Ms. burke invested $53,650, part at 10.5% and the rest at 12%. if the income from the 10.5% investment is one third of that from the 12% investment, how much did she invest at each rate?

$14,800 at 10.5%

$38,850 at 12%

Step-by-step explanation:

Investment at 10.5% (x):

(0.12[$53,650 - x])/0.105x = 3

$6,438 - 0.12x = 0.315x

0.435x = $6,438

x = $14,800

Investment at 12%:

= $53,650 - $14,800

= $38,850

Investments: @ 10.5%, $14,800; @ 12%, $38,850

Proof: (income from 1st is 1/3 that of the income from the 2nd):

= (0.105[$14,800])/(0.12[$38,850])

= $1,554/$4,662

= 1/3

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)

answer:   b

step-by-step explanation:

x2 = 16

x can not be a negative number because 16 is positive

the only answer would be positive 8