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ser-zykov [4K]
3 years ago
7

if one angle of the right triangle is 32 degrees and the length of the opposite side is 11 cm, then the length of the hypotenuse

is 20.8 cm. true or false?
Mathematics
1 answer:
Angelina_Jolie [31]3 years ago
6 0
Sine of the angle is opposite over hypotenuse, so:
Opp/hyp = sin32 degrees
Hyp = opp/sin32 = 20.8. True
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Given g(x) = −3x + 4
Goshia [24]

Answer:

The average rate of change of <em>g</em> from <em>x</em> = <em>a</em> to<em> x</em> = <em>a</em> + <em>h</em> is -3.

Step-by-step explanation:

We are given the function:

g(x) = -3x + 4

And we want to determine its average rate of change of the function for <em>x</em> = <em>a</em> and <em>x</em> = <em>a</em> + <em>h</em>.

To determine the average rate of change, we find the slope of the function between the two points. In other words:

\displaystyle \text{Avg} = \frac{g(a + h) - g(a) }{(a + h ) - a}

Simplify:

\displaystyle \begin{aligned}  \text{Avg} &= \frac{g(a + h) - g(a) }{(a + h ) - a} \\ \\ &=\frac{(-3(a+h) + 4) - (-3a+4)}{h} \\ \\ &= \frac{(-3a -3h + 4) + (3a - 4) }{h} \\ \\ &= \frac{-3h}{h} \\ \\ &= -3\end{aligned}

In conclusion, the average rate of change of <em>g</em> from <em>x</em> = <em>a</em> to <em>x</em> = <em>a</em> + <em>h</em> is -3.

This is the expected result, as function <em>g</em> is linear, so its rate of change would be constant.

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2 years ago
Jonathan buys two baseball bats for $43 each they are on sale for 45% off he also bought a glove that was originally priced at 2
vladimir2022 [97]

Hi There!

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Baseball Bats:

43 x 0.45 = $19.35 as the amount off.

43 - 19.35 = $23.65 with the discount.

23.65 x 2 = $47.3 for two bats.

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Glove:

28 x 0.25 = $7 as the amount off.

28 - 7 = $21 with the discount.

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Together:

21 + 47.3 = $68.3 as the total before taxes.

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With Taxes:

68.3 x 0.055 = $3.7565 as the tax amount.

68.3 - 3.7565 = $64.5435

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Answer:

Not Rounded: $64.5435

Rounded: $64.54

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Hope This Helps :)

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