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3 years ago

Simplify this expression below as much as possible. (7+4i)+(9+5i)-(2+5i)

Mathematics

2 answers:

gtnhenbr [62]3 years ago

7 0

Answer:

7+4i+9+5i-2-5i

7+4i+9-2

4i+7+9-2

4i+14

anzhelika [568]3 years ago

4 0

Answer: 14 + 4i

Step-by-step explanation:

(7 + 4i) + (9 + 5i) - (2 + 5i)

Group the real part and the imaginary part of the complex number

(a + bi) ± (c + di) = (a ± c) + (b ± d)i

(7 + 9 - 2) + (4 + 5 - 5)i

7+9-2=14 and 4+5-5=4

Therefore, (7+4i)+(9+5i)-(2+5i) is equal to 14 + 4i

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How much pure acid should be mixed with 6 gallons of a 20% acid solution in order to get a 90% acid solution?

beks73 [17]

So, how much acid is there in 6 gallons? well is 20% acid or (20/100), so the amount of acid in it just (20/100) * 6 or 1.2, the rest is say water.

now, if we want a 90% solution, and say we add "y" gallons, how much acid is in it? well (90/100) * y, or 0.9y.

now let's add "x" gallons of pure acid, now, pure acid is just pure acid, so is 100% acid, how much acid is there in it? (100/100) * x, or 1x or just x.

we know whatever "x" and "y" amounts are, they -> x + 6 = y

and we also know that x + 1.2 = 0.9y

$\bf \begin{array}{lccclll}
&\stackrel{gallons}{acid}&\stackrel{acid~\%}{quantity}&\stackrel{acid~gallons}{quantity}\\
&------&------&------\\
\textit{pure acid}&x&1.00&x\\
\textit{20\% sol'n}&6&0.20&1.2\\
------&------&------&------\\\
mixture&y&0.90&0.9y
\end{array}
\\\\\\
\begin{cases}
x+6=\boxed{y}\\
x+1.2=0.9y\\
----------\\
x+1.2=0.9\left( \boxed{x+6} \right)
\end{cases}
\\\\\\
x+1.2=0.9x+5.4\implies x-0.9x=5.4-1.2\implies 0.1x=4.2
\\\\\\
x=\cfrac{4.2}{0.1}\implies x=\stackrel{gallons}{42}$

3 0

3 years ago

Type an integer or decimal 0.16(y-5)+0.12y=0.20y-0.9

Over [174]

Answer:

16y

Step-by-step explanation:

4 0

3 years ago

Flying against the wind, an airplane travels 7520 kilometers in 8 hours. Flying with the wind, the same plane travels 6500 kilom

bezimeni [28]

Answer:

Rate of plane in still air = 1120 km/h

Rate of wind = 180 km/h

Step-by-step explanation:

Let the rate (speed) of the plane in still air = u km/h

Let the rate (speed) of the wind = v km/h

Formula for speed is:

$Speed = \dfrac{Distance}{Time}$

Given that against the wind, airplane travels 7520 km in 8 hours.

The speed against the wind will be slower so,

Against the wind, speed = (u -v ) km/h

Using above formula:

$(u-v) = \dfrac{7520}{8} km/h\\(u-v) = 940 km/h ..... (1)$

Given that with the wind, airplane travels 6500 km in 5 hours.

The speed with the wind will be faster so,

With the wind, speed = (u +v ) km/h

Using above formula:

$(u+v) = \dfrac{6520}{5} km/h\\(u+v) = 1300 km/h ..... (2)$

Adding (1) and (2) to solve for u and v:

$2u = 2240\\\Rightarrow u = 1120\ km/h$

Putting u in (1):

$1120-u=940\\\Rightarrow u = 180\ km/h$

So, the answers are:

Rate of plane in still air = 1120 km/h

Rate of wind = 180 km/h

6 0

3 years ago

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the

GaryK [48]

Answer:

So profit is denoted by Y
Selling price is denoted by X

Hencd we have Y= X + B

Where Be can be a constant for example how much he already sold or etc.

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3 0

3 years ago

Is -4 1/5 less than. greater than or equal to -4 9/10

Natalija [7]

-4 1/5 is greater than -4 9/10

8 0

4 years ago