Corresponding sides in the triangles MOP and MNQ are
MO and MN,
OP and NQ,
PM and QM.
Ratios of the corresponding sides for similar triangles should be the same.
MQ/MP =MN/MO
MQ/(MQ+QP) = MN/(MN+NO)
5/(5+x) = 6/(6+18/5)
5*(6+18/5)=6(5+x)
30+18 = 30 +6x
18=6x
x=3 =QP
Answer:oufonsrgonsrgnrsosgnsogwo0on93rhskgv oaoef
Step-by-step explanation:
iaeiuaefiaef ebf efa fcade emma jog 123e oefofoinsfnfsaefosefnhsfnalnfaogh
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! :)
I'm pretty sure that the answer is 12C4 = (12p4)/4! = (12*11*10*9)/4*3*2*1 = 495
Hope this helps
Answer:
m<ADC = 42°
Step-by-step explanation:
Based on the inscribed angle theorem, the inscribed angle, m<ADC is ½ the measure of minor arc AC.
If minor arc is given as 84°, therefore:
m<ADC = ½(84)
m<ADC = 42°