Betsy, a recent retiree, requires $6000 per year in extra income. she has $50,000 to invest and can invest in b-rated bonds paying 13% per year or in a certificate of deposit (cd) paying 5% per year. how much money should be invested in each to realize exactly $6,000 in interest per year?

Total funds available with Betsy = $50,000

Interest rate in B-rated bonds = 13% per year

Let amount invested in B-rated bonds be x

Interest rate in certificate of deposit (CD) = 5% per year

Amount invested in CD = 50,000-x

Now, we have to determine x such that Betsy can get exactly $6,000 in interest per year. Hence:

x * 13% + (50,000 - x) * 5% = 6,000

⇒ 0.13x - 0.05x + 2,500 = 6,000

⇒ 0.08x = 3,500

⇒ x = 43,750

Hence, Betsy should invest $43,750 in B-rates bonds

And 50,000 - x = 50,000 - 43,750 = 6,250

And she should invest 6,250 in CD

the dimensions are:

step-by-step explanation:

we want to find the dimensions of a rectangular box with volume of

we factor to obtain;

we rewrite the rightmost factor to obtain;

recall that:

we apply difference of two squares formula to obtain;

hence the dimensions are

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1