.5$.

<p>$y = 120$ (D)</p> Signup and view all the answers

Given $y$ varies jointly as $x$ and $z$ and inversely as $w$, and $y = 6$ when $x = -6$, $z = -9$, and $w = 3$, determine the constant of variation, $k$.

<p>$k=1/3$ (A)</p> Signup and view all the answers

Given $y$ varies directly as $t^2$ and inversely as $x$, and $y = 192$ when $t = 8$ and $x = 3$, find the constant of variation, $k$.

<p>$k = 9$ (B)</p> Signup and view all the answers

If $y$ varies jointly as $x$ and $z$ and inversely as $w$, and given the constant of variation $k=1/3$. Write the equation that represents this relationship.

<p>$y = \frac{1}{3} \cdot \frac{xz}{w}$ (D)</p> Signup and view all the answers

If $y$ varies directly as $t^2$ and inversely as $x$, where the constant of variation is $k = 9$, what is the equation that represents this relationship?

<p>$y = \frac{9t^2}{x}$ (A)</p> Signup and view all the answers

What type of variation is represented by the equation $y = kxz$?

<p>Joint variation (A)</p> Signup and view all the answers

In the relationship 'y varies directly as x', if x doubles, what happens to y?

<p>y doubles (D)</p> Signup and view all the answers

What does 'k' represent in the equation for direct variation, $y = kx$?

<p>The constant of variation (C)</p> Signup and view all the answers

In inverse variation, if one variable increases, what happens to the other variable?

<p>It decreases (A)</p> Signup and view all the answers

What type of variation includes both direct and inverse variation in the same equation?

<p>Combined variation (A)</p> Signup and view all the answers

If $y$ varies directly as $x$, which equation represents this relationship?

<p>$y = kx$ (D)</p> Signup and view all the answers

If $y$ varies inversely as $x$, which equation represents this relationship?

<p>$y = k/x$ (C)</p> Signup and view all the answers

What is the first step in solving a variation problem?

<p>Find the constant of variation (D)</p> Signup and view all the answers

If $y$ varies directly as the square of $x$, the equation is:

<p>$y = kx^2$ (B)</p> Signup and view all the answers

In the equation $y = kxz$, what kind of variation is represented?

<p>Joint variation (B)</p> Signup and view all the answers

If y varies inversely as the square root of x, the equation is:

<p>$y = k/\sqrt{x}$ (C)</p> Signup and view all the answers

What does it mean for $y$ to vary directly as $x$?

<p>As $x$ increases, $y$ increases. (B)</p> Signup and view all the answers

Which of the following is an example of inverse variation?

<p>Fewer workers, more time to complete the same work (B)</p> Signup and view all the answers

If $y$ varies inversely as $x$ and $y = 4$ when $x = 3$, what is the value of $k$?

<p>12 (A)</p> Signup and view all the answers

If $z$ varies jointly as $x$ and $y$, and $z = 6$ when $x = 2$ and $y = 1$, what is the value of the constant of variation, $k$?

<p>3 (A)</p> Signup and view all the answers

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