Which value of the variable is a solution of the inequality?

1 answer:

5 0

The value that the variable can be to be a solution to the inequality is if the variable represents -6, values of -9 and -8 are smaller than -7 as they appear even further away from zero.

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If (2i/2+i)-(3i/3+i)=a+bi, then a=<br>A. 1/10<br>B. -10<br>C. 1/50<br>D. -1/10

Verizon [17]

Answer:

Option A is correct.

Step-by-step explanation:

We are given:

$\frac{2i}{2+i}-\frac{3i}{3+i} = a+bi$

We need to find the value of a.

The LCM of (2+i) and (3+i) is (2+i)(3+i)

$=\frac{2i(3+i)}{(2+i)(3+i)}-\frac{3i(2+i)}{(2+i)(3+i)}\\=\frac{6i+2i^2}{(2+i)(3+i)}-\frac{6i+3i^2}{(2+i)(3+i)}\\=\frac{6i+2i^2-(6i+3i^2)}{(2+i)(3+i)}\\=\frac{6i+2i^2-6i-3i^2)}{5+5i}\\=\frac{-i^2}{5+5i}\\i^2=-1\\=\frac{-(-1)}{5+5i}\\=\frac{1}{5+5i}$

Now rationalize the denominator by multiplying by 5-5i/5-5i

$=\frac{1}{5+5i}*\frac{5-5i}{5-5i} \\=\frac{5-5i}{(5+5i)(5-5i)}\\=\frac{5-5i}{(5+5i)(5-5i)}\\(a+b)(a-b)= a^2-b^2\\=\frac{5(1-i)}{(5)^2-(5i)^2}\\=\frac{5(1-i)}{25+25}\\=\frac{5(1-i)}{50}\\=\frac{1-i}{10}\\=\frac{1}{10}-\frac{i}{10}$

We are given

$\frac{2i}{2+i}-\frac{3i}{3+i} = a+bi$

Now after solving we have:

$\frac{1}{10}-\frac{i}{10}=a+bi$

So value of a = 1/10 and value of b = -1/10

So, Option A is correct.

8 0

4 years ago

James is participating in a 5-mike walk to raise money for a charity. He has received $300 in fixed pledges and raises $11 extra

Vanyuwa [196]

Your equation would be like this:

y=11x+300

because 11 depends on 'X" how many miles he walks and then just add 300 to that because that is the fixed amount

I hope I've helped!

8 0

3 years ago

A 4 3/4-foot pipe has a 3 1/4-foot pipe fitted to it. How long is the new pipe?

lesantik [10]

1/4 is the anwers because you need to reduce the fraction

3 0

3 years ago

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When Jennifer purchases her house, she pays a 3% realtor commission for the $1800,000 loan amount. How much commission did Jenni

ankoles [38]

Answer:

$54,000