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)
Answer:
Francine has just set up her Christmas tree. 40% of her ornaments are red. If she has 30 ornaments, then how many are red?
Step-by-step explanation:
Answer:
18 cm^2
Step-by-step explanation:
The legs of a right triangle are the base and height of the triangle.
Since C is a right angle, AB is the hypotenuse.
AC and BC are the legs and the base and height.
sin 75 = BC/12
BC = 12 sin 75
cos 75 = AC/12
AC = 12 cos 75
area = bh/2 = (12 sin 75)(12 cos 75)/2
area = 18 cm^2
Notice the picture below
the directrix is above the focus point, meaning the parabola is vertical and is opening downwards
now, "p" is the distance from the vertex to the focus point or the directrix, so that means, the vertex is between those two fellows, over the axis of symmetry, x = -2, since "p" is 1 unit, that puts the vertex at -2,5
since the parabola is opening downwards, that means the "p" value is negative, so is -1
Answer:
5.4%
Step-by-step explanation:
percent error = |(measured - actual value) / actual value * 100| = |(7.8-7.4) / 7.4 * 100| ≈ 5.4%
