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Vesnalui [34]
3 years ago
11

Use synthetic division to find the quotient when 3x^3-13x^2+2x-5 is divided by x-4?

Mathematics
1 answer:
AlexFokin [52]3 years ago
7 0

Answer:

Step-by-step explanation:

4_|   3    -13    2   -5

      <u>         12    -4   -8</u>

       3     -1     -2    -13

3x^2 - x - 2 - 13/(x - 4)

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Answer:

Three-fourths

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

∠QSR≅∠XZY ---> given problem

∠QRS≅∠XYZ ---> given problem

so

△QRS ~ △XYZ ----> by AA Similarity theorem

Remember that, if two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

That means

\frac{QS}{XZ}=\frac{QR}{XY}=\frac{RS}{YZ}

∠Q≅∠X

∠R≅∠Y

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<em>In the right triangle XYZ</em>

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tan(X)=\frac{YZ}{XZ} ---> opposite side angle X divided by adjacent side angle X

substitute the given values

tan(X)=\frac{9}{12}

Simplify

tan(X)=\frac{3}{4}

Remember that

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so

tan(Q)=tan(X)

therefore

tan(Q)=\frac{3}{4} ---->Three-fourths

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