What is the sum of the complex numbers 3 − 4i and 5 + 3i ?

Answer:

21

Step-by-step explanation:

this requires practical assumption.

take 9 for example

5 more than 9 means 9 - 5 = 4

4 is a square number

21 = 21 - 5 = 16

16 is a square number

34 = 34 - 5 = 29

29 is not a square number

35 = 35 - 5 = 30

30 is not a square number

65 = 65 - 5 = 60

60 is not a square number

76 = 76 - 5 = 71

71 is not a square number

Answer:

(1) TRUE.

(2) FALSE.

(3) FALSE.

(4) TRUE.

(5) FALSE.

Step-by-step explanation:

(1) [tex]\sqrt{32} = 2^{\frac{5}{2} }[/tex]

[tex]2^{\frac{5}{2} } = (\sqrt{2} )^5 = (\sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2}) = 4\sqrt{2}\\\\\sqrt{32} = \sqrt{16 \ \times \ 2}\ = \ \sqrt{16} \ \times \ \sqrt{2} \ = \ 4\sqrt{2}[/tex]

Thus, the equation is TRUE.

(2) [tex]16^{\frac{3}{8} } = 8^2[/tex]

[tex]16^{\frac{3}{8} } =(2^4)^{\frac{3}{8} } = 2^\frac{3}{2} }= (\sqrt{2} )^3 = (\sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2}) = 2\sqrt{2} \\\\8^2 = 64[/tex]

Thus, the equation is FALSE.

(3) [tex]4^{\frac{1}{2} } = \sqrt[4]{64}[/tex]

[tex]4^{\frac{1}{2} }= \sqrt{4} = 2\\\\\sqrt[4]{64} = (64)^{\frac{1}{4} } = (2^6)^{\frac{1}{4} }= 2^{\frac{6}{4} } = 2^{\frac{3}{2} }=(\sqrt{2} )^3 = (\sqrt{2} \times \sqrt{2} \times \sqrt{2} ) = 2\sqrt{2}[/tex]

Thus, the equation is FALSE.

(4) [tex]2^8 = (\sqrt[3]{16} )^6[/tex]

[tex]2^8 = 256\\\\ (\sqrt[3]{16} )^6 = (16)^{\frac{6}{3} } = (2^4)^{\frac{6}{3} } = (2)^{\frac{24}{3} } = 2^8 = 256[/tex]

Thus, the equation is TRUE.

(5) [tex](\sqrt{64} )^{\frac{1}{3} } = 8^{\frac{1}{6} }\\\\[/tex]

[tex]8^{\frac{1}{6} } = (2^3)^{\frac{1}{6} } = 2^{\frac{3}{6} } = 2^{\frac{1}{2} } = \sqrt{2} \\\\(\sqrt{64} )^{\frac{1}{3} } = (2^6)^{\frac{1}{3} } = 2^{\frac{6}{3} } = 2^2 = 4[/tex]

Thus, the equation is FALSE.

Answer:

a) 15160 gallons

b) 3032 gallons

Step-by-step explanation:

Given that for every penny increase in the price of gasoline there is a decrease of 1516 gallons sold per week

a) when she raises the price by 10 cents per gallon

There will be a decrease of ( 1516 * 10 ) gallons sold per week i.e. = 15160 gallons

b) when she decrease the price by 2 cents per gallon

There will be an increase ( 2 * 1516 ) gallons sold per week  i.e. = 3032 gallons

Answer:

40 Feet

Step-by-step explanation:

1 inch = 10 feet

4 inch = 4 * (10 feet)

4 inch = 40 feet

Answer:

18 mph so B is correct 16+2= 18

Answer:

B

Step-by-step explanation:

Answer:

Lily is correct.

Step-by-step explanation:

Lily is correct.  There is no such thing as AAA congruence.  James has proved that the three angles are the same, but the triangles could still be of different sizes.

Answer:

The first answer, 3 times the square root of x squared is correct.

Answer:

70

Step-by-step explanation:

200 - 130

Answer:

280

Step-by-step explanation:

subtract

Answer:300

Step-by-step explanation:

Answer

92%

Explanation

23 out of 25 people voted Abdul.

So that means [tex]\frac{23}{25}[/tex] people voted Abdul.

When you divide 23 by 25 you get 0.92 which is 92% (multiply by 100).

You divide because a fraction means the numerator divided by the denominator.

Answer:

it is b

Step-by-step explanation:

Answer:

15/50×100=30%

Step-by-step explanation:

Answer:

35

~

Just simplify the expression and you'll get:  

35

~

You might be wondering why isn't the answer 0, since anything multiplied by 0 is 0.

~

It's because to answer this question, you will need to use PEMDAS.

P, Parenthesis.

E, Exponents.

M, Multiply.

D, Divide.

A, Addition.

S, Subtraction.

~

Since we don't have parenthesis, exponents, a division sign, or subtraction sign.

All we need to do is Mutiply, and Add.

~

First we multiply, because of the PEMDAS order.

7 * 0 = 0

~

Then, since we used one of the 7's to multiply. (The one next to the 0)

We add the rest of them, not including the last seven.

There are six, sevens.

But we already used one.

So we will add only the other five.

7 + 7 + 7 + 7 + 7 = 35.

7 * 5 = 35

~

And that's it.

You got your answer, 35.

Answer:

33.8

Step-by-step explanation:

33.8 is the closest to half of 65.

9514 1404 393

Answer:

  125

Step-by-step explanation:

The proportion you want is ...

  [tex]\dfrac{\text{part}}{\text{whole}}=\dfrac{65}{\text{?}}=\dfrac{52}{100}\\\\6500=52\cdot\text{?}\qquad\text{cross multiply}\\\\\dfrac{6500}{52}=125=\text{?}\qquad\text{divide by 52}[/tex]

52% of 125 is 65.

__

Comment on the formulation

You can write the same proportion 4 ways. I find it convenient to choose one that has the unknown in the numerator. Here, that means you would write it ...

  whole/part = 100/52 = ?/65

Then the solution is one step: multiply by 65.

Answer:

y-4= 1/2(x+2)

Step-by-step explanation:

Answer:

His weekly allowance is $5.50.

Step-by-step explanation:

12.03 - 6.53 = $5.50

I'm not 100% sure this is accurate. Good Luck!

Answer:

8

Step-by-step explanation:

from A to B it's 8 units long

Answer:

Y=6

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Answer:

y=−2/5x+4/5y

Step-by-step explanation:

Hope's this helps

Answer:

First box is the one all the way on the right

Second box Is the second one from the left

Third box Is the first one on the left

Last box is the 3rd one from the left

Step-by-step explanation:

Answer:

Not enough data

Step-by-step explanation:

Answer:

$2857.60 because when yu multiply the loan times the % yu get 1428.80 because it’s the end of 1 year and the question is asking for the end of 2 years so yu have to double it.

Step-by-step explanation:

Answer:

0.156

Step-by-step explanation:

Answer:

5/32

Step-by-step explanation:

[tex] \frac{5}{8} \div 4 \\ \\ = \frac{5}{8} \times \frac{1}{4} \\ \\ = \frac{5 \times 1}{8 \times 4} \\ \\ = \frac{5}{32} [/tex]

Step-by-step explanation:

davis is right.