In the given diagram , TY is a tangent to the circle TVS . If <SVT = 48° and |VS| = |ST| . What is < VTY.​

∠VTY = 84°

Step-by-step explanation:

because ΔTSV is isosceles (ST = SV) then ∠VTS = ∠SVT = 48°

Then ∠VST = 84°   (180 - 48 - 48 = 84)

Well, I'm going back to the picture is worth a thousand words again.

Sketch attached:

A line from S to the center bisects ∠VST into two 42° angles.

A line from T to the center forms a 42° angle with line ST.

48°-42° = 6° = angle from perpendicular line CTR to line VT.

90° - 6° = 84° for ∠VTY

answer: bea's uncle is 25 years old.

step-by-step explanation:

given the equation , we can say that the variable "x" represents the age of bea's uncle. then to find his age, we need to solve for "x":

we must add 15 to both sides of the equation:

now we need to divide both sides of the equation by 3:

therefore, we can conclude that bea's uncle is 25 years old.

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)