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alexandr402 [8]
3 years ago
7

Simplify. x^2-3x-18/x+3

Mathematics
1 answer:
andre [41]3 years ago
7 0

Answer:

1. Option C is correct

2. Option A is correct

3. Option C is correct

4. Option B is correct

5. Option D is correct

Step-by-step explanation:

1. x^2-3x-18/x+3

Factorize the numerator

x^2-6x+3x-18/x+3

x(x-6)+3(x-6)/x+3

(x+3)(x-6)/x+3

x-6

x-6 where x≠6

Option C is correct.

2. x-2/x^2+4x-12

Factorizing the denominator

x-2/x^2+6x-2x-12

x-2/x(x+6)-2(x+6)

x-2/(x-2)(x+6)

1/x+6

1/x+6 where x≠-6

Option A is correct.

3. 5x^3/7 x^3+x^4

5x^3/7x^3+x^4

5x^3/x^3(7+x)

5/7+x

Option C is correct

5/7+x where x≠-7

4. Simplify x/6x-x^2

x/6x-x^2

x/x(6-x)

1/6-x

Option B is correct

1/6-x where x≠6

5. 2/3a * 2/a^2

Multiplying both terms

4/3a^3

Option D is correct.

4/3a^3 where a≠0

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NEED HELP ASAP. 20 POINTS!!! The graph of a limacon curve is given. Determine which equation is correct for the graph.
posledela

Answer:

The equation r = 3 - cos Ф is correct for the graph ⇒ 3rd answer

Step-by-step explanation:

Equations of the form r = a + b sin Ф, r = a - b sin Ф, r = a + b cos Ф, and r = a - b cos Ф represent limacons

  • Equations r = a + b sin Ф, r = a - b sin Ф are symmetric to the vertical axis
  • Equations r = a + b cos Ф, r = a - b cos Ф are symmetric to the horizontal axis
  • The shape of the limacons depends on the values of a and b

∵ The figure is a circle

- That means a is greater than twice b

∴ a > 2b

∵ The circle is symmetric to the x axis

∵ The majority of the circle lies in quadrants two and three

- That means most of the graph at the negative part of x

∴ The form of the equation is r = a - b cos Ф

Lets look to the answer to find the right one

∵ a > 2b

∴ a = 3 and b = 1 because 3 > 2(1)

∴ The answer is r = 3 - cos Ф

The equation r = 3 - cos Ф is correct for the graph

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