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natulia [17]
3 years ago
12

Write the following mixed decimals as mixed numbers and reduce to lowest terms. a. 17.45 b. 92.004 c. 4.2 d. 157.43

Mathematics
2 answers:
Allisa [31]3 years ago
7 0

Answer and Step-by-step explanation:

Since we have given that

a) 17.45

Mixed number : 17+\dfrac{45}{100}=17\dfrac{45}{100}

Lowest term : 17\dfrac{9}{20}

2) 92.004

Mixed number : 92+\dfrac{4}{1000}=92\dfrac{4}{1000}

Lowest term : 92\dfrac{1}{250}

3) 4.2

Mixed number : 4+\dfrac{2}{10}=4\dfrac{2}{10}

Lowest term : 4\dfrac{1}{5}

4) 157.43

Mixed number : 157+\dfrac{43}{100}=157\dfrac{43}{100}

Lowest term : 157\dfrac{43}{100}

Marta_Voda [28]3 years ago
4 0

Answer:

Part A) 17\frac{9}{20}

Part B) 92\frac{1}{500}

Part C)2\frac{1}{5}

Part D) 157\frac{43}{100}

Step-by-step explanation:

<u>Part A)</u> 17.45

we know that

17.45=17+0.45

0.45=\frac{45}{100} =\frac{9}{20}

substitute

17+\frac{9}{20}=17\frac{9}{20}

<u>Part B)</u> 92.004

we know that

92.004=92+0.004

0.004=\frac{4}{1,000} =\frac{1}{250}

substitute

92+\frac{1}{500}=92\frac{1}{500}

<u>Part C)</u> 4.2

we know that

4.2=4+0.2

0.2=\frac{2}{10} =\frac{1}{5}

substitute

2+\frac{1}{5}=2\frac{1}{5}

<u>Part D)</u> 157.43

we know that

157.43=157+0.43

0.43=\frac{43}{100}

substitute

157+\frac{43}{100}=157\frac{43}{100}

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The diagram provided is an isosceles triangle. An isosceles triangle has two sides having equal measure and two base angles also having equal measure.

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Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning.
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Suppose that the height (in centimeters) of a candle is a linear function of

the amount of time (in hours) it has been burning.

Let x be the amount of time in hours

Let y be the heoght of a candle in centimeters

The two points are then as (9,24.5) and (23,17.5).

\mathrm{Find\:the\:line\:}\mathbf{y=mx+b}\mathrm{\:passing\:through\:}\left(9,\:24.5\right)\mathrm{,\:}\left(23,\:17.5\right)

\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(9,\:24.5\right),\:\left(x_2,\:y_2\right)=\left(23,\:17.5\right)

m=\frac{17.5-24.5}{23-9}

m=-0.5

\mathrm{Plug\:the\:slope\:}-0.5\mathrm{\:into\:}y=mx+b

y=\left(-0.5\right)x+b

\mathrm{Plug\:in\:}\left(9,\:24.5\right)\mathrm{:\:}\quad \:x=9,\:y=24.5

24.5=\left(-0.5\right)\cdot \:9+b

24.5=\left(-0.5\right)\cdot \:9+b

-4.5+b=24.5

b=29

\mathrm{Construct\:the\:line\:equation\:}\mathbf{y=mx+b}\mathrm{\:where\:}\mathbf{m}=-0.5\mathrm{\:and\:}\mathbf{b}=29

y=-0.5x+29

Now plug in x=21, we get

y=-0.5*21+29=18.5

Thus the height of the candle after 21 hours is 18.5 centimeters.

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