By the Triangle Inequality Theorem, the sum of two sides should be greater than the length of the third side, while the difference of these two sides should be less than the length of this third side. Normally you would take the absolute value of the difference of these two side as you wouldn't know which is greater than the other!
The simplest way to prove whether these line segments can form a triangle, is by going against this theory. Let us prove that the line segment don't form a triangle. As you can see, adding 7 and 1 is greater than 1, respectively 7 and 7 is greater than 1. Thus -
<u><em>Solution = A. True</em></u>
<span>(0.5, -1)
f^-1(x) and f(x) are inverse functions of each other. That means that for all x, f^-1(f(x)) = x and f(f^-1(x)) = x. So for f^-1(x) we've been given the point (-1, 0.5) which means that we have an x value of -1 and a y value of 0.5. So if we swap the x and y values, we'll have a valid point for function f(x). Therefore an x value of 0.5 and a y value of -1 will work. So the answer is (0.5, -1). Notice that no math has to be done, you just need to know the meaning of inverse functions.</span>
Hello :
the discriminat of each quadratic equation : ax²+bx+c=0 ....(a <span>≠ 0) is :
</span><span>Δ = b² -4ac
1 ) </span>Δ > 0 the equation has two reals solutions : x = (-b±√Δ)/2a
2 ) Δ = 0 : one solution : x = -b/2a
3 ) Δ <span>< 0 : no reals solutions
in this exercice : -3x²-2x+6 =0.....a = -3 b = -2 c =6
calculate : </span>Δ............................
<span>-|2x-10|-1=2 has NO solutions, because the absolute value function is never negative. Can be 0, can be positive, but can NOT be negative.
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