Two angles are Complementary to each other. One angle is 30 degrees what is the measure of the other angle

1 answer:

4 0

Complementary angles equal to 90 degrees.
so, you are given that one angle is 30 degrees
the other angle is unknown, x
30 + x = 90
subtract 30 from both sides
x = 60

The measure of the other angle is 60 degrees.

Hope this helps

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n the sequence $121, 1221, 12221, \dots ,$ the $n$th number consists of $n$ copies of the digit $2$, surrounded by two $1$s. How

balandron [24]

The $n$ th number in the sequence can be expressed as

$a_n=10^{n+1}+\displaystyle2\sum_{i=2}^n10^i+21$

Extracting the $n$ th term from the sum gives

$a_n=10^{n+1}+2\cdot10^n+\displaystyle2\sum_{i=2}^{n-1}10^i+21$

and $10^{n+1}+2\cdot10^n=10^n(10+2)=12\cdot10^n$ . 3 divides both 12 and 21, so $12\cdot10^n$ and 21 contribute no remainder.

This leaves us with

$a_n\equiv10\cdot\underbrace{222\ldots222}_{n-2\text{ copies}}\pmod3$

Recall that a decimal integer is divisible by 3 if its digits add to a multiple of 3. The digits in $10\cdot222\ldots222$ are $n-2$ copies of 2 and one 0, so the digital sum is $2(n-2)=2n-4$ .

If $n=3k$ for $k=0,1,2,3,\ldots$ , then the digital sum is $2(3k)-4=6k-4$ , which is not divisible by 3.
If $n=3k+1$ , then the sum is $2(3k+1)-4=6k-2$ , which is not divisible by 3.
If $n=3k+2$ , then the sum is $2(3k+2)-4=6k$ , which is always divisble by 3.

This means that roughly 1/3 of the first $n$ numbers in this sequence are divisible by 3; among the first 100 terms, they occur for $n=2,5,8,\ldots,95,98$ , of which there are 33.

7 0

3 years ago

Read 2 more answers

Luis found two bicycles he likes. The price of the first bicycle is $73.59. The price of the second bicycle is $98.50. Estimate

Anuta_ua [19.1K]

The difference is $24.91. how I got the answer.

I just kept adding til I got the right number, so to make it quick, I knew that I could add 20+73.59=93.59. then I added 4.91+20+73.59=$98.50.

You could do subtraction if that make it easier on you!

I hope this helps!

5 0

2 years ago

What is the midpoint of (2, 13) and (0, 11)? WHAT IS THE X VALUE? *

Fudgin [204]

Answer:

(1, 12)

Step-by-step explanation:

midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

= $(\frac{2 + 0}{2} , \frac{13 + 11}{2} )$