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-BARSIC- [3]
3 years ago
5

How many and what type of solutions does the equation have?

Mathematics
2 answers:
Natali [406]3 years ago
7 0
Let's solve the equation 2k^2 = 9 + 3k
First, subtract each side by (9+3k) to get 0 on the right side of the equation
2k^2 = 9 + 3k
2k^2 - (9+3k) = 9+3k - (9+3k)
2k^2 - 9 - 3k = 9 + 3k - 9 - 3k
2k^2 - 3k - 9 = 0

As you see, we got a quadratic equation of general form ax^2 + bx + c, in which a = 2, b= -3, and c = -9.
Δ = b^2 - 4ac
Δ = (-3)^2 - 4 (2)(-9)
Δ<u /> = 9 + 72
Δ<u /> = 81

Δ<u />>0 so the equation got 2 real solutions:
k = (-b + √Δ)/2a = (-(-3) + √<u />81) / 2*2 = (3+9)/4 = 12/4 = 3
AND
k = (-b -√Δ)/2a = (-(-3) - √<u />81)/2*2 = (3-9)/4 = -6/4 = -3/2

So the solutions to 2k^2 = 9+3k are k=3 and k=-3/2

A rational number is either an integer number, or a decimal number that got a definitive number of digits after the decimal point.

3 is an integer number, so it's rational.
-3/2 = -1.5, and -1.5 got a definitive number of digit after the decimal point, so it's rational.

So 2k^2 = 9 + 3k have two rational solutions (Option B).

Hope this Helps! :)
Komok [63]3 years ago
6 0

Answer:

Step-by-step explanation:

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7 0
2 years ago
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Answer:

See diagram

Step-by-step explanation:

The line with the slope of -\dfrac{3}{2} has the equation

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3 years ago
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Step-by-step explanation:

  • In integers loss is represented by negative integers whereas profit is represented by positive numbers.

Given, Beginning price =  $24.75

Over the next 5 days,

On Monday, gain of  $2.50 represented by + $2.50.

On Tuesday, loss of $3.25 represented by - $3.25 .

On Wednesday,  loss of $0.75 represented by - $0.75.

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On Friday, gain of $4.75 represented by + $4.75.

Price of the share of stock at the end of Friday = (Beginning price)+ ( + $2.50 - $3.25- $0.75+ $1.25+ $4.75)

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Hence, the correct option is B. $29.25.

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