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1 answer:
For a better understanding of the solution given here please find the attached file which has the relevant diagram.
To answer this question we will have to make use of <u>the Isosceles Triangle Theorem</u> which states that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle. Thus, as a corollary we know that is EF is the angle bisector of the vertex angle ∠E, then, EF is the perpendicular bisector of the of the base DK.
Please follow the diagram of a complete understanding of the logic and the solution.
As EF is the angle bisector as given in the question, thus we will have:
.
Also, from the Theorem we know that KF will be half of DK and thus, KF will be: centimeters.
Likewise, from the same theorem we have:
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Answer:
see below
Step-by-step explanation:
The function f(x) is the absolute value function scaled vertically and shifted up. Neither of those transformations affects the interval on which it is increasing. The absolute value function increases for x > 0. (It is neither increasing nor decreasing at x=0.)
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The function g(x) is a parabola that opens downward. Consequently, it is increasing for all values of x to the left of its vertex (or line of symmetry). That line of symmetry can be found as ...
x = -b/(2a) = -(8)/(2·(-1)) = 4
So g(x) is increasing from -∞ to 4, but at x=4 is neither increasing nor decreasing.
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Then the interval on which both functions are increasing is ...
{x > 0} ∩ {x < 4} = {0 < x < 4}
This will be graphed as a line between 0 and 4 with open circles at each end.
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The second attachment shows the two functions so you can see where their slopes are positive.
to change any decimal to a fraction, we simply <u>use as many zeros on the denominator as there are decimals and lose the dot</u>.
1.18 has two decimals, so we'll use two zeros at the bottom, and lose the dot.