Given: △UEP, m∠E = 90°

OM
⊥
EP
, OM=r, UP=c
Find: Perimeter of △EPU

Triangles and Congruency

The perimeter of ΔEPU = 2 × (c+ r )

Step-by-step explanation:

Given OM = r and UP = c  and OM⊥EP

⇒ EM = r ( As OM ⊥EP, OM = r So OM = EM)

If we draw a line joining OP , then we get two triangles ΔOMP and ΔOBC

where B is point on UP and OB is radius

Both ΔOMP and ΔOBC will be congruent, OM and OB are radius.

EP = EM  + MP

⇒ MP = EP -r

If we draw a line joining OU , then we get two triangles ΔOUB and ΔOUA

where A is point on UE and OA is radius

Both ΔOUA and ΔOUB will be congruent, OA and OB are radius.

UE = UA + AE

EA = r ( As OA ⊥ UE, OM = r So OA= EM)

UP = UB + BP

c = UB + BP

Since ΔOUA and ΔOUB are  congruent and ΔOMP and ΔOBC are congruent

⇒ UB = UA and MP = BP

⇒ c = UA + MP

so the perimeter of ΔEPU = EU + UP + EP

⇒ Perimeter = EU + c + EP

⇒ Perimeter = UA + AE + c + EM + MP

⇒ Perimeter = UA + r + c + r + MP

⇒ Perimeter = c+ r + c + r

⇒ Perimeter =  2 × (c+ r )

Hence , the perimeter of ΔEPU = 2 × (c+ r )

a) at most means it can cost $12 or less

so the inequality sign would be ≤

you would then need to multiply the number of toppings by the 0.35 for each one and add it to the cost of the cheese pizza.

the equation would be 9.99 + 0.35x ≤ 12

b) using the above equation:

9.99 + 0.35x ≤ 12

subtract 9.99 from each side:

0.35x ≤2.01

divide both sides by 0.35:

x ≤ 2.01 / 0.35

x ≤5.74

at most you could have 5 toppings.

the 5 topping pizza would cost: 0.35 x 5 = 1.75 + 9.99 = $11.74

we know that

major arc is defined as the bigger arc connecting two points on the edge of a circle. measure of major arc is always more than ° or π radian

in this problem

the mayor arc is bac

find the ratio of the measure of the major arc to the measure of the minor arc

therefore

the answer is the option