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solniwko [45]
3 years ago
5

Factor completely and find the roots of the following. X^2+12x+27=0

Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
8 0

Answer:

x = - 9, x = - 3

Step-by-step explanation:

Given

x² + 12x + 27 = 0

To factorise the quadratic

Consider the factors of the constant term (+ 27) which sum to give the coefficient of the x- term (+ 12)

The factors are + 9 and + 3, since

9 × 3 = 27 and 9 + 3 = 12, hence

(x + 9)(x + 3) = 0

Equate each factor to zero and solve for x

x + 9 = 0 ⇒ x = - 9

x + 3 = 0 ⇒ x = - 3

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First, subtract 2/3 from both sides and you get \frac{5}{6} k =  \frac{2}{3}
Then multiply both sides by 6/5 and you get k =  \frac{4}{5}
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X = 5y/(z-4y) <br><br> make y subject
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Which function represents g(x), a reflection of f(x) = 6(one-third) Superscript x across the y-axis?
Rasek [7]

The function g(x)=6(3)^{x} represents a reflection of f(x)=6(\frac{1}{3})^{x} across the y-axis ⇒ 3rd answer

Step-by-step explanation:

Let us revise the reflection across the axes

  • If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)
  • If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)

∵ f(x)=6(\frac{1}{3})^{x}

∵ g(x) is the image of f(x) after reflection across the y-axis

- From the rule above reflection across the y-axis changes the sign of x

∴ g(x)=6(\frac{1}{3})^{-x}

∵ (a)^{-n}=(\frac{1}{a})^{n}

∵ (\frac{1}{a})^{-n}=(a)^{n}

∴ (\frac{1}{3})^{-x}=(3)^{x}

∴ g(x)=6(3)^{x}

The function g(x)=6(3)^{x} represents a reflection of f(x)=6(\frac{1}{3})^{x} across the y-axis

Learn more:

You can learn more about reflection in brainly.com/question/5017530

#LearnwithBrainly

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Step-by-step explanation:

16 arrangement can be done

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Step-by-step explanation:

Total number of students = 8

Number of student who has passed Exam P/1 = 1

Number of student who has passed Exam FM/2 = 1

No student has passed more than one exam.

According to question, exactly three students from a randomly chose group of four students have not passed Exam P/1 or Exam FM/2.

So, Probability will be

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Hence, there is probability of 0.57 chances that exactly three students from a group of four students have not passed Exam P/1 or Exam FM/2.

4 0
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