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4 years ago

Which expression is equivalent to (4+3i)^2+(6-I)^2

Mathematics

1 answer:

zhenek [66]4 years ago

8 0

Answer:

$\large\boxed{(4+3i)^2+(6-i)^2=42+12i}$

Step-by-step explanation:

$(4+3i)^2+(6-i)^2\qquad\text{use}\ (a\pm b)^2=a^2\pm2ab+b^2\\\\=4^2+2(4)(3i)+(3i)^2+6^2-2(6)(i)+i^2\\\\=16+24i+9i^2+36-12i+i^2\qquad i=\sqrt{-1}\to i^2=-1\\\\=16+24i+9(-1)+36-12i+(-1)\\\\=16+24i-9+36-12i-1\qquad\text{combine like terms}\\\\=(16-9+36-1)+(24i-12i)\\\\=42+12i$

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NEED HELP NOW I have 31 stamps total. I have 4 more 1-cent stamps than 8-cent stamps and twice as many one cent stamps as 12 cen

krek1111 [17]

x = number of 1-cent stamps

y = number of 8-cent stamps

z = number of 12-cent stamps

We have 31 stamps all together, so x+y+z = 31.

"I have 4 more 1-cent stamps than 8-cent stamps" means we have the equation x = y+8. Whatever y is, add 8 to it to get x. Solve for y to get y = x-8.

You also have "twice as many one cent stamps as 12 cent stamps", so x = 2z. Solving for z gets you z = 0.5x

-------------

x+y+z = 31

x+x-8+z = 31 ... y replaced with x-8

x+x-8+0.5x = 31 ... plug in z = 0.5x

2.5x-8 = 31

2.5x = 31+8

2.5x = 39

x = 39/2.5

x = 15.6

Your teacher made a typo somewhere because we should get a positive whole number result for x (since x is a count of how many 1-cent stamps we have).

8 0

4 years ago

28. The edges of a cube are all increased by

Zolol [24]

Answer:

Percentage increase in volume will be

33.1

Step-by-step explanation:

Let the each edge of cube be

100

units.

Then its volume is

100

1000000

cubic units.

If each edge increases by

it becomes

110

units

and volume becomes

110

1331000

cubic units

Therefore increase in volume is

1331000

−

1000000

331000

cubic units

and percentage increase in volume is

331000

1000000

100

331

33.1

7 0

3 years ago

6. Parker, Inc. used Excel to run a least-squares regression analysis, which resulted in the following output: Regression Statis

aleksley [76]

Answer:

"34,814" is the correct solution.

Step-by-step explanation:

The given values are:

Intercept coefficient,

$\beta_0 = 23,859$

Production coefficient,

$\beta_1 = 3.13$

Units sold,

x = 3,500

Now,

The total cost will be:

⇒ $\bar{y}=\beta_0+\beta_1 x$

On substituting the estimated values, we get

⇒ $=23,859+3.13\times 3,500$

⇒ $=23,859+10,955$

⇒ $=34,814$

4 0

3 years ago

Determine the zeroes of the polynomial

Anna71 [15]

Answer:

3,7/6

Step-by-step explanation:

$(\sqrt{x^2-4x+3} )+(\sqrt{x^{2} -9} )-(\sqrt{4x^2-14x+6} )\\=(\sqrt{x^2-x-3x+3} )+(\sqrt{(x^2-3^2})-(\sqrt{4x^2-2x-12x+6})\\ =(\sqrt{x(x-1)-3(x-1)} )+\sqrt{(x+3)(x-3)}-\sqrt{2x(2x-1)-6(2x-1)} \\=\sqrt{(x-1)(x-3)}+\sqrt{(x+3)(x-3)} -\sqrt{2(2x-1)(x-3)} \\=\sqrt{x-3} (\sqrt{x-1} +\sqrt{x+3} -\sqrt{2(2x-1)} )\\$

$\sqrt{x-3} =0~gives~x=3\\or~\sqrt{x-1} +\sqrt{x+3} -\sqrt{2(2x-1)} =0\\or~ \sqrt{x-1} +\sqrt{x+3} =\sqrt{2(2x-1)} \\squaring\\x-1+x+3+2\sqrt{x-1} \sqrt{x+3} =2(2x-1)\\2x+2+2\sqrt{(x-1)(x+3)} =4x-2\\2\sqrt{x^2-x+3x-3} =2x-4\\\sqrt{x^2+2x-3} =x-2\\again ~squaring\\x^2+2x-3=x^2-4x+4\\\\2x+4x=4+3\\6x=7\\x=\frac{7}{6}$

8 0

3 years ago

John sales model boats from a booth at a local fair. He purchases each model boat from a distributor for five dollars and the lo

poizon [28]

Answer and explanation:

Profit from sale of model boats = Sales -costs(costs of goods purchases + expenses or charges by the local fair)

John's profit from the sale of model boats can be represented by the equation:

P= 50x-(5x+80)

Where P is profit from the sale of the model boats and x is number of model boats bought and sold. The 80 is constant as it is a fixed cost paid to the local fair.

For example if John buys and sells 20 model boats, he would make profit of:

Substitute x=20 in equation above

P= 50×20-(5×20+80)

P=1000-180

P=$820

It could be said that John is in a very profitable business and his profit is also dependent on volume of sales because the lower his sales the closer he gets to making a loss and not profit

7 0

3 years ago