Given
R is the interior of ∠ TUV.
m∠ RUV=30degrees, m∠ TUV=3x+16, and m∠ TUR=x+10.
Find the value of x and the m ∠TUV.
To proof
As given in the question
m ∠TUV=3x+16, and m ∠TUR=x+10
thus
m∠ RUV = m∠ TUV - m∠ TUR
= 3x + 16 - x -10
= 2x + 6
As given
m ∠RUV=30°
compare both the values
we get
30 = 2x + 6
24 = 2x
12 = x
put this value in the m ∠TUV= 3x+16
m ∠TUV= 12× 3 +16
= 52°
Hence proved
Answer: False
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Explanation:
I'll use x in place of p.
The original equation 10x^2-5x = -8 becomes 10x^2-5x+8 = 0 after moving everything to one side.
Compare this to ax^2+bx+c = 0
We have
Plug those three values into the discriminant formula below
d = b^2 - 4ac
d = (-5)^2 - 4(10)(8)
d = 25 - 40*8
d = 25 - 320
d = -295
The discriminant is negative, which means we have no real solutions. If your teacher has covered complex or imaginary numbers, then you would say that the quadratic has 2 complex roots. If your teacher hasn't covered this topic yet, then you'd simply say "no real solutions".
Either way, this quadratic doesn't have exactly one solution. That only occurs when d = 0. Therefore, the original statement is false.
