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Setler [38]
2 years ago
7

In a bag of beads, the ratio of the number of orange to blue to white is 13:7:4. If the number of orange beads minus the number

of white beads is 54, how many blue beads are there?
HELPPP MARKING AS BRANLIEST IF U ANSWER THIS
Mathematics
1 answer:
mamaluj [8]2 years ago
5 0

Answer:

42 blue beads

Step-by-step explanation:

Solution:

<em> </em><em>Let's </em><em>suppose </em><em>the </em><em>numbers </em><em>as </em><em>1</em><em>3</em><em>x</em><em>,</em><em> </em><em>7</em><em>x</em><em> </em><em>and </em><em>4</em><em>x</em><em> </em><em>respectively</em><em>.</em><em>.</em>

<em>Where,</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>Orange </em><em>=</em><em> </em><em>1</em><em>3</em><em>x</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>Blue </em><em>=</em><em> </em><em>7</em><em>x</em>

<em> </em><em> </em><em> </em><em> </em><em>White </em><em>=</em><em> </em><em>4</em><em>x</em>

<em>According </em><em>to </em><em>the </em><em>question</em><em>,</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>1</em><em>3</em><em>x</em><em> </em><em>-</em><em> </em><em>4</em><em>x</em><em> </em><em>=</em><em> </em><em>5</em><em>4</em>

<em>or,</em><em> </em><em>9</em><em>x</em><em> </em><em>=</em><em> </em><em>5</em><em>4</em>

<em>or,</em><em> </em><em>x </em><em>=</em><em> </em><em>5</em><em>4</em><em>/</em><em>9</em>

<em>or,</em><em> </em><em>x</em><em>=</em><em> </em><em>6</em>

<em>Now,</em>

<em> </em><em> </em><em> </em><em>Blue </em><em>beads </em><em>=</em><em> </em><em>7</em><em>x</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>=</em><em> </em><em>7</em><em> </em><em>×</em><em> </em><em>6</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>=</em><em> </em><em>4</em><em>2</em><em>.</em><em>.</em>

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Solution:

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Step-by-step explanation:

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Answer:

\begin{gathered} A=\text{ 12}\degree \\ B=\text{ 114}\degree \\ C=54\degree \end{gathered}

Step-by-step explanation:

To calculate the angles of the given triangle, we can use the law of cosines:

\begin{gathered} \cos (C)=\frac{a^2+b^2-c^2}{2ab} \\ \cos (A)=\frac{b^2+c^2-a^2}{2bc} \\ \cos (B)=\frac{c^2+a^2-b^2}{2ca} \end{gathered}

Then, given the sides a=2, b=9, and c=8.

\begin{gathered} \cos (A)=\frac{9^2+8^2-2^2}{2\cdot9\cdot8} \\ \cos (A)=\frac{141}{144} \\ A=\cos ^{-1}(\frac{141}{144}) \\ A=11.7 \\ \text{ Rounding to the nearest degree:} \\ A=12º \end{gathered}

For B:

\begin{gathered} \cos (B)=\frac{8^2+2^2-9^2}{2\cdot8\cdot2} \\ \cos (B)=\frac{13}{32} \\ B=\cos ^{-1}(\frac{13}{32}) \\ B=113.9\degree \\ \text{Rounding:} \\ B=114\degree \end{gathered}\begin{gathered} \cos (C)=\frac{2^2+9^2-8^2}{2\cdot2\cdot9} \\ \cos (C)=\frac{21}{36} \\ C=\cos ^{-1}(\frac{21}{36}) \\ C=54.3 \\ \text{Rounding:} \\ C=\text{ 54}\degree \end{gathered}

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