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3 years ago

Constant of variation

Mathematics

1 answer:

Zinaida [17]3 years ago

8 0

Answer:

The constant of variation in a direct variation is the constant (unchanged) ratio of two variable quantities.

Step-by-step explanation:

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The price of an item has risen to $169 today. Yesterday it was $130. Find the percentage increase.

mamaluj [8]

Answer:30%

Step-by-step explanation:

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1 year ago

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3 years ago

Calculate 4 and 3/4 divided by 2 and 5/12

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Step-by-step explanation:

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3 years ago

Suppose h(x)=3x-2 and j(x) = ax +b. Find a relationship between a and b such that h(j(x)) = j(h(x))

sergejj [24]

Answer:

$\displaystyle a = \frac{1}{3} \text{ and } b = \frac{2}{3}$

Step-by-step explanation:

We can use the definition of inverse functions. Recall that if two functions, f and g are inverses, then:

$\displaystyle f(g(x)) = g(f(x)) = x$

So, we can let j be the inverse function of h.

Function h is given by:

$\displaystyle h(x) = y = 3x-2$

Find its inverse. Flip variables:

$x = 3y - 2$

Solve for y. Add:

$\displaystyle x + 2 = 3y$

Hence:

$\displaystyle h^{-1}(x) = j(x) = \frac{x+2}{3} = \frac{1}{3} x + \frac{2}{3}$

Therefore, a = 1/3 and b = 2/3.

We can verify our solution:

$\displaystyle \begin{aligned} h(j(x)) &= h\left( \frac{1}{3} x + \frac{2}{3}\right) \\ \\ &= 3\left(\frac{1}{3}x + \frac{2}{3}\right) -2 \\ \\ &= (x + 2) -2 \\ \\ &= x \end{aligned}$

And:

$\displaystyle \begin{aligned} j(h(x)) &= j\left(3x-2\right) \\ \\ &= \frac{1}{3}\left( 3x-2\right)+\frac{2}{3} \\ \\ &=\left( x- \frac{2}{3}\right) + \frac{2}{3} \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}$

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3 years ago

The line plot shows students favorite pizza toppings. Which can you find using the line plot: the median, mode, range, or outlie

DiKsa [7]

Answer:

The mode is pepperoni. This data set isn't numerical.

Step-by-step explanation:

The data set is skewed right.

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4 years ago