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Greeley [361]
3 years ago
13

............................              

Mathematics
1 answer:
Debora [2.8K]3 years ago
7 0
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What is the midpoint of (-9,5) and (21,-7)
stellarik [79]

Answer:

(6,13)

Step-by-step explanation:

use midpoint formula

(-9 + 21) ÷2 , (5+21) ÷2

12 ÷2 , 26 ÷ 2

6, 13

so the midpoint is at coordinates (6,13)

7 0
3 years ago
Read 2 more answers
What are the types of roots of the equation below?<br> - 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 - 9) = 0

  1. (x² -  9) = (x² - 3²) = (x - 3)(x + 3) [using algebraic identity, (a + b)(a - b) = a² - b²]
  2. 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

5 0
1 year ago
How long will it take a seal swimming at a speed of 8 miles per hour to travel 52 miles
Olin [163]
8\ miles\ per\ 1\ hour\\&#10;52\ miles\ per\ x\ hour\\\\&#10;proportion:\\&#10;8-1\\52-x\\\\cross\ multiplication\\\\&#10;8x=52\ \ \ | divide\ by\ 8\\\\&#10;x=6.5\\\\&#10;It\ will\ take\ 6.5\ hours.
7 0
3 years ago
The value of a stock increases at a rate of 1/2% per year. If the initial value of the stock $40 a share, when will the value of
natka813 [3]

Answer:

After 50 years the stock value will be $50 per share.

Step-by-step explanation:

Simple Interest Equation (Principal + Interest)

A = P(1 + rt)

Where:

A = Future amont = $50

P = Principal Amount = $40

r = Rate of Interest per year in decimal; r = R/100 = 0.5/100 = 0.005

t = Time Period involved in months or years  

Plug in the values

50 = 40(1 + 0.005t)

50 / 40 = (1 + 0.005t)

5/4 = 1 + 0.005t

5/4 - 1 = 0.005t

0.25 = 0.005t

t = 0.25 / 0.005

t = 50 years

4 0
3 years ago
Read 2 more answers
Find the Area please help me
Serggg [28]

Step-by-step explanation:

Area for a right angle triangle = 1/2 bh

b = Base

h = Height

A = 1/2×bh

= 1/2 × 2c^3d^2 × 4c

= (2c^3d^2 × 4c) / 2

= c^3d^2 × 2c

= 2c^4 × d^2

7 0
2 years ago
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