in circle k secant pec intersects chord bkd at f if ae is congruent to ab the measure of arc ed is 32 and arc bc: arc cd is 2:1 then find the measure of angle p

60°

Step-by-step explanation:

Diameter of circle = BD ; Hence, BD = 180°

Arc BC : CD = 2 : 1

BD = BC + CD = 180

BC = 2/3 * 180 = 120°

CD = 1/3 * 180 = 60°

Since ED = 32°

BE = 180 - 32 = 148°

BA = AE

BE = BA + AE

BA = AE = 148° / 2 = 74°

Arc ABC = BA + BC

Arc ABC = 74° + 120 = 194°

P = (Arc ABC - AE) / 2

P =(194 - 74) / 2

P = 120 / 2

P = 60°

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.

more detail

step-by-step explanation: