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krok68 [10]
3 years ago
5

The number 0.35 is a(n) __________ number because __________.

Mathematics
2 answers:
worty [1.4K]3 years ago
8 0
Rational number because /An irrational number has endless non-repeating digits to the right of the decimal point.
nordsb [41]3 years ago
8 0

Answer:

The number 0.35 is a <u>rational</u> number because <u>it can be written as a fraction</u>.

Step-by-step explanation:

We have been given an incomplete sentence. We are supposed to complete our given sentence.

Sentence:

The number 0.35 is a(n) __________ number because __________.

We know that 0.35 is a rational number as we can represent it as a fraction.

Since 0.35 has two digits after decimal, so we will multiply and divide 0.35 by 100 as:

0.35\times \frac{100}{100}=\frac{3.5\times 100}{100}=\frac{35}{100}=\frac{5*7}{5*20}=\frac{7}{20}.

Therefore, the correct word for 1st blank is 'rational' and correct expression for 2nd blank is 'it can be written as a fraction \frac{7}{20}.

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3 years ago
20.) A=49.23 degrees, c=54.8Solve the right triangle. Express angles in decimal degrees.
vivado [14]

\begin{gathered} a=41.50 \\ b=35.78 \\ B=40.76\text{ \degree} \\  \end{gathered}

Explanation

Step 1

a) let

\begin{gathered} A=49.23\text{ \degree} \\ c=54.8\text{ \degree} \end{gathered}

b) b value

to find the measure of side b we can use cosine function

\begin{gathered} cos\theta=\frac{adjacent\text{ side}}{hypotenuse} \\ replace \\ cos\text{ 49.23=}\frac{b}{54.8} \\ b=54.8*cos49.23 \\ b=35.78 \end{gathered}

c) angle B

to find the measure of Angle B we can use sine function

\begin{gathered} sin\theta=\frac{opposite\text{  side}}{hypotenuse} \\ replace \\ sin\text{ B=}\frac{35.78}{54.8} \\ sin\text{ B= 0.65}\Rightarrow inverse\text{ function to isolate B} \\ B=\sin^{-1}(0.65) \\ B=40.76 \end{gathered}

d) side a

\begin{gathered} sin\theta=\frac{opposite\text{ side}}{hypotenuse} \\ sin\text{ A=}\frac{a}{c}=\frac{\placeholder{⬚}}{\placeholder{⬚}} \\ sin\text{ 49.23=}\frac{a}{54.8} \\ multiply\text{ both sides by 54.8} \\ 54.8s\imaginaryI n\text{49.23=}\frac{a}{54.8}*54.8 \\ 41.50=a \end{gathered}

so, the answer is

\begin{gathered} a=41.50 \\ b=35.78 \\ B=40.76\text{ \degree} \\  \end{gathered}

I hope this helps you

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