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2 years ago

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rosijanka [135]2 years ago

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

Mars2501 [29]

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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2 years ago

How many different symbols can be represented by In Morse code, symbols are represented by variable-length sequences of dots and

larisa86 [58]

Answer:

126 different symbols can be represented in Morse code

Step-by-step explanation:

We need to sum up the number of sequences using one single place, two places, three places, four places and so on until sequences of six places (dots and dashes).

For each case we use the fundamental counting principle.

For one single place we may have 2 possible sequences (a dash or a dot)

For two places (example: .. or ._) we may have 2*2 sequences, since each place may be filled with either dash or dot (2 possible ways) and then we multiply the ways each place can be filled, thus $2^2$

Similarly, for three places we may have 2*2*2 sequences, thus $2^3$

For four places we may have 2*2*2*2 sequences, thus $2^4$

And so on.

So, notice the total up to arrangements of six symbols, is:

$2+2^2+2^3+2^4+2^5+2^6=126$

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2 years ago

Which of the following are steps in the process in solving application problems using the two-order system?

SCORPION-xisa [38]

<span>Assign two variables for the unknowns.
Write two equations using the assigned variables.
Solve the pair of equations.</span>

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2 years ago

How many counting numbers are less than 3 units from the number 4

HACTEHA [7]

I'm guessing that by "counting numbers" you're refering to "integers."

Why not actually write out the numbers that qualify, and then count them?

{2, 3, 5, 6} is a set of four numbers, all of which are fewer than 3 units away from the (central) number 4. Some people would include 4 itself in this set.

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2 years ago

Solve y= -2^(-x-3)= -4

Nat2105 [25]

Y= -4

Hope that help

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2 years ago