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2 years ago

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

Mathematics

1 answer:

bezimeni [28]2 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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Evaluate 2(x - 4) + 3x - x2 for x = 2. O A. -6 O B. -2 O C. 6 O D. 2

Olenka [21]

Answer:

B. -2

Step-by-step explanation:

2(x - 4) + 3x - x2

2(2 - 4) + 3(2) - (2)2

2(-2) + 6 - 4

-4 + 6 - 4

-8 + 6

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8 0

3 years ago

School a rented 1 van and 3 buses with 89 students. School b rented 4vans and 3 buses with. 131 students. Each van and each bus

iogann1982 [59]

Answer:18

Step-by-step explanation:

3 0

2 years ago

I need help checking these

insens350 [35]

Answer:

180cm^2 & 472ft^2

Step-by-step explanation:

answer of 16 number

h2=p2+b2 ,therefore

h=100+80

h=180

answer of question 17

h2=p2+b2

576=p2+104

576-104=p2

472=p2

6 0

3 years ago

2 Which of the following polynomials is not written in standard form?

Varvara68 [4.7K]

Answer:

Step-by-step explanation:

Standard form is written in the order of the exponent on a variable from highest to lowest.

#1 exponents go 2, 1 , then zero. So, this is standard form.

#2 exponents go 2 then zero, so this is standard form.

#3 exponents go 1 then 2 then zero, so this is not in standard form.

#4 exponents go 3 to 2 to 1, so this is still in standard form.

hope this helps!

8 0

2 years ago

Half of a set of the parts are manufactured by machine A and half by machine B. Ten percent of all the parts are defective. Six

baherus [9]

Answer:

The probability that a part was manufactured on machine A is 0.3

Step-by-step explanation:

Consider the provided information.

It is given that Half of a set of parts are manufactured by machine A and half by machine B.

P(A)=0.5

Let d represents the probability that part is defective.

Ten percent of all the parts are defective.

P(d) = 0.10

Six percent of the parts manufactured on machine A are defective.

P(d|A)=0.06

Now we need to find the probability that a part was manufactured on machine A, and given that the part is defective :

$P(A|d) =\frac{P(A \cap d)}{P(d)}$

$P(A|d) =\frac{P(d|A)\times P(A)}{P(d)}\\P(A|d)= \frac{0.06\times 0.5}{0.10}$

$P(A|d)= 0.3$

Hence, the probability that a part was manufactured on machine A is 0.3

8 0

2 years ago