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2 years ago

Find the real numbers x and y that make the equation true. (2 points) -3 + yi = x + 6i

Mathematics

1 answer:

stealth61 [152]2 years ago

7 0

Answer:

x = - 3, y = 6

Step-by-step explanation:

For the 2 sides to be equal then the coefficients of the imaginary terms and the real terms must be equal.

Given

- 3 + yi = x + 6i , then

x = - 3 and y = 6

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What is the simplified form of 12x/900x²y4z6?

zalisa [80]

Answer:

$360xy^2|xz^3|$

Step-by-step explanation:

Given expression:

$12x \sqrt{900x^2y^4z^6}$

$\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:$

$\implies 12x \sqrt{900}\sqrt{x^2}\sqrt{y^4}\sqrt{z^6}$

Replace 900 with 30² :

$\implies 12x \sqrt{30^2}\sqrt{x^2}\sqrt{y^4}\sqrt{z^6}$

$\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:$

$\implies 12x \cdot 30|x|\sqrt{y^4}\sqrt{z^6}$

$\implies 360x|x|\sqrt{y^4}\sqrt{z^6}$

(We need to use the absolute value of √x² since the x term was originally to the power of 2, which means the value of x² is always positive since the exponent is even).

$\textsf{Apply exponent rule} \quad \sqrt{a^m}=a^{\frac{m}{2}}:$

$\implies 360x|x|\cdot y^{\frac{4}{2}}\cdot z^{\frac{6}{2}}$

Simplify:

$\implies 360xy^2|xz^3|$

(We need to use the absolute value of z³ since the z term was original to the power of 6, which means the value of z⁶ is always positive since the exponent is even).

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1 year ago

What is the inverse of x=4-4y+y^2

Zarrin [17]

To find invers
1. solve for y
2. replace y with xinverse

so

x=4-4y+y^2
reorder right side
x=y^2-4y+4
factor right side
x=(y-2)^2
squaer root both sides
+/-√x=y-2
add 2 to both sides
2+/-√x=y
switch x and y
2+/-√y=xinverse

xinverse=2+√y or 2-√y
subtract 4 from both sides

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3 years ago

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Anna11 [10]

Answer:

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Equation Form:

x=7/15,y=−13/5

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

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2 years ago

Center c of the circle above has coordinates of (4, 3). what is the circumference of the circle?

Angelina_Jolie [31]

Well if it is touching the x-axis, the radius is 3 units.
C = 2 * pi * r = (2)(3.14)(3) = 18.8 or so

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