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2 years ago

How do you find the base of this triangle? (Picture should be able to be seen)

Mathematics

1 answer:

vazorg [7]2 years ago

5 0

The idea being, when you run a perpendicular line to the base, from the right-angle in a right-triangle, like in this case, what you end up with is, three similar triangles, a Large triangle containing the two smaller ones, a Medium triangle and a Small one, check the picture below.

since all three are similar, we can use the proportions on the corresponding sides, as you see in the picture, the base of the triangle then will just be x + y.

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If (x+2) is a factor of 3x^2-4kx-4k^2, then find the value(s) of k

IRINA_888 [86]

Answer:

The values of k will be:

$k=-1,\:k=3$

Step-by-step explanation:

Let the expression of polynomial P be

$P\left(x\right)=3x^2-4kx-4k^2$

Let the expression if the polynomial Q be

$\:Q\left(x\right)=\:\left(x+2\right)\:$

Plug in Q(x) = 0

0 = x+2

x = -2

As (x+2) is a factor of 3x²-4kx-4k²

substitute x = -2 in the the polynomial

3x²-4kx-4k² = 0

$3\left(-2\right)^2-4k\left(-2\right)-4k^2\:=0$

$12+8k-4k^2=0$

Write in the standard form ax²+bx+c = 0

$-4k^2+8k+12=0$

Factor out common term -4

$-4\left(k^2-2k-3\right)=0$

Factor k²-2k-3: (k+1)(k-3)

$-4\left(k+1\right)\left(k-3\right)=0$

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

$k+1=0\quad \mathrm{or}\quad \:k-3=0$

solving k+1=0

k+1 = 0

k = -1

solving k-3=0

k-3=0

k = 3

Thus, the values of k will be:

$k=-1,\:k=3$

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