4). What is 75% of 150?

I need help with 10-12

makkiz [27]

Answer:

Step-by-step explanation:

10) Triangle ABC is similar to triangle EDC. This means that

AB/ED = BC/DC = AC/EC

Therefore,

(3x - 5)/32 = (5x - 5)/56

Cross multiplying, it becomes

56(3x - 5) = 32(5x - 5)

168x - 280 = 160x - 160

168x - 160x = 280 - 160

8x = 120

x = 120/8 = 15

11) Triangle JKL is similar to triangle triangle MKN. This means that

JK/MK = KL/KN = JL/MN. Therefore,

32/12 = (3x - 2)/(x + 1)

Cross multiplying, it becomes

32(x + 1) = 12(3x - 2)

32x + 32 = 36x - 24

36x - 32x = 32 + 24

4x = 56

x = 56/4 = 14

12) Triangle BCD is similar to triangle GEF. This means that

BC/GE = CD/EF = BD/GF. Therefore,

(x + 4)/51 = (2x - 7)/57

Cross multiplying, it becomes

57(x + 4) = 51(2x - 7)

57x + 228 = 102x - 357

102x - 57x = 228 + 357

45x = 585

x = 585/45 = 13

7 0

4 years ago

A trust fund worth $25,000 is invested in two different portfolios. This year, one portfolio is expected to earn 5.25% interest

solong [7]

Answer:

$12 000 in Portfolio 1 and $13 000 in Portfolio 2

Step-by-step explanation:

The formula for simple interest is

I = Prt

For each portfolio, t = 1 yr

For Portfolio 1, i = 5.25 % = 0.0525

For Portfolio 2, i = 4 % = 0.04

Let x = amount invested in Portfolio 1. Then

25 000 - x = amount invested in Portfolio 2 and

$\begin{array}{rcr}0.0525x + 0.04(25000- x) & = & 1150\\0.0525x+ 1000 - 0.04x & = & 1150\\0.0125x + 1000 & = & 1150\\0.0125x & = & 150\\x & = & 12000\\\end{array}$

25 000 - x = 25 000 - 12 000 = 13 000

So, $12 000 is invested in Portfolio 1 and $13 000 is invested in Portfolio 2.

Check:

$\begin{array}{rcl}0.0525 \times 12000 + 0.04(25000 - 12000)& = & 1150\\630 + 0.04(13000) & = & 1150\\630 + 520 & = & 1150\\1150 & = & 1150\\\end{array}$