Solve x2 + 12x + 6 = 0 using the completing-the-square method.

1 answer:

7 0

X^2+12x+6=0 subtract 6 from both sides...

x^2+12x=-6 halve linear coefficient, square it, and add it to both sides...

x^2+12x+36=30 now the left side is a perfect square...

(x+6)^2=30 take square root of both sides...

x+6=30^(1/2) subtract 6 from both sides...

x=-6-30^(1/2) and -6+30^(1/2)

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in circle O the radius is 4ft and the measure of minor arc ab is 120 degrees find the length of minor arc ab to the nearest inte

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Answer:

$8\:\text{ft}$

Step-by-step explanation:

The length of the arc is proportional to the degree measure it in encompasses. Since there are 360 degrees in a circle and the arc is 120 degrees, the arc's length will be $\frac{120}{360}=\frac{1}{3}$ of the circle's length (circumference).

The circumference of a circle is given by $2\pi r$ , where $r$ is the radius of the circle. Therefore, the circumference of the circle is $2\pi(4)=8\pi$ . As we found earlier, the length of the arc is $\frac{1}{3}$ of this circumference. Therefore, the arc's length is $8\pi\cdot \frac{1}{3}=\frac{8\pi}{3}$ .