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2 years ago

Will give brainliest if correct

Mathematics

1 answer:

Nuetrik [128]2 years ago

6 0

Answer:

Step-by-step explanation:

$|\angle AEC|=(4x)^o \quad\implies\quad |\angle AED|=180^o-(4x)^o\\\\\\\widehat{AC}=120^o\quad\implies\quad |\angle AOC|=120^o\\\\|\angle AOC|=120^o \quad\implies\quad |\angle ADC|=\frac12\cdot120^o=60^o\\\\\\\widehat{BD}=(2x)^o\quad\implies\quad |\angle BOD|=(2x)^o\\\\|\angle BOD|=(2x)^o \quad\implies\quad |\angle ADC|=\frac12\cdot(2x)^o=x^o\\\\\\ \Delta ADE:\\\\180^o-(4x)^o+60^o+x^o=180^o\\\\-(3x)^o=-60^o\\\\x=20^o\\\\\\|\angle AED|=180^o-4\cdot20^o=100^o$

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You roll a 6-sided die.

Lerok [7]

Answer:

$\huge\boxed{\text{P(not factor of 35) = } \frac{2}{3}}$

Step-by-step explanation:

We can use basic probability to find the probability that this roll is not a factor of 35.

First off, we know that with a six sided die there are 6 possible things we can roll.

1, 2, 3, 4, 5, or 6

Now, what are the factors of 35? The factors of 35 will be any whole number that can be multiplied by another whole number to get 35.

We know $1 \cdot 35 = 35$ , so two factors are 1 and 35.
We know $5 \cdot 7 = 35$ , so two factors are 5 and 7.

Therefore, the factors of 35 are 1, 5, 7, 35.

Both 5 and 7 are inside the range of 1-6. So the probability of rolling a side that's a factor of 35 will be $\frac{2}{6} = \frac{1}{3}$ since there are two factors and 6 possible options.

This means, logically, there is a $\frac{4}{6} = \frac{2}{3}$ chance of not rolling a factor of 35.

Hope this helped!

5 0

2 years ago

Prove the following by induction. In each case, n is apositive integer.<br> 2^n ≤ 2^n+1 - 2^n-1 -1.

frutty [35]

<h2>Answer with explanation:</h2>

We are asked to prove by the method of mathematical induction that:

$2^n\leq 2^{n+1}-2^{n-1}-1$

where n is a positive integer.

Let us take n=1

then we have:

$2^1\leq 2^{1+1}-2^{1-1}-1\\\\i.e.\\\\2\leq 2^2-2^{0}-1\\\\i.e.\\2\leq 4-1-1\\\\i.e.\\\\2\leq 4-2\\\\i.e.\\\\2\leq 2$

Hence, the result is true for n=1.

Let us assume that the result is true for n=k

i.e.

$2^k\leq 2^{k+1}-2^{k-1}-1$

Now, we have to prove the result for n=k+1

i.e.

<u>To prove:</u> $2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1$

Let us take n=k+1

Hence, we have:

$2^{k+1}=2^k\cdot 2\\\\i.e.\\\\2^{k+1}\leq 2\cdot (2^{k+1}-2^{k-1}-1)$

( Since, the result was true for n=k )

Hence, we have:

$2^{k+1}\leq 2^{k+1}\cdot 2-2^{k-1}\cdot 2-2\cdot 1\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{k-1+1}-2\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-2$

Also, we know that:

$-2$

(

Since, for n=k+1 being a positive integer we have:

$2^{(k+1)+1}-2^{(k+1)-1}>0$ )

Hence, we have finally,

$2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1$

Hence, the result holds true for n=k+1

Hence, we may infer that the result is true for all n belonging to positive integer.

i.e.

$2^n\leq 2^{n+1}-2^{n-1}-1$ where n is a positive integer.

6 0

3 years ago

Write the inequality shown by the graph

garik1379 [7]

Answer:

The answer should be m < -2.5

Step-by-step explanation:

I was taught this before and my teacher always said if its a open circle then its > or < if its a closed circle then it should have the line under it, and the line is going down so it would be Less than sign

4 0

2 years ago

What is equivalent decimal for 0.85

Alex_Xolod [135]

Answer:

17/20

Step-by-step explanation:

0.85 = 85/100 = 17/20

The number 0.85 can be written using the fraction 85/100 which is equal to 17/20 when reduced to lowest terms.

5 0

2 years ago

An arithmetic sequence is represented by the explicit formula A(n) = 2 +(n − 1)(− 5)

Reil [10]

Answer:

a+(n-1)d please do you get it or

8 0

2 years ago

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