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mote1985 [20]
3 years ago
12

Name a pair of vertical angles (easy question)

Mathematics
1 answer:
Nata [24]3 years ago
6 0

<baf and <dae are vertical

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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
Sara was thinking of a number. Sara halves the number and gets an answer of 38.5. Form an equation with x for the information
lbvjy [14]

Answer:The equation wth x in the information can be written as

1/2 x = 38.5 , Upon solving, the number = 77

Step-by-step explanation:

Let the number Sara was thinking about be x

halving the number to get an answer = 38.5 can be expressed as

 1/2 X = 38.5

The equation with x in the information can be written as

1/2 x = 38.5

solving it becomes

1/2 x= 38.5

x = 38.5 x 2

x=77

The number Sara was thinking about = 77

4 0
3 years ago
Given f(x) = -3x - 2 find the foloeing
emmainna [20.7K]

Answer:

f(x) = -3x - 2

F(0)=-2

F(1)= -5

Domain R

Range R

Step-by-step explanation:

6 0
3 years ago
Help me with this problem that I'm stuck on!
jok3333 [9.3K]
                              4/(x+1) = 3/x + 1/15
Should we make common denominators with everything, we get
           4*15*x / [15x(x+1)] = 3*15*(x+1)/[15x(x+1)] + x(x+1)/[15x(x+1)]
Multiply both sides of the equation by the denominator to cancel them
                                         60x = 45(x+1) + x(x+1)
                                         60x = 45x + 45 + x^2 + x
                       x^2 - 14x + 45 = 0
                               (x-9)(x-5)  = 0
The answer to this question is that the solutions are x=9 and x=5.
6 0
3 years ago
Plz plz plz help❤I'll help back
Rama09 [41]
The answer is forty four 44

3 0
3 years ago
Read 2 more answers
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