The perimeter of an isosceles triangle is 7x+5y-8 units and the length of the base of the triangle is x-y-2 units. What is the length, in units, of each of the congruent sides of the triangle?

3x + 3y - 3 units each

Step-by-step explanation:

An isosceles triangle is one that has two equal sides and angles.

given: perimeter = 7x + 5y - 8 units

          base length = x - y -2 units

The length of each congruent sides can be determined as follows:

Let the length of the sides be represented by t. Since the sides have equal length, then;

7x + 5y - 8 = t + t + (x - y -2)

7x + 5y - 8 = 2t + (x - y -2)

⇒ 2t = 7x + 5y - 8 - (x - y -2)

       = 7x + 5y - 8 - x + y + 2

collecting like terms,

2t  = 6x + 6y - 6

    = 2(3x + 3y - 3)

divide both sides by 2,

t = 3x + 3y - 3

Therefore, the congruent sides are 3x + 3y - 3 units each.

45

step-by-step explanation:

to find a percentage, add a decimal in front and multiply it by the other number.

.25 times 180= 45

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%