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3 years ago

Angles R and Z are complementary. If m ∠R = 26˚, what is the measure of angle Z?

Mathematics

2 answers:

zysi [14]3 years ago

5 0

Answer:

Step-by-step explanation:

(note:Two angles are called complementary when their measures add to 90 degrees.)

90-26=64

Lemur [1.5K]3 years ago

5 0

Answer:

$\boxed {\boxed {\sf m\angle Z=64 \textdegree}}}$

Step-by-step explanation:

Complementary angles add to 90 degrees. Since angles R and Z are complementary, their sum must be 90.

$\angle R + \angle Z= 90$

We know the measure of angle R is 26 degrees.

$26+ \angle Z=90$

Since we are solving for the measure of angle Z, we must isolate it. 26 is being added. The inverse of addition is subtraction, so subtract 26 from both sides.

$26-26 \angle Z= 90-26\\\angle Z= 90=26 \\\angle Z=64$

The measure of angle Z is 64 degrees.

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Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.

-BARSIC- [3]

Answer:

Step-by-step explanation:

Hello, please consider the following.

$3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)$

So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

$4^n+17$ is divisible by 3. We will prove it by induction.

Step 1 - for n = 1

4+17=21= 3*7 this is true

Step 2 - we assume this is true for k so $4^k+17$ is divisible by 3

and we check what happens for k+1

$4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17$

$3\cdot 4^k$ is divisible by 3 and

$4^k+17$ is divisible by 3, by induction hypothesis

So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that $4^n+17$ is divisible by 3 for all positive integers n.

Thanks

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3 years ago