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3 years ago

The reduced row-echelon form of the augmented matirx of a system of equations is given. Find the solution of the system.

Mathematics

1 answer:

vodomira [7]3 years ago

3 0

Answer:

option C)

(19,2,5)

Step-by-step explanation:

| 4 | x

| 12 | y

| 5 | z

After reducing the matrix in row-echelon form we are left with three equation as following

Equation 1

0x + 0y + 1z = 5

Equation 2

0x + y1 + 2z = 12

Equation 3

1x + 0y -3z = 4

<h3>Solution</h3>

As in first equation

0 + 0 + z = 5

z = 5

Put this value of z in equation 2 and 3

y + 2(5) = 12

y + 10 =12

y = 12 - 10

y = 2

x + 0 -3(5) = 4

x - 15 = 4

x = 4 + 15

x = 19

<h3 /><h3>So the solution of the system is (x,y,z) = (19,2,5)</h3>

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4 years ago

Consider the points A (45, 29), B (9,- 7) and C (5. – 11) Find the slope of AB.

Papessa [141]

The slope is 1. if you do y^2-y^1/x^2-x^1 you will get -36/-36 which simplified is 1.

3 0

3 years ago

A drawer is filled with 7 black shirts, 5 white shirts, and 10 gray shirts.

igomit [66]

Answer:

5/11

Step-by-step explanation:

7+5+10=22

fraction of grey t-shirts would be 10/22

simplify it and u get 5/11

6 0

4 years ago

PLEASE HELP ASAP! THIS IS TIMED! WILL MARK BRAINLIEST IF ANSWER IS CORRECT!

IgorC [24]

Answer:

Step-by-step explanation:

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8 0

3 years ago

The minimum distance between two fence posts is 4 feet. The maximum distance is 10 feet. A. Represent these two distances on a n

dybincka [34]

Answer:

Part A) The number line in the attached figure

Part B) The absolute value equation is $\left|x-7\right|=3$

Step-by-step explanation:

Part A) Represent these two distances on a number line

we know that

The minimum distance between two fence posts is 4 feet, and the maximum distance is 10 feet

Let

x ----> the distance between the two fence post

$4\leq x \leq 10$

The interval is -------> [4,10]

using a graphing tool

see the attached figure

In a number line the solution is the shaded area at right of x=4 (close circle) and at the left of x=10 (close circle)

Part B) Write an absolute value equation that represents the minimum and maximum distances

Find the midpoint of the interval [4,10]

$M=(\frac{x1+x2}{2})$

substitute the values

$M=(\frac{4+10}{2})$

$M=(7)$

The distance from the midpoint to the endpoints of the interval is 3 feet

The absolute value equation is

$\left|x-7\right|=3$

<em>Verify</em>

<u>Solve the absolute value</u>

case 1) positive value

$+(x-7)=3$

Solve for x

$x=7+3=10\ ft$ ----> maximum distance

case 2) negative value

$-(x-7)=3$

Solve for x

$-x+7=3$

$x=7-3=4\ ft$ ----> minimum distance

3 0

3 years ago