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3 years ago

If BC = 6.5, CD = 7.8, and AD = 12.2, find AB to the nearest tenth.

Mathematics

1 answer:

Sladkaya [172]3 years ago

6 0

This can be solved using the angle bisector theorem. Note that line segment AD is the angle bisector of triangle DAB from angle DAB. Therefore, we know that the ratios $\frac{\text{AD}}{\text{CD}}$ and $\frac{\text{AB}}{\text{CB}}$ are equal. Solving, we get $\frac{\text{12.2}}{\text{7.8}}=\frac{\text{AB}}{\text{6.5}}$ . Cross multiplying, we get $79.3 = 7.8x$ , and solving this equation we get $x = 10.1666... \approx 10.2$ . 10.2 is your answer.

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Step-by-step explanation:

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Read 2 more answers

Help with matrices please? Any wrong/not applicable answers will be reported and BLOCKED

marin [14]

m x H = $\left[\begin{array}{ccc}-25&37.5&-12.5\\\9\end{array}\right]$

Step-by-step explanation:

Step 1; Multiply 5 with this matrix $\left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right]$ and we get a matrix $\left[\begin{array}{ccc}-5&10\\20&40\\\end{array}\right]$

Multiply the fraction $\frac{2}{5}$ with the matrix $\left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right]$ and we get $\left[\begin{array}{ccc}-\frac{2m}{5} &\frac{4m}{5} \\\frac{8m}{5} &\frac{16m}{5} \\\end{array}\right]$

Step2; Now equate corresponding values of the matrices with each other.

-5 = $\frac{-2m}{5}$ and so on. By equating we get the value of m as $\frac{25}{2}$

Step 3; Add the matrices to get the value of matrix m.

Adding the three matrices on the RHS we get $\left[\begin{array}{ccc}2&9&-9\\\end{array}\right]$ .

Step 4; Adding the matrices on the LHS we get the resulting matrix as H +

$\left[\begin{array}{ccc}4&6&-8\\\9\end{array}\right]$ . Equating the matrices from step 3 and 4 we get the value of H as $\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right]$

Step 5; Now to find the value of m x H we need to multiply the value of $\frac{25}{2}$ with the matrix $\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right]$

Step 6; Multiplying we get the matrix m x H = [ -25 $\frac{75}{2}$ $\frac{-25}{2}$ ]

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