A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue. Trapezoid E F G H is shown. F G is Maple Drive, G H is Garden road, E H is Pine avenue, and E F is Elm Street. Sides F G and E H are parallel. Angle G is 108 degrees. In trapezoid EFGH, EF ≅ HG. What is the measure of the angle between Elm Street and Pine Avenue? 54° 72° 108° 144°

72°

Step-by-step explanation:

From the information given:

A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue.

We are also told that there is a  Trapezoid EFGH with EH as the Pine avenue and EF as the Elm street.

However, side FG and EH are parallel.

∠G = 108°

From the property of parallel lines :

since FG || EH

Then  ∠G = ∠H  = 108°  (i.e corresponding angle will also be equal)

The required angle between Elm Street and Pine Avenue would be interior angles +  180°  given that  alternate angles are also equal.

The required angle between Elm Street and Pine Avenue = 180° - 108°

The required angle between Elm Street and Pine Avenue = 72°

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%