Consider the functions f(x) = x to the second power + 9x and g(x) =1/x.

1 answer:

8 0

Let's first calculate the inner functions, then fill in in the outer one:

g(-1) = 1/-1 = -1.
f(-1) = (-1)^2 + 9(-1) = 1 - 9 = -8

And then

f(1/2) = (1/2)^2 + 9(1/2) = 1/4 + 9/2 = 19/4
g(19/4) = 4/19

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Use always, sometimes or never to make a true statement:

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Answer:

1. Intersecting lines are always coplanar

2. Two planes never intersect in exactly one point

3. Three points are always coplanar

4. A plane containing two points of a line always contains the entire line

5. Four points are sometimes coplanar

6. Two lines never meet in more than one point.

7. Two skew lines are never coplanar

8. Line TQ and Line QT are always the same line.

Step-by-step explanation:

Note: Coplanar means "In the same plane"

1. Each line exist in many planes. But different lines must share at least one plane for them to intersect. That is why intersecting lines are always coplanar.

2. Two planes never intersect at exactly one point because only lines intersect at a point. Planes can only intersect along a line.

3.Three points are always coplanar because in geometry, a group of points are coplanar because there is a geometric plane that they all lie on.

4. A plane containing two points of a line always contains the entire line. Yes

5. Four points are only sometimes coplanar because there is a probability that they may all not lie on the same plane

6. Two lines never meet in more than one point because lines are basically straight and cannot bend over to intersect at another point

7. Two skew lines are never coplanar because skews lines are lines that do not intersect and are never parallel.

8. Line TQ and Line QT are always the same line because a line is straight and extends from one point to the other. So, if a line is labelled TQ calling it QT means the same thing

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