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! :)
3/8 = 0,375
5/12 = 0,416
5/12 is bigger
Solving for x
x=3/8m-5/4,m
Solving for m
m=10/3+8/3x,x
Step-by-step explanation:
Since , internal sum of angle of triangle is 180°
So,
66 + x +49 + x+83 = 180
or, 198 + 2x = 180
or, 2x = 180 -198
or, 2x = -18
hence, x = - 9
Now angle A = x + 49
= (-9) + 49
= 40
<u>Hence </u><u>measure</u><u> </u><u>of </u><u>angle </u><u>A </u><u>is </u><u>4</u><u>0</u><u>°</u><u>.</u>
A polygon is a two-dimensional closed object. The polygon that best describes a stop sign is a regular octagon.
<h3>What is a polygon?</h3>
A polygon is a two-dimensional closed object with n number of straight sides that is flat or planar and the value of n is always greater than 2 (n>2).
<h3>What is an octagon?</h3>
An octagon is a polygon that has 8 number of sides.
As we know that a stop sign has 8 sides, therefore, the polygon that is in the shape of the stop sign is an octagon.
An octagon has 8 sides, and as it is mentioned in the problem that sides and angles appear to be congruent, therefore, the polygon must be a regular polygon.
Hence, the polygon that best describes a stop sign is a regular octagon.
Learn more about Polygon:
brainly.com/question/17756657
