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navik [9.2K]
3 years ago
10

What is the solution to the system of equations?

Mathematics
1 answer:
Llana [10]3 years ago
3 0

Solution in attachment.

<h3>x = -6, y = 9, z = -3</h3>

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Rationalize the denominator of sqrt -49 over (7 - 2i) - (4 + 9i)
zubka84 [21]
\sqrt{ \frac{-49}{(7-2i)-(4+9i) } } &#10;

This one is quite the deal, but we can begin by distributing the negative on the denominator and getting rid of the parenthesis:

\frac{ \sqrt{-49}}{7-2i-4-9i}

See how the denominator now is more a simplification of like terms, with this I mean that you operate the numbers with an "i" together and the ones that do not have an "i" together as well. Namely, the 7 and the -4, the -2i with the -9i.
Therefore having the result: 

\frac{ \sqrt{-49} }{3-11i}

Now, the \sqrt{-49} must be respresented as an imaginary number, and using the multiplication of radicals, we can simplify it to \sqrt{49}  \sqrt{-1}
This means that we get the result 7i for the numerator.

\frac{7i}{3-11i}

In order to rationalize this fraction even further, we have to remember an identity from the previous algebra classes, namely: x^2 - y^2 =(x+y)(x-y)
The difference of squares allows us to remove the imaginary part of this fraction, leaving us with a real number, hopefully, on the denominator.

\frac{7i (3+11i)}{(3-11i)(3+11i)}

See, all I did there was multiply both numerator and denominator with (3+11i) so I could complete the difference of squares.
See how (3-11i)(3+11i)= 3^2 -(11i)^2 therefore, we can finally write:

\frac{7i(3+11i)}{3^2 - (11i)^2 }

I'll let you take it from here, all you have to do is simplify it further.
The simplification is quite straightforward, the numerator distributed the 7i. Namely the product 7i(3+11i) = 21i+77i^2.
You should know from your classes that i^2 = -1, thefore the numerator simplifies to -77+21i
You can do it as a curious thing, but simplifying yields the result:
\frac{-77+21i}{130}
7 0
3 years ago
Pick the correct answer :)
amm1812
= 3a^2b(cuberoot(b^2)) - 3a^2b^3(square root(3a))

answer is the first choice

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Lyrx [107]

Answer:

1 or 100%.

Step-by-step explanation:

The probability of rolling less than 7 is equal to the probability of rolling 1 or 2 or 3 or 4 or 5 or 6. That is 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 6/6. So any number from the dice can come up when you roll it because a perfect dice has 6 sides.

6 0
2 years ago
Write and solve the equation for the following situation:
tamaranim1 [39]

Answer:

B.) x + (x + 16) = 90

2x+16=90

2x=90-16

x=74/2

x=37

8 0
3 years ago
Read 2 more answers
Eight toy makers each carved 25 blocks and 15 cars how many toys did they crave in all
Stella [2.4K]

Answer:

320

Step-by-step explanation:

25 + 15 = 40 toys each

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8 x 40 = 320 totals carved in all

6 0
3 years ago
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