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Varvara68 [4.7K]
3 years ago
10

Solve the equation for all real solutions in simplest form. z^2 - 12z +9= -3

Mathematics
1 answer:
Mars2501 [29]3 years ago
3 0

Answer:

Solving the equation for all real solutions in simplest form.

z^2 - 12z +9= -3 we get \mathbf{z=10.9\: or\: z=1.1}

Step-by-step explanation:

We need to solve the equation for all real solutions in simplest form.

z^2 - 12z +9= -3

First simplifying the equation:

z^2 - 12z +9+3= -3+3\\z^2 - 12z +12= 0

Now, we can solve the equation using quadratic formula:

z=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

we have a = 1, b=-12 and c=12

Putting values in formula and finding values of x

z=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\z=\frac{-(-12)\pm\sqrt{(-12)^2-4(1)(12)}}{2(1)}\\z=\frac{12\pm\sqrt{144-48}}{2}\\z=\frac{12\pm\sqrt{96}}{2}\\z=\frac{12\pm9.8}{2}\\z=\frac{12+9.8}{2}\:or\:z=\frac{12-9.8}{2}\\z=10.9\:or\:z=1.1

So, we get value of z: z=10.9 or z=1.1

Solving the equation for all real solutions in simplest form.

z^2 - 12z +9= -3 we get \mathbf{z=10.9\: or\: z=1.1}

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Answer:

B

Step-by-step explanation:

The compound interest formula is A = P (1+r/n)^nt where:

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  • t is the number of years

Substitute a value into each variable to solve.

  • P = $147 since 10% of 1,470 is being invested which makes P = 0.10(1470) = 147.
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  • n = 12 because it is compounded monthly meaning 12 times a year.
  • t = 25 since it will earn for 25 years.

A = P (1+r/n)^{nt}\\A = 147(1 + \frac{0.035}{12})^{12*25}\\A = 147 ( 1 + 0.002916)^{300}\\A = 147(1.002916)^{300}\\A = 352.19

Repeat this process for each formula.

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3 years ago
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A teacher is four time as old as a student .in 20 years, the student 's age will be half of the teacher 's age. How old are they
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Let the present age of student be x
Present of teacher will be 4x

After 20 years,
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According to the given condition after 20 years,
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