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3 years ago

What's the prime factorization of 105

1 answer:

8 0

105 is a composite number. 105 = 1 x 105, 3 x 35, 5 x 21, 7 x 15. Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105. Prime factorization: 105 = 3 x 5 x 7.

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What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?

astraxan [27]

ANSWER

The value of the expression is
$- 1$

EXPLANATION

Method 1: Rewrite as product of
${i}^{2}$

The expression given to us is,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4}$

We use the fact that
${i}^{2} = - 1$
to simplify the above expression.

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{0} \times {i}^{1} \times {i}^{3} \times {i}^{2} \times {i}^{4}$

This implies,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{0} \times {i}^{2} \times {i}^{2} \times {i}^{2} \times {i}^{2} \times {i}^{2}$

We substitute to obtain,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = 1\times - 1 \times - 1 \times - 1\times - 1 \times - 1$

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = 1\times 1 \times 1 \times - 1 = - 1$

Method 2: Use indices to solve.

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{0 + 1 + 2 + 3 + 4}$

This implies that,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{10}$

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = ( {{i}^{2}} )^{5}$

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = ( - 1 )^{5} = - 1$

8 0

3 years ago

Read 2 more answers

What is the reciprocal of 1/3 ? Enter your answer in the space below, using a slash mark (/) as a fraction bar when needed.

MrRa [10]

Answer:

3/1 = 3

Step-by-step explanation:

reciprocal of 1/3 = 3/1

Hope it helps you in your learning process.

8 0

3 years ago

Find the sum of 16+22+28+...+112

Elodia [21]

Im not 100 percent positive that this is correct but I think the answer is
184

6 0

3 years ago

My Question: Q=1/2P+15, for P

Mekhanik [1.2K]

P=2(9-15) is what i got first i simplify 1/2p to p/2, then subtract from both sides, multply both sides by 2, then regroup terms, and last switch sides

8 0

3 years ago

How do you write an equation of a line given y-intercept -8 and slope 3/4

Lostsunrise [7]

Answer:

$y = \frac{3}{4} x-8$

Step-by-step explanation:

You can us the equation y = m x + c to answer this question.

In ,

y = m x + c

m = slope

c = y - intercept

So, they have already given in the question that,

m = 3/4

c = (-8)

Therefore, you can simply put 3/4 and (-8) instead of m and c respectively like this.

y = m x + c

y = 3/4x - 8

Hope this helps you.

Let me know if you have any other questions :-)

4 0

3 years ago

Read 2 more answers