In rhombus abcd the measure in inches of ab is 3x+2 and bc is x+12 find the number of inches in the length of dc

Rule: All four sides of a rhombus are the same length

So AB = BC

Use this to solve for x

AB = BC

3x+2 = x+12

3x-x = 12-2

2x = 10

x = 5

If x = 5, then

AB = 3*x+2 = 3*5+2 = 15+2 = 17

and

BC = x+12 = 5+12 = 17

Both sides are 17 as expected, so the proper x value is confirmed.

So DC is also 17 since AB = DC

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°

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%