1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
-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:

You might be interested in
A Web music store offers two versions of a popular song. The size of the standard version is 2.1 megabytes (MB). The size of the
liq [111]
If the number of downloads of the standard version is x, and the high quality is x, 2.1*x+4.1*y=2761 (not 1010 due to that this is multiplied by 2.1 and 4.1, therefore representing the total amount of megabytes) In addition, there are 1010 total downloads, and it's either 2.1 MB or 4.1 MB, so x+y=1010.

We have 
2.1x+4.1y=2761
x+y=1010

Multiplying the second equation by -2.1 and adding it to the first equation, we get 2y=2761-1010*2.1=640 and by dividing both sides by 2 we get y=320 downloads of the high quality version


5 0
3 years ago
Which expression is equivalent to 3x+10−x+12<br> a.24x<br> b.4x + 22<br> c.26x<br> d.2x + 22
jok3333 [9.3K]
The answer is:  [D]:  2x + 22  .
______________________________________________
8 0
3 years ago
What’s the distance from c to d ?
Anon25 [30]
It’s 5 since you’d use Pythagorean theorem
3 0
3 years ago
Please give me the answer
Tcecarenko [31]

Answer:

7 units

Step-by-step explanation:

hope I helped today

8 0
3 years ago
Read 2 more answers
The terminal point of Dis ( 1/2,3/2). What is cos 0?
nydimaria [60]

Answer:

<em>(c). </em>\frac{1}{2}<em> </em>

Step-by-step explanation:

The <u><em>cosine</em></u> is the <em>"x" coordinate</em> of the terminal point on the unit circle.

Thus the answer is <em>(c). </em>\frac{1}{2}

5 0
3 years ago
Other questions:
  • V = 5x + 2y<br> X = 3<br> y = -4<br> a) Work out the value of V.
    15·2 answers
  • How old would a person born in 25 BC be on their birthday in AD 25?
    14·1 answer
  • WORTH 30 : can you please help me with my homework questions 14-18
    8·1 answer
  • 60731903239__8DEE49CD-5BBC-40E2-A8F5-59B32FE3879C.jpeg
    10·1 answer
  • 20x+5 and 24x-1 what is x<br> they are should equal the same number when u find x and plug em in
    9·2 answers
  • Sally Pays £25 for two tubes of paint a blue tube and a red tube. the blue tube cost £7 more than the red tube.
    14·1 answer
  • Write in standard form a)0.00000678 b)3170000
    15·1 answer
  • Juan had his car washed at the speedy clean car wash. He paid $20 for a car wash. He gave a 15% tip to the attendant who washed
    13·1 answer
  • You want to buy a pet iguana. You already have $12 and plan to save$9 per week.
    15·2 answers
  • 1.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!