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3 years ago

1. Nine decreased by three times the

Mathematics

1 answer:

Nesterboy [21]3 years ago

6 0

It’s gonna be -9 there’s your answer

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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

Reverse the two digits of my age, divide by three, add 20, and the result is my age. How many years old am I

lapo4ka [179]

Answer:

48 years old.

Step-by-step explanation:

Let the age be xy or 10x + y.

Reverse the two digits of my age, divide by three, add 20, and the result is my age, convert this to equation:

(10y + x)/3 + 20 = 10x + y
(10y + x)/3 = 10x + y - 20
10y + x = 3(10x + y - 20)
10y + x = 30x + 3y - 60
30x - x + 3y - 10y = 60
29x - 7y = 60

We should consider both x and y are between 1 and 9 since both the age and its reverse are 2-digit numbers.

Possible options for x are:

29x ≥ 7*1 + 60 = 67 ⇒ x > 2, at minimum value of y,

and

29x ≤ 7*9 + 60 = 123 ⇒ x < 5, at maximum value of y.

So x can be 3 or 4.

29*3 - 7y = 60
87 - 7y = 60
7y = 27
y = 27/7, discarded as fraction.

29*4 - 7y = 60
116 - 7y = 60
7y = 56
y = 8

So the age is 48.

6 0

1 year ago

Points A and B have opposite x-coordinates but the same y-coordinates.

n200080 [17]

Answer:

Step-by-step explanation:

start before a and count until you get to B

5 0

3 years ago

What is the Value of x when x + 10=4?

Kisachek [45]

Answer:

-6

Step-by-step explanation

x+10=4

x=4-10

x=-6

5 0

3 years ago

I’m practically begging someone please help me!!

Oliga [24]

My guys is is not just (5, -10)?

6 0

3 years ago