Given data:
The first point given iis (a, b)=(-6,2).
The second point given is (c,d)=(0, -6).
The expression for the slope is,
m=(d-b)/(c-a)
Substitute the given points in the above expression.
m=(-6-2)/(0-(-6))
=(-8)/(6)
=-4/3
Thus, the slope of the line is -4/3, so (C) option is correct.
Remember that the radicand (the area under the root sign) must be positive or zero for a radical with an even index (like the square root or fourth root, for example). This is because two numbers squared or to the fourth power, etc. cannot be negative, so there are no real solutions when the radicand is negative. We must restrict the domain of the square-root function.
If the domain has already been restricted to
, we can work backwards to add 11 to both sides. We see that
must be under the radicand, so the answer is
A.
This is a fairly tedious problem. The only way to solve that I see is to simply list out all the possible cases and go through each one by one. You'll use the triangle inequality theorem to see if the triangles can be formed. The theorem says that a+b > c must be true for all sets of pairs. In other words, take any two sides and add them up. The sum must be greater than the third side.
Going through all the combos possible (that I could find), this is what I got
Blue9,Green7,Orange4
Blue9,Green7,Purple12
Blue9,Green7,Red3
Blue9,Green7,Yellow5
Blue9,Orange4,Purple12
Blue9,Purple12,Yellow5
Green7,Orange4,Yellow5
Green7,Red3,Yellow5
Orange4,Red3,Yellow5
In all, I count 9 cases. So the answer to problem 1 is 9.
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For problem 2, the best way may be to pick two segments at a time instead of one. However, I have a feeling that will take just as long as the first method. I haven't tried it out. Even though going through the rods one at a time takes a while, it's probably the best option so you don't overlook any cases.
2(5+ square root of 8)
=2(5+2.8284271247)
=2(7.8284271247)
=15.656854249
Square root of
15.656854249
=3.9568743029
