Study the following figure, where two concentric circles share center C. Segment AB is a diameter of the larger circle.
Segment AB intersects a chord of the smaller circle, PQ, at a right angle at point Z.
Segment AB intersects a chord of the larger circle, MN, at a right angle at point 0.

If MO=7x-4, and NO=6x, what is the length of MN

Length of MN = 48 units

Step-by-step explanation:

AB is the diameter of the larger circle which is perpendicular to both the chords PQ (chord of the smaller circle) and MN(chord of the larger circle).

Theorem says,

"Radius or a diameter of a circle which is perpendicular to the chord divides the chord in two equal parts."

Therefore, MO ≅ ON

m(MO) = m(ON)

7x - 4 = 6x

7x - 6x = 4

x = 4

m(MN) = m(MO) + m(ON)

           = (7x - 4) + (6x)

           = 13x - 4

           = (13 × 4) - 4

           = 52 - 4

           = 48

Length of chord MN will be 48 units.

that there are 12 data points

step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.