Find the equation of the line passing through the points (2, 4) and (3, 2). y = [? ]x + [ ]

What are the types of roots of the equation below? - 81=0

Tju [1.3M]

Option B, that is Two Complex and Two Real which are x + 3, x - 3, x + 3i and x - 3i, are the types of roots of the equation x⁴ - 81 = 0. This can be obtained by finding root of the equation using algebraic identity.

<h3>What are the types of roots of the equation below?</h3>

Here in the question it is given that,

the equation x⁴ - 81 = 0

By using algebraic identity, (a + b)(a - b) = a² - b², we get,

⇒ x⁴ - 81 = 0

⇒ (x² + 9)(x² - 9) = 0

(x² - 9) = (x² - 3²) = (x - 3)(x + 3) [using algebraic identity, (a + b)(a - b) = a² - b²]
x² + 9 = 0 ⇒ x² = -9 ⇒ x = √-9 ⇒ x= √-1√9 ⇒x = ± 3i

⇒ (x² + 9) = (x - 3i)(x + 3i)

Now the equation becomes,

[(x - 3)(x + 3)][(x - 3i)(x + 3i)] = 0

Therefore x + 3, x - 3, x + 3i and x - 3i are the roots of the equation

To check whether the roots are correct multiply the roots with each other,

⇒ [(x - 3)(x + 3)][(x - 3i)(x + 3i)] = 0

⇒ [x² - 3x + 3x - 9][x² - 3xi + 3xi - 9i²] = 0

⇒ (x² +0x - 9)(x² +0xi - 9(- 1)) = 0

⇒ (x² - 9)(x² + 9) = 0

⇒ x⁴ - 9x² + 9x² - 81 = 0

⇒ x⁴ - 81 = 0

Hence Option B, that is Two Complex and Two Real which are x + 3, x - 3, x + 3i and x - 3i, are the types of roots of the equation x⁴ - 81 = 0.

Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: What are the types of roots of the equation below?

x⁴ - 81 = 0

A) Four Complex

B) Two Complex and Two Real

C) Four Real

Learn more about roots of equation here:

brainly.com/question/26926523

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5 0

1 year ago

Seventy percent of all vehicles examined at a certain emissions inspection station pass the inspection. Assuming that successive

LenaWriter [7]

Answer:

(a) The probability that all the next three vehicles inspected pass the inspection is 0.343.

(b) The probability that at least 1 of the next three vehicles inspected fail is 0.657.

(c) The probability that exactly 1 of the next three vehicles passes is 0.189.

(d) The probability that at most 1 of the next three vehicles passes is 0.216.

(e) The probability that all 3 vehicle passes given that at least 1 vehicle passes is 0.3525.

Step-by-step explanation:

Let X = number of vehicles that pass the inspection.

The probability of the random variable X is P (X) = 0.70.

(a)

Compute the probability that all the next three vehicles inspected pass the inspection as follows:

P (All 3 vehicles pass) = [P (X)]³

$=(0.70)^{3}\\=0.343$

Thus, the probability that all the next three vehicles inspected pass the inspection is 0.343.

(b)

Compute the probability that at least 1 of the next three vehicles inspected fail as follows:

P (At least 1 of 3 fails) = 1 - P (All 3 vehicles pass)

$=1-0.343\\=0.657$

Thus, the probability that at least 1 of the next three vehicles inspected fail is 0.657.

(c)

Compute the probability that exactly 1 of the next three vehicles passes as follows:

P (Exactly one) = P (1st vehicle or 2nd vehicle or 3 vehicle)

= P (Only 1st vehicle passes) + P (Only 2nd vehicle passes)

+ P (Only 3rd vehicle passes)

$=(0.70\times0.30\times0.30) + (0.30\times0.70\times0.30)+(0.30\times0.30\times0.70)\\=0.189$

Thus, the probability that exactly 1 of the next three vehicles passes is 0.189.

(d)

Compute the probability that at most 1 of the next three vehicles passes as follows:

P (At most 1 vehicle passes) = P (Exactly 1 vehicles passes)

+ P (0 vehicles passes)

$=0.189+(0.30\times0.30\times0.30)\\=0.216$

Thus, the probability that at most 1 of the next three vehicles passes is 0.216.

(e)

Let X = all 3 vehicle passes and Y = at least 1 vehicle passes.

Compute the conditional probability that all 3 vehicle passes given that at least 1 vehicle passes as follows:

$P(X|Y)=\frac{P(X\cap Y)}{P(Y)} =\frac{P(X)}{P(Y)} =\frac{(0.70)^{3}}{[1-(0.30)^{3}]} =0.3525$

Thus, the probability that all 3 vehicle passes given that at least 1 vehicle passes is 0.3525.

7 0

3 years ago

What is the solution to the system of linear equations?

AlexFokin [52]

X=8-y

2(8-y)=10
16-2y=10
-2y=10-16
-2y=-6
y=3

x+3=8
x=8-3
x=5

(5,3) is the answer :)

8 0

3 years ago

How many sides does a regular polygon have if its interior angles A. 156 B. 162

Kruka [31]

I) 156 degrees
The exterior angle is 180-156
=24
The number of sides= $\frac{360}{24}$
The number of sides= 15 sides

ii) 162 degrees
The exterior angle= 180-162
=18
The number of sides= $\frac{360}{18}$
= 20 sides

4 0

3 years ago

8. How many ways can a committee of 5 students be chosen from a student council of 30 students? Is the order in which the member

tankabanditka [31]

Answer: A committee of 5 students can be chosen from a student council of 30 students in 142506 ways.

No , the order in which the members of the committee are chosen is not important.

Step-by-step explanation:

Given : The total number of students in the council = 30

The number of students needed to be chosen = 5

The order in which the members of the committee are chosen does not matter.

So we Combinations (If order matters then we use permutations.)

The number of combinations of to select r things of n things = $^nC_r=\dfrac{n!}{r!(n-r)!}$

So the number of ways a committee of 5 students can be chosen from a student council of 30 students= $^{30}C_5=\dfrac{30!}{5!(30-5)!}$

$=\dfrac{30\times29\times28\times27\times26\times25!}{(120)\times25!}=142506$

Therefore , a committee of 5 students can be chosen from a student council of 30 students in 142506 ways.

4 0

3 years ago