Answer:
−3 < x ≤ 1
Step-by-step explanation:
The domain of a function is the set of x-values.
In this graph, the open circle at (-3, -4) means the segment goes back up to this point but this point is not part of the segment itself.
The closed circle at (1, 2) means this is the endpoint and part of the segment.
This means the x-values range from almost -3 up to and including 1; this gives us the inequality
−3 < x ≤ 1
A subtracted from b means b-a
7g+11 subtracted from 12 means 12-(7g+11)=12-1(7g+11)=12-7g-11=12-11-7g=1-7g
Answer:
Step-by-step explanation:
a.
The polynomial w^2+18w+84 cannot be factored
The perfect square trinomial is w^2+18w + 81
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The reason the original can't be factored is that solving w^2+18w+84=0 leads to no real solutions. Use the quadratic formula to see this. The graph of y = x^2+18x+84 shows there are no x intercepts. A solution and an x intercept are basically the same. The x intercept visually represents the solution.
w^2+18w+81 factors to (w+9)^2 which is the same as (w+9)(w+9). We can note that w^2+18w+81 is in the form a^2+2ab+b^2 with a = w and b = 9
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b.
The polynomial y^2-10y+23 cannot be factored
The perfect square trinomial is y^2-10y + 25
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Using the quadratic formula, y^2-10y+23 = 0 has no rational solutions. The two irrational solutions mean that we can't factor over the rationals. Put another way, there are no two whole numbers such that they multiply to 23 and add to -10 at the same time.
If we want to complete the square for y^2-10y, we take half of the -10 to get -5, then square this to get 25. Therefore, y^2-10y+25 is a perfect square and it factors to (y-5)^2 or (y-5)(y-5)
