Given:
pb tangent
pv, pu secants

if m vu= 80° and m st= 40°, then ∠1 =
if m vu= 70° and m st= 30°, then ∠2 =
if m vb= 60° and m bs = 30°, then ∠3 =
if vs = 9, sp = 12 and ut = 4, then tp =

Part a) If m VU= 80° and m ST= 40°, then ∠1 =

we know that

The measurement of the external angle is the semi-difference of the arcs it comprises.

so

therefore

the answer Part a) is

∠1 =

Part b) If m VU= 70° and m ST= 30°, then ∠2 =

we know that

The measure of the internal angle is the semi- sum of the arcs comprising it and its opposite.

so

the answer Part b) is

∠2 =

Part c) If m VB= 60° and m BS = 30°, then ∠3 =

we know that

The measurement of the external angle is the semi-difference of the arcs it comprises.

so

therefore

the answer Part c) is

∠3 =

Part d) If VS = 9, SP = 12 and UT = 4, then TP =

we know that

The Intersecting Secants Theorem  states that when two secant lines intersect each other outside a circle, the products of their segments are equal.

so

we have

substitute

using a graphing tool------> to resolve the second order equation

see the attached figure

the solution is

therefore

the answer Part d) is

1= 40

2=50

3=15

TP= 14

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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