Answer:
Construct MN.
Since M is the midpoint of OA, OM = MA
Similarly, N is the midpoint of OB.
Thus, ON = NB.
Now, in Δs OMN and OAB,
∠MON = ∠AOB (common angle)
(sides are in proportional ratio; OA = 2OM and OB = 2ON)
∴ Δs OMN and OAB are similar (2 sides are in proportion, with the included angle)
Since they are similar, then ∠OMN = ∠OAB (corresponding angles of similar triangles are equal)
But since ∠OMN = ∠OAB, then that means MN || AB (corresponding angles of two lines must be equal since they also sit relative to the transverse line, OA)
Thus, AB || MN (QED)
The expression that describes all of the values for which the graph is positive and decreasing is all real values of x where x < -1
<h3>Which describes all of the values for which the graph is positive and decreasing?</h3>
The equation of the function is given as:
f(x) = (x - 3)(x + 1)
When the value of the graph is positive, we have:
f(x) > 0
So, the function becomes
(x - 3)(x + 1) > 0
Split the above inequality
x - 3 > 0 and x + 1 > 0
Solve for x in the inequalities
x > 3 and x > -1
Hence, the expression that describes all of the values for which the graph is positive and decreasing is all real values of x where x < -1
Read more about intervals at:
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Answer:904.78
Step-by-step explanation:
