Solve the system of equations using cramer's rule -x+y-3z=-4 3x-2y+8z=14 2x-2y+5z=7

Answers

Answer 1

Answer: System of Equations
$-1x + 1y - 3z = -4 \n3x - 2y + 8z = 14 \n2x - 2y + 5z = 7$

Coefficient Matrix's Determinant
$D = \left[\begin{array}{ccc}-1&1&-3\n3&-2&8\n2&-2&5\end{array}\right]$

Answer Column
$\left[\begin{array}{ccc}-4\n14\n7\end{array}\right]$

Dx: Coefficient Determinant with Answer-Column values in X-Column
$D_(x) = \left[\begin{array}{ccc}-4&1&-3\n14&-2&8\n7&-2&5\end{array}\right]$

Dy: Coefficient Determinant with Answer-Column Values in Y-Column
$D_(y) = \left[\begin{array}{ccc}-1&-4&-3\n3&14&8\n2&7&5\end{array}\right]$

Dz: Coefficient Determinant with Answer-Column Values in Z-Column
$D_(z) = \left[\begin{array}{ccc}-1&1&-4\n3&-2&14\n2&-2&7\end{array}\right]$

Evaluating each Determinant
$D= \left[\begin{array}{ccc}-1&1&-3\n3&-2&8\n2&-2&5\end{array}\right] \nD = (-1 * (-2) * 5) + (1 * 8 * 2) + (-3 * 3 * (-2)) - (2 * (-2) * (-3)) - (-2 * 8 * (-1)) - (5 * 3 * 1) \nD = (10) + (16) + (18) - (12) - (16) - (15) \nD = 10 + 16 + 18 - 12 - 16 - 15 \nD = 26 + 18 - 12 - 16 - 15 \nD = 44 - 12 - 16 - 15 \nD = 32 - 16 - 15 \nD = 16 - 15 \nD = 1$

$D_(x) = \left[\begin{array}{ccc}-4&1&-3\n14&-2&8\n7&-2&5\end{array}\right] \nD_(x) = (-4 * (-2) * 5) + (1 * 8 * 7) + (-3 * 14 * (-2)) - (7 * (-2) * (-3)) - (-2 * 8 * (-4)) - (5 * 14 * 1)) \nD_(x) = (40) + (56) + (84) - (42) - (64) - (70) \nD_(x) = 40 + 56 + 84 - 42 - 64 - 70 \nD_(x) = 96 + 84 - 42 - 64 - 70 \nD_(x) = 180 - 42 - 64 - 70 \nD_(x) = 138 - 64 - 70 \nD_(x) = 74 - 70 \nD_(x) = 4$

$D_(y) = \left[\begin{array}{ccc}-1&-4&-3\n3&14&8\n2&7&5\end{array}\right] \nD_(y) = (-1 * 14 * 5) + (-4 * 8 * 2) + (-3 * 3 * 7) - (2 * 14 * (-3)) - (7 * 8 * (-1)) * (5 * 3 * (-4)) \nD_(y) = (-70)+ (-64) + (-63) - (-84) - (-56) - (-60) \nD_(y) = -70 - 64 - 63 + 84 + 56 + 60 \nD_(y) = -134 - 63 + 84 + 56 + 60 \nD_(y) = -197 + 84 + 56 + 60 \nD_(y) = -113 + 56 + 60 \nD_(y) = -57 + 60 \nD_(y) = 3$

$D_(z) = \left[\begin{array}{ccc}-1&1&-4\n3&-2&14\n2&-2&7\end{array}\right] \nD_(z) = (-1 * (-2) * 7) + (1 * 14 * 2) + (-4 * 3 * (-2)) - (2 * (-2) * (-4)) - (-2 * 14 * (-1)) - (7 * 3 * 1) \nD_(z) = (14) + (28) + (24) - (16) - (28) - (21) \nD_(z) = 14 + 28 + 24 - 16 - 28 - 24 \nD_(z) = 42 + 24 - 16 - 28 - 21 \nD_(z) = 66 - 16 - 28 - 21 \nD_(z) = 50 - 28 - 21 \nD_(z) = 22 - 21 \nD_(z) = 1$

$x = (D_(x))/(D) = (4)/(1) = 4 \ny = (D_(y))/(D) = (3)/(1) = 3 \nz = (D_(x))/(D) = (1)/(1) = 1 \n(x, y, z) = (4, 3, 1)$

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Math Help? 10 points.

Answers

Hello,

Answer B

the LCD of the fractions or the LCM of the denominators is
2*5*19*x^4y² (all factors with the most exponent.)
==> 190 x^4 y²

Solve for x in the equation 6x = 42.A. x = 7
B. x = 48
C. x = 36
D. x = 6

Answers

The answer is A because to get the answer you divide by 6 on both sides to get the variable alone and X=7 or you can simply use a guess and check method by taking the multiple choice answers and substituting X with the number and the one that equals 42 is the answe

Answer:

A. x=7

Step-by-step explanation:

PENN

Round 2.56×0.03 to the nearest hundredth

Answers

2.56 times 0.03 is 0.0768 then round to hundredth is 0.08 i think

John is going to invest $820 and leave it in an account for 19 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest tenth of a percent, would be required in order for John to end up with $1,830?

Answers

John would need an interest rate of 7.6% in order to end up with $1,830 after 19 years of investing $820 compounded quarterly

One number is 4 more than another, and their sum is 60. What is the smaller number?

Answers

According to your question, there are 2 unknown numbers mentioned.Let the 2 unknown numbers be represented by the variables x & y, thenx is considered to be one of the numbers being more than y by the addition of 4, .ie.x = 4 + y --- (1)The sum of the 2 numbers is 60, i.e.x + y = 60 --- (2)To find the smaller number, we solve eqn (1) & (2) using the concept of substitution, i.e. substitute 4 + y for x in eqn (2), i.e.4 + y + y = 604 + 2y = 602y = 60 - 42y = 56y = 28 ...Ans.Recall that x is more than y by 4, then 28 is the smaller number.

(I’ll give brainliest)

Answers

Answer:

i cant read it sorry

Step-by-step explanation:

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