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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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1 year ago
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3 years ago
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Solve the inequality shown below.<br> -2(q-22)+q+12&gt;0
Andru [333]
<span><span><span><span>−<span>2<span>(<span>q−22</span>)</span></span></span>+q</span>+12</span>>0</span>
Step 1: Simplify both sides of the inequality.<span><span><span>
−q</span>+56</span>>0</span>
Step 2: Subtract 56 from both sides.<span><span><span><span>
−q</span>+56</span>−56</span>><span>0−56</span></span><span><span>
−q</span>><span>−56</span></span>
Step 3: Divide both sides by -1.<span><span><span>
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4 0
3 years ago
I really need help with this question!
m_a_m_a [10]

Answer:

(s-6)/r

option D

Step-by-step explanation:

The slope-intercept form a line is y=mx+b where m is the slope and b is the y-intercept.

Compare y=mx+b and y=cx+6, we see that m=c and c is the slope.

Now we are also given that (r,s) is on our line which means s=c(r)+6.

We need to solve this for c to put c in terms of r and s as desired.

s=cr+6

Subtract 6 on both sides:

s-6=cr

Divide both sides by r:

(s-6)/r=c

The slope in terms of r and s is:

(s-6)/r.

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3 years ago
A square billboard has an area of 625 ft squared. What is the length of the side of the billboard?
goldenfox [79]

Answer:

figured it out is 25

Step-by-step explanation:

hope this helps:)

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