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postnew [5]
3 years ago
12

Multiply the expression and simplify: (x -2) (x^2 + 3x -5) *Show all work*

Mathematics
1 answer:
Gwar [14]3 years ago
4 0

(x-2)(x^2+3x-5)\qquad\text{use distributive property}\\\\=(x)(x^2)+(x)(3x)+(x)(-5)+(-2)(x^2)+(-2)(3x)+(-2)(-5)\\\\=x^3+3x^2-5x-2x^2-6x+10\qquad\text{combine like terms}\\\\=x^3+(3x^2-2x^2)+(-5x-6x)+10\\\\=\boxed{x^3+x^2-11x+10}

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The diameter of a circle is 9 ft. Find its area to the nearest tenth.
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Step-by-step explanation:

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What is the estimate value of 976 divided by 0.188
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3 years ago
Write the complex number in polar form:
emmasim [6.3K]

9514 1404 393

Answer:

  2√30 ∠-120°

Step-by-step explanation:

The modulus is ...

  √((-√30)² +(-3√10)²) = √(30 +90) = √120 = 2√30

The argument is ...

  arctan(-3√10/-√30) = arctan(√3) = -120° . . . . a 3rd-quadrant angle

The polar form of the number can be written as ...

  (2√30)∠-120°

_____

<em>Additional comments</em>

Any of a number of other formats can be used, including ...

  (2√30)cis(-120°)

  (2√30; -120°)

  (2√30; -2π/3)

  2√30·e^(i4π/3)

Of course, the angle -120° (-2π/3 radians) is the same as 240° (4π/3 radians).

__

At least one app I use differentiates between (x, y) and (r; θ) by the use of a semicolon to separate the modulus and argument of polar form coordinates. I find that useful, as a pair of numbers (10.95, 4.19) by itself does not convey the fact that it represents polar coordinates. As you may have guessed, my personal preference is for the notation 10.95∠4.19. (The lack of a ° symbol indicates the angle is in radians.)

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3 years ago
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