Use Gauss-Jordan elimination to solve the following linear system.x – 6y – 3z = 4
–2x – 3z = –8
–2x + 2y – 3z = –14

Answers

Answer 1

Answer: $\begin{cases}x-6y-3z=4&(1)\n-2x-3z=-8&(2)\n-2x+2y-3z=-14&(3)\end{cases}$

First eliminate $y$ by adding $(1)$ to three times $(3)$ . This gives

$(x-6y-3z)+3(-2x+2y-3z)=4+3(-14)\iff -5x-12z=-38$

This reduces the system of one of two equations and two unknowns:

$\begin{cases}-5x-12z=-38&(1)^*\n-2x-3z=-8&(2)^*\end{cases}$

You can eliminate $z$ by subtracting $(1)^*$ and four times $(2)^*$ to get

$(-5x-12z)-4(-2x-3z)=-38-4(-8)\iff3x=-6\implies x=-2$

Back-substitute to find $z$ and $y$ . You should end up with $(x,y,z)=(-2,-3,4)$ .

Answer 2

Answer:

Answer:

(-2,-3,4)

Step-by-step explanation:

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What is more than ½ and less than 1

Answers

The number that is more than 1/2 and less than 1 is 3/4. To understand this better, let's break it down into fractions. 1/2 is equivalent to 2/4, so we need a fraction that is greater than 2/4 but less than 4/4 (which is equivalent to 1). 3/4 fits this criteria as it is greater than 2/4 but less than 4/4. Therefore, 3/4 is the number that is more than 1/2 and less than 1.

It takes 120 minutes for a hose to fill a swimming pool. If the pool drain is open, it takes 360 minutes to fill the pool. If the pool is full, the hose is off, and drain is open, how many minutes does it take to empty the pool?

Answers

I would look at this problem like this:

In those 360 the hose is working, and it's working the same as during the 120 when it filled the pool. Since 360 is three times 120, it means that it filled the pool three times this time. But the pool was only filled once!

This means that twice the pool was drained in those 360 minutes: this makes one draining every 180 minutes. - this is the answer!

Answer:

180 minutes

Step-by-step explanation:

A wheel of radius 10 cm is turning at a rate of 5 revolutions Calculate: the distance moved by a point on the rim in 2 seconds

Answers

Answer:

15°

Step-by-step explanation:

Angular velocity= 5rev/ min

= 10π/ min

But 1 min= 60 secs

= Angle turned/ 2secs

= 10π/(60×2)

= π/12 × 180/π= 15°

Simplify the expression. 6p5

Answers

If you are considering P of the permutation and combination. Then simply pit the figure 6P5 in calculator and your answer will be 720. Or if not calculator then the formula is P(n,r)= n(factorial)/ (n-r)factorial.

How do you write 56/50 as a percentage

Answers

Answer:

112%.

Step-by-step explanation:

To write 56/50 as a percentage, you can follow these steps:

1. Divide the numerator (top number) by the denominator (bottom number): 56 ÷ 50 = 1.12.

2. Multiply the result by 100 to convert it to a percentage: 1.12 × 100 = 112%.

Therefore, 56/50 can be written as 112%. This means that the fraction 56/50 is equivalent to 112 out of 100, or 112%.

Example:

Let's say you have 56 apples and you want to express it as a percentage of a total of 50 apples. To find out what percentage 56 apples is out of 50, you can use the fraction 56/50. By following the steps above, you find that it is equal to 112%. This means that 56 apples represents 112% of the total of 50 apples.

Make x the subject of the following... 2z = 3r + x