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2 years ago

Perform the indicated operation & simplify. Express the answer as a complex number. ( 6 − 7 i ) ( − 8 + 3 i ) =___

Mathematics

1 answer:

slega [8]2 years ago

6 0

( 6 − 7 i ) ( − 8 + 3 i )

First FOIL:

( 6 − 7 i ) ( − 8 + 3 i ) = -48 + 18i + 56i -21i^2

Combine like terms

= -48 + 74i -21i^2

Convert i^2 = -1

= -48 + 74i -21(-1)

And simplify

= -48 + 74i + 21

= -27 + 74i

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A marine aquarium has a small tank and a large tank, each containing only red and blue fish. In each tank, the ratio of red fish

Anna007 [38]

Answer:

Ratio of blue fish in the small tank to the red fish in large tank is 10 : 6279

Step-by-step explanation:

Let the number of red fish and blue fish in the large tank are x and y respectively.

Similarly ratio of red fish and blue fish in the small tank are x' and y' respectively.

Since in each tank ratio of the red fish to blue fish is 333 : 444

That means x : y = 333 : 444

Or $\frac{x}{y}=\frac{333}{444}$

⇒ $\frac{x}{y}=\frac{3}{4}$

⇒ y = $\frac{4x}{3}$ --------(1)

Similarly x' : y' = 333 : 444

⇒ $\frac{x'}{y'}=\frac{333}{444}$

⇒ $\frac{x'}{y'}=\frac{3}{4}$

⇒ x' = $\frac{3y'}{4}$ ------(2)

Ratio of the fish in large tank to the fish in small tank is 464646 : 555

So (x + y) : (x' + y') = 464646 : 555

$\frac{x+y}{x'+y'}=\frac{464646}{555}$

Now we replace the values of x and y' from equation (1) and equation (2)

$\frac{(x+\frac{4x}{3})}{(\frac{3y'}{4}+y')}=\frac{464646}{555}$

$\frac{\frac{7x}{3}}{\frac{7y'}{4}}=\frac{464646}{555}$

$\frac{4}{3}\times \frac{x}{y'}=\frac{464646}{555}$

$\frac{x}{y'}=\frac{3}{4}\times \frac{464646}{555}$

$\frac{x}{y'}=\frac{232323}{370}$

$\frac{y'}{x}=\frac{370}{232323}$

$\frac{y'}{x}=\frac{10}{6279}$

Therefore, ratio of blue fish in the small tank to the red fish in large tank is 10 : 6279

4 0

3 years ago

A diameter is a chord. <br> True or false and why?

Lena [83]

Answer:

true.

A chord that passes through the center of a circle is called a diameter and is the longest chord.

Step-by-step explanation:

A diameter satisfies the definition of a chord, however, a chord is not necessarily a diameter. This is because every diameter passes through the center of a circle, but some chords do not pass through the center. Thus, it can be stated, every diameter is a chord, but not every chord is a diameter.

i hope this helps you. :)

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2 years ago

Joey, who is 8 years old, is a star player for his school's basketball team. His latest shot is shown on the graph, which repres

stira [4]

B) Joey released the ball at a height of 4 feet.

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2 years ago

Read 2 more answers

Let x = a bi and y = c di and z = f gi which statements are true? check all of the boxes that apply. x y = y x (x × y) × z = x ×

Alex73 [517]

A complex number is a part of a number system that includes a real unit and an imaginary unit. All the statements are true except C and E.

<h3>What is a Complex Number?</h3>

A complex number is a part of a number system that includes the real numbers as well as a particular element labelled i, sometimes known as the imaginary unit, and which obeys the equation i² = 1.

As it is given that x=(a+bi), y=(c+di), and z=(f+gi), therefore, we need to plug in the values to check which all are true.

A.) x+y=y+x

$x+y=y+x\\a+bi+c+di=c+di+a+bi$

As the two sides of the equation are equal, the equation is true.

B.) (x × y) × z = x × (y × z)

$(x \times y) \times z = x \times (y \times z)\\\\\ [ (a+bi) \times (c+di) ]\times (f+gi) = (a+bi) \times [(c+di) \times (f+gi)]\\\\(ac+adi+bci-bd) \times (f+gi)= (a+bi) \times (cf+cgi+fdi-dg)$

$(ac+adi+bci-bd) \times (f+gi)= (a+bi) \times (cf+cgi+fdi-dg)\\\\\\acf+adfi+bcfi-bdf+acgi-adg-bcg-bdgi = acf+acgi+afdi-adg + bcfi-bcg-bfd-bdgi$

As the two sides of the equation are equal, the equation is true.

C.) x−y=y−x

$x-y=y-x\\\\(a+bi)-(c+di)=(c+di)-(a+bi)\\\\a+bi-c-di=c+di-a-bi$

As the two sides of the equation are not equal, the equation is not true.

D.) (x+y)+z=x+(y+z)

$(x+y)+z=x+(y+z)\\\\(a+bi+c+di)+f+gi = a+bi+(c+di+f+gi)\\\\a+bi+c+di+f+gi = a+bi+c+di+f+gi$

As the two sides of the equation are equal, the equation is true.

E.) (x−y)−z=x−(y−z)

$(x-y)-z=x-(y-z)\\\\(a+bi-c-di)-f-gi = a+bi-(c+di-f-gi)\\\\a+bi-c-di-f-gi =a+bi-c-di+f+gi)$

As the two sides of the equation are not equal, the equation is not true.

Hence, all the statements are true except C and E.

Learn more about Complex Number:

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1 year ago

Which of the following scale factors would produce a larger image?

wariber [46]

Answer:

D. 3/2 because when it comes to showing a larger image as the question asks you need to find the biggest fraction/number and 1/2 is 0.5 B is 0.66 C is obviously 1 and D. is 1.5

Step-by-step explanation:

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2 years ago