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podryga [215]
3 years ago
11

GIVING BRAINLIEST TO PERSON WHO HELPS

Mathematics
1 answer:
zavuch27 [327]3 years ago
4 0
The left one
The two triangles are congruent because they apply the rule of S-A-S (side - angle - side)
side AB = side AD
angle BAC = angle DAC
side AC on triangle 1 = side AC on triangle 2

The right one
The two triangles are congruent because they apply the rule of R-H-S (right angle - hypotenuse - side)
angle HGJ = angle JLK
hypotenuse GJ = hypotenuse LJ
side HJ = side JK
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I'm confused. Can someone help?
VARVARA [1.3K]

a.

The polynomial w^2+18w+84 cannot be factored

The perfect square trinomial is w^2+18w + 81

----------

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

================================================

b.

The polynomial y^2-10y+23 cannot be factored

The perfect square trinomial is y^2-10y + 25

---------

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)

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