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Fed [463]
3 years ago
11

If z = (5 + 12i) ÷ (3 + 4i), then |z| = _____. 5/13 1(2/3) 2(3/5) 3

Mathematics
2 answers:
Maurinko [17]3 years ago
6 0

Answer:

i have the answer

Step-by-step explanation:

the correct answer is 2 and three fifths. good luck

Marta_Voda [28]3 years ago
3 0
\dfrac{5+12i}{3+4i}=\dfrac{5+12i}{3+4i}\cdot\dfrac{3-4i}{3-4i}=\dfrac{15-20i+36i-49i^2}{3^2-(4i)^2}\\\\=\dfrac{15+16i+49}{9-16i^2}=\dfrac{64+16i}{9+16}=\dfrac{64+16i}{25}=2.56+0.64i


z=a+bi\\\\|z|=\sqrt{a^2+b^2}\\\\z=2.56+0.64i\to a=2.56;\ b=0.64\\\\|z|=\sqrt{2.56^2+0.64^2}=\sqrt{6.9632}=\sqrt{\dfrac{69632}{10000}}=\sqrt{\dfrac{4096\cdot17}{100}}\\\\=\dfrac{64\sqrt{17}}{100}=0.64\sqrt{17}\approx2.6=2\dfrac{3}{5}
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Justin and his children went into a grocery store and he bought $18 worth of bananas and mangos. Each banana costs $0.60 and eac
Igoryamba

Answer:

x=10 and y= 8.

Step-by-step explanation:

Given that the cost of 1 banana = $0.60

Cost of 1 mango = $1.50.

Total cost= $ 18  

Here, x be the number of bananas and y be the numbers of mangos,

As the number of bananas is 2 more than the number of mangos,

So, x=y+2

\Rightarrow y=x-2 \cdots(i)

Cost of x bananas =\$ 0.60 \times x

Cost of y mangos =\$ 1.50 \times y

Total cost = 0.6x+1.5y

\Rightarrow 18 = 0.6x+1.5y\\\\\Rightarrow 1.5y=18-0.6x\\\\\Rightarrow y= 12 - 0.4 x \cdots(ii).

Solving both the equations (i) as well as (ii), graphically as shown in the figure by plotting both the graphs.

Both the graphs intersect at the point (10,8) as shown in the graph.

So, the solution of both the equations is, (x,y)=(10,8). i.e

The number of bananas = x= 10 and

the number of mangos = y = 8.

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3 years ago
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Step-by-step explanation:

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