Which of the following represents the zeros of the function

1 answer:

3 0

<span>g(x) = x^3 - 9x^2 + 2x + 48 ?

Probe some roots. When you use x = - 2

you will have: (-2)^3 - 9(-2)^2 + 2(-2) + 48 = -8 - 36 - 4 + 48 = 0

So, - 2 is a root

From that you can divide x^3 - 9x^2 + 2x + 48 by x + 2 and you will get

x^2 - 11x + 24

Then you can factor that: (x - 8)(x - 3)

So, the three roots are x = - 2, x = 3 and x = 8, which is the option B.

Answer: option B. x = 8, x = -2 , and x = 3
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Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

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Answer:

$6+2\sqrt{21}\:\mathrm{cm^2}\approx 15.17\:\mathrm{cm^2}$

Step-by-step explanation:

The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.

Vertices A, B, and C form a right triangle with legs $AB=3$ , $BC=4$ , and $AC=5$ . The two legs, 3 and 4, represent the triangle's height and base, respectively.

The area of a triangle with base $b$ and height $h$ is given by $A=\frac{1}{2}bh$ . Therefore, the area of this right triangle is:

$A=\frac{1}{2}\cdot 3\cdot 4=\frac{1}{2}\cdot 12=6\:\mathrm{cm^2}$

The other triangle is a bit trickier. Triangle $\triangle ADC$ is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by: