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2 years ago

Please help it's the SLOPE

Mathematics

1 answer:

Maksim231197 [3]2 years ago

3 0

Answer:

$- \frac{4}{5}$

Step-by-step explanation:

Please see the attached picture.

$slope \\ = \frac{1 - ( - 3)}{ - 3 - 2} \\ = \frac{1 + 3}{ - 5} \\ = - \frac{4}{5}$

☆In the gradient formula,

(x1, y1) is the first coordinate and (x2, y2) is the second coordinate.

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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

#SPJ9

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7 months ago

1. What is the slope of the line that passes through the given points? (2, 12) and (6, 11)

Y_Kistochka [10]

Answer:

-1/4x

Step-by-step explanation:

11-12/6-2 = -1/4

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2 years ago

List 3 values that would make this inequality true 8+y>11

alina1380 [7]

You could use so many for example 4, 10, 57, 5729, any number above 4 would work since that plus 8 would be greater than 11

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2 years ago

Felix wrote several equations and determined that only one of the equations has no solution. Which of these equations has no sol

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A. 3(x-2)+x=4x+6 has no solution.

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2 years ago

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If PQRS is a rhombus, which statements must be true? Check all that apply.

bezimeni [28]

These statements are true:

$\bold{First.} \ \overline{PS} \ is \ parallel \ to \ \overline{QR}$

This is true because of the definition of a rhombus which states that opposite sides are parallel.

$Then \ \overline{PS} \ is \ opposite \ to \ \overline{QR}$

$\bold{Second.} \ \overline{PR} \ is \ perpendicular \ to \ \overline{QS}$

This is true because the diagonals of a rhombus bisect each other at right angles.

$\bold{Third.} \ \overline{PQ}=\overline{RS}$

This is true because the four sides of a rhombus are all equals.

$\bold{Fourth.} \ \angle PQR \ is \ supplementary \ to \ \angle QPS$

This is also true. Two angles are supplementary when they add up to 180 degrees. Angles in rhombus are equal two to two. Let's name:

$\angle PQR = \alpha \ and \ \angle QPS = \beta$

Then it is true that:

$\angle PQR=\angle PSR \ and \ \angle QPS=\angle QRS$

Besides, a rhombus is a quadrilateral and it is true that the interior angles of a quadrilateral add up to 360 degrees, thus:

$2\alpha+2\beta=360 \\ \\ \therefore \boxed{\alpha+\beta = 180^\circ}$

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2 years ago

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