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2 years ago

PLEASE HELP!! I need help on problems #5, #6, #9, #10 Picture attached Thank you!

Mathematics

1 answer:

Romashka-Z-Leto [24]2 years ago

6 0

Answer:

5. TS ≅ ML

6. ∠N≅∠U

9. m∠P = 80°

10. QR = 3

Step-by-step explanation:

The congruent symbol ≅ indicates that the two shapes have the same angle and side lengths.

5. TS are the third and second letter in RSTUV. The third and second letters in KLMNO are ML. TS ≅ ML

6. N is the fourth letter in KLMNO. The fourth letter is RSTUV is U. ∠N≅∠U

9. ∠P is congruent to ∠W. Notice they are both on the longer side and the wider angle. Since m∠P ≅ m∠W, and m∠W = 80°, then m∠P = 80°

10. QR is congruent to XY. They are both the shortest sides of the shape. QR ≅ XY and XY = 3, then QR = 3

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Answer:

The answer to your question is number 3.

Step-by-step explanation:

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2 years ago

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2 years ago

I NEED HELP!! please show all work

PtichkaEL [24]

Take the logarithm of both sides. The base of the logarithm doesn't matter.

$4^{5x} = 3^{x-2}$

$\implies \log 4^{5x} = \log 3^{x-2}$

Drop the exponents:

$\implies 5x \log 4 = (x-2) \log 3$

Expand the right side:

$\implies 5x \log 4 = x \log 3 - 2 \log 3$

Move the terms containing x to the left side and factor out x :

$\implies 5x \log 4 - x \log 3 = - 2 \log 3$

$\implies x (5 \log 4 - \log 3) = - 2 \log 3$

Solve for x by dividing boths ides by 5 log(4) - log(3) :

$\implies \boxed{x = -\dfrac{ 2 \log 3 }{ 5 \log 4 - \log 3 }}$

You can stop there, or continue simplifying the solution by using properties of logarithms:

$\implies x = -\dfrac{ \log 3^2 }{ \log 4^5 - \log 3 }$

$\implies x = -\dfrac{ \log 9 }{ \log 1024 - \log 3 }$

$\implies \boxed{x = -\dfrac{ \log 9 }{ \log \frac{1024}3 }}$

You can condense the solution further using the change-of-base identity,

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