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timama [110]
3 years ago
7

What are the roots of the equation 16x2 + 40x + 27 = 0 in simplest a + bi form?

Mathematics
1 answer:
bezimeni [28]3 years ago
7 0

9514 1404 393

Answer:

  -5/4 +i(√2)/4 and -5/4 -i(√2)/4

Step-by-step explanation:

I find simplest form to be easier to get to if the leading coefficient is 1. Dividing by 16, we have ...

  x^2 +5/2x +27/16 = 0

Completing the square by adding and subtracting the square of half the x-coefficient, we get ...

  (x^2 +5/2x +25/16) +27/16 -25/16 = 0

  (x +5/4)^2 = 2/16

Subtracting 2/16, taking the square root, and subtracting 5/4 gives ...

  x +5/4 = ±√(-2/16)

  x = -5/4 ±i(√2)/4

The roots are -5/4 +i(√2)/4 and -5/4 -i(√2)/4.

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If mBC= 24 ft, mAC = 2x+1, and the mBA=7x-4, what is the value of x?
Andreas93 [3]

Answer:

x = 3

Step-by-step explanation:

BC = 24

AC = 2x + 1

BA = 7x - 4

Required

Find x

The given parameters shows that A is a point on BC;

So:

BC = BA + AC

Substitute values for BC, BA, AC

24 = 7x - 4 + 2x + 1

Collect Like Terms

24 + 4 - 1 = 7x + 2x

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Solve for x

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2 years ago
The probability that an individual is left-handed is 0.12. in a class of 39 students, what is the probability of finding five le
Snezhnost [94]

We are given:

p = probability = 0.12<span>
n = total students = 39 </span>

x = left handers = 5<span>
u = mean = p* n = 4.68 
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Calculating for the z score:

z = (x – u) / σ<span>
z = (5 – 4.68) / 2.03</span>

<span>z = 0.1576 = 0.16

</span>

Using the standard tables for z, the p value is:

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Hence there is a 56.36% chance.

<span> </span>

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