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4 years ago

rewrite as equivalent rational expressions with denominator (3x−8)(x−5)(x−3). 4/3x2−23x+40,9x/3x2−17x+24

Mathematics

1 answer:

saul85 [17]4 years ago

3 0

Answer:

Step-by-step explanation:

\frac{4}{3x²-23x+40}

=\frac{4}{3x²-15x-8x+40}

=\frac{4}{3x(x-5)-8(x-5)}

=\frac{4}{(x-5)(3x-8)}

=\frac{4(x-3)}{(x-5)(3x-8)(x-3)}

\frac{9x}{3x²-17x+24}

=\frac{9x}{3x²-9x-8x+24}

=\frac{9x}{3x(x-3)-8(x-3)}

=\frac{9x}{(x-3)(3x-8)}

=\frac{9x(x-5)}{(3x-8)(x-5)(x-3)}

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If ∠A and ∠B are supplementary and m∠A = 37°45', then m∠B = ______.

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Answer: 142°15'

Explanation:

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Answer:

Step-by-step explanation:

$(\frac{3}{4})^6 \times (\frac{16}{9})^5=(\frac{4}{3})^{x+2}$

$\frac{3^6}{4^6} \cdot \frac{16^5}{9^5}=\frac{4^{x+2}}{3^{x+2}}$

$\frac{3^6}{4^6} \cdot \frac{(4^2)^5}{(3^2)^5}=\frac{4^{x+2}}{3^{x+2}}$

$\frac{3^6}{4^6} \cdot \frac{4^{10}}{3^{10}}=\frac{4^{x+2}}{3^{x+2}}$

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This implies

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-(x+2)=-4.

x+2=4 implies x=2 since subtract 2 on both sides gives us x=2.

Solving -(x+2)=-4 should give us the same value.

Multiply both sides by -1:

x+2=4

It is the same equation as the other.

You will get x=2 either way.

Let's check:

$(\frac{3}{4})^6 \times (\frac{16}{9})^5=(\frac{4}{3})^{2+2}$

$(\frac{3}{4})^6 \times (\frac{16}{9})^5=(\frac{4}{3})^{4}$

Put both sides into your calculator and see if you get the same thing on both sides:

Left hand side gives 256/81.

Right hand side gives 256/81.

Both side are indeed the same for x=2.

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