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Mathematics

1 answer:

oksano4ka [1.4K]3 years ago

5 0

Answer:

Step-by-step explanation:

1. Move circle with center X, 2 units to the right and 8 units down to produce circle with radius 6 and center at the origin

2. Dilate this circle with a factor of 1/2 (or compress this circle with a factor of 2) to produce a circle with radius 3

3. Now move this circle 4 units to the right and 2 units up to produce circle Y.

CircleX can be transformed into circle Y by translations and a dilation, therefore the two circles are similar

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NARA [144]

Answer: (3x+5)(x+2)

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3 years ago

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The difference of three times a number and six is nine.

Dafna11 [192]

Answer:

The number is 3

Step-by-step explanation:

3 times 3 is 9

6 times 3 is 18

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4 years ago

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

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