A person has $10,100 to invest in two different stock. Stock ABC costs $32 per share and pays dividends of $1.20 per share. Stock XYZ costs $23 per share and pays dividends of $1.40 per share. If she wants to earn a total of $540 in dividends, how much money should be invested in company ABC?

$ 3199.0

Step-by-step explanation:

Let the number of shares of ABC = x

and XYZ = y

writing each as a linear equation

32 x + 23 y = 10100  equation 1

1.2 x + 1.4 y = 540

1.4 y = 540 - 1.2 x

y = (  540 - 1.2 x) / 1.4

substitute for y in equation 1

32 x + 23( 540 - 1.2 x) / 1.4 = 10100

32 x + 8871.43 - 19.71 x = 10100

collect the like terms

32 x -  19.71 x = 10100 - 8871.43

12.29 x = 1228.57

x = 1228.57 / 12.29 = 99.97

the amount of money to be invested in ABC shares = 99.97 × $ 32 = $ 3199.0

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!