Rewrite this equation in standard form. 11x + 10x^ = 6

Which of the following are square roots of —8 + 8i/3? Check all that apply.

8090 [49]

Answer:

Options (2) and (3)

Step-by-step explanation:

Let, $\sqrt{-8+8i\sqrt{3}}=(a+bi)$

$(\sqrt{-8+8i\sqrt{3}})^2=(a+bi)^2$

-8 + 8i√3 = a² + b²i² + 2abi

-8 + 8i√3 = a² - b² + 2abi

By comparing both the sides of the equation,

a² - b² = -8 -------(1)

2ab = 8√3

ab = 4√3 ----------(2)

a = $\frac{4\sqrt{3}}{b}$

By substituting the value of a in equation (1),

$(\frac{4\sqrt{3}}{b})^2-b^2=-8$

$\frac{48}{b^2}-b^2=-8$

48 - b⁴ = -8b²

b⁴ - 8b² - 48 = 0

b⁴ - 12b² + 4b² - 48 = 0

b²(b² - 12) + 4(b² - 12) = 0

(b² + 4)(b² - 12) = 0

b² + 4 = 0 ⇒ b = ±√-4

b = ± 2i

b² - 12 = 0 ⇒ b = ±2√3

Since, a = $\frac{4\sqrt{3}}{b}$

For b = ±2i,

a = $\frac{4\sqrt{3}}{\pm2i}$

= $\pm\frac{2i\sqrt{3}}{(-1)}$

= $\mp 2i\sqrt{3}$

But a is real therefore, a ≠ ±2i√3.

For b = ±2√3

a = $\frac{4\sqrt{3}}{\pm 2\sqrt{3}}$

a = ±2

Therefore, (a + bi) = (2 + 2i√3) and (-2 - 2i√3)

Options (2) and (3) are the correct options.

6 0

3 years ago

Which situation could be represented by the graph?

Ymorist [56]

The correct option which resembles with the given graph is $\fbox{\begin\\\ optionA and optionC\\\end{minispace}}$ .

Further explanation:

From the given graph the it is observed that the interval is $[8,11)$ which is a half open interval or it can be said that it is a half closed interval.

A half closed or a half open interval is an interval in which one end point of the interval is included but the other point is not included.

For example:

In an interval of the form $[a,b)$ the point $a$ is included in the set but the point $b$ is not included in the set.

Similarly, in the interval $[8,11)$ the point $8$ is included in the set but the point $11$ is not included in the set.

In order to determine the correct option which resembles with given graph form interval for each option.

Option A:

As per the statement in option A the age of the student must be at least $8$ years and not more than $11$ years that is the age of the student is either $8$ years or greater than $8$ years and less than $11$ years.

As per the above statement the interval formed is $\fbox{\begin\\\ [8,11)\\\end{minispace}}$ in which $8$ is included in the set and $11$ is not included which means it is a half closed or half opoen interval.

Therefore, $\fbox{\begin\\\ optionA\\\end{minispace}}$ is a correct option.

Option B:

As per the statement in option B the amount of money the babysitter can earn is between $\$8$ and $\$11$ per hour.

As per the above statement the interval formed is $\fbox{\begin\\\ (8,11)\\\end{minispace}}$ in which both of the end points are not included in the set which means that it is an open interval.

Therefore, $\fbox{\begin\\\ optionB\\\end{minispace}}$ is an incorrect option.

Option C:

As per the statement in option C the time required to complete a program in college cannot be less than $8$ hours and the time must be less than $11$ hours.

From the above statement it is concluded that the time required can be $8$ hours or more than $8$ hours but it has to be less than $11$ hours.

So, as per the above the statement the interval formed is $\fbox{\begin\\\ [8,11)\\\end{minispace}}$ .

Therefore, $\fbox{\begin\\\ optionC\\\end{minispace}}$ is a correct option.

Option D:

As per the statement in option D the age of the dogs is either $8$ years old or below $8$ years and age of the dog must be greater than $11$ tears.

As per the above statement the interval formed is $\fbox{\begin\\\ (-\infty,8) \bigcup(11,\infty)\\\end{minispace}}$ .

Therefore, the $\fbox{\begin\\\ optionD\\\end{minispace}}$ is an incorrect option.

So, $\fbox{\begin\\\ optionA and optionC\\\end{minispace}}$ are the correct options which resembles with the given graph.

Learn more:

A problem on composite function brainly.com/question/2723982
A problem to find radius and center of circle brainly.com/question/9510228
A problem to determine intercepts of a line brainly.com/question/1332667

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Sets

Keywords: Interval, set, open interval, closed interval, half open interval, half closed interval, set theory, program, community college, babysitters, veterinary clinic, ages, students.

5 0

3 years ago

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Name the sets of numbers to which -5 belongs to

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It would belong to integers, rational, and real numbers.

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Answer:

d-2 < -1

Step-by-step explanation:

4 0

3 years ago

Which of the following graphs best represents f(x) = −2 sin(4x) + 3?

Artist 52 [7]

The graph for f(x) = sin x is a sinusoidal graph.

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has an amplitude of 2 or the highest point is 2 and a period of
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the graph is shifted 3 points upward.

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3 years ago