Use cramer’s rule to solve for x: x + 4y − z = −14 5x + 6y + 3z = 4 −2x + 7y + 2z = −17
a=
ax=
a= -240, -120, 120, 240.
ax= -240, -120, 120, 240.
x=

A = -120

AX = -240

X = 2

Step-by-step explanation:

∵ x + 4y - z = -14

∵ 5x + 6y + 3z = 4

∵ -2x + 7y + 2z = -17

∴ A = 1(6×2 - 3×7) + (-4)(2×5 - 3×-2) + (-1)(5×7 - 6×-2)

∴ A = 1(12 - 21) + (-4)(10 - -6) + (-1)(35 - -12)

∴ A = -9 + (-4)(16) + (-1)(47) = -9 - 64 - 47 = -120

To find X replace the column of X by the column of the answer

∴ AX = -14(6×2 - 3×7) + (-4)(4×2 - 3×-17) + (-1)(4×7 - 6×-17)

∴ AX = -14(12 - 21) + (-4)(8 - -51) + (-1)(28 - -102)

∴ AX = 126 + (-4)(59) + (-1)(130) = 126 - 236 - 130 = -240

∴ X = AX/A = -240/-120 = 2

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)

alaska, florida, nevada, south dakota, texas, washington and wyoming, tenessee and new hampshire.

step-by-step explanation: