Solve the following system of equations using matrices​ (row operations).

x-y=3
6x-5z=36
6y+2z=18

Answers

Answer 1

Answer:

(6,3,0)

Step-by-step explanation:

Given,

x -  y + 0z  =  3

6x -  0y - 2z = 36

0x + 6y + 2z = 18

You have the following augmented matrix:

(1) 1     -1     0      3

(2) 6    0   -2      36

(3) 0    6    2       18

Let's (3) add to (2) and divide by 6

(1)  1    -1    0       3

(2) 1     1    0       9

(3) 0    6   2       18

Now, let's (2) add  to (1) and divide by 2

(1)  1   0    0     6

(2) 1    1    0     9

(3) 0   6   2     18

Let's (3) ÷ 2

(1)  1    0   0     6

(2) 1    1   0      9

(3) 0   3   1      9  

Let's (1) subtract from (2)

(1)  1   0   0     6

(2) 0   1   0     3

(3) 0   3   1     9

Finally, let's (2) multiply by 3 and subtract from (3)

(1)  1   0   0     6

(2) 0   1   0     3

(3) 0   0   1     0

Thus,

x = 6, y = 3 and z = 0

The answer is (6, 3, 0)

We have to verify the answer

6 - 3 = 3  ⇒⇒ 3 = 3

6*6 - 5*0 = 36   ⇒⇒ 36 = 36

6*3 + 2*0 = 18    ⇒⇒ 18 = 18  


Related Questions

Plzzz help I don’t have a lot of time

Answers

Answer:

7

Step-by-step explanation:

It’s a right angle, so you can add the two expressions togther to get 90, then isolate x.

(8r-6)+(5r+5)=90

13r-1=90 (combine like terms)

13r-1+1=90+1 (add 1, addition property of equality)

13r=91

13r/13=91/13

r=7

A multiple-choice test contains 25 questions, each with 4 answers. Assume a student just guesses on each question. (a) What is the probability that the student answers more than 20 questions correctly

Answers

Answer:

9.68*10^-10

Step-by-step explanation:

The problem above can be solved using the binomial probability relation :

Where ;

P(x = x) = nCx * p^x * q^(n-x)

n = number of trials = 25

p = 1/4 = 0.25

q = 1 - p = 0.75

x = 20

P(x > 20) = p(x = 21) + p(x = 22) +.. + p(x = 25)

Using the binomial probability calculator to save computation time :

P(x > 20) = 9.68*10^-10

NEED HELP ASAP!!
use the vertical line test to determine if the relation whose graph is provided is a function
(graph and answers pictured)

Answers

Answer:

Yes, this graph represents a function

Step-by-step explanation:

The function passes the vertical line test, which tests for if any input has more than one unique output by moving a vertical line from left to right. If the vertical line doesn't pass 2 or more points at a time, then the function is indeed a function.

Answer:

The graph does represent a function

Step-by-step explanation:

The function is at about 30y = x^3

Graph the image of kite JKLM after a translation 3 units up.​

Answers

The new points for the translation:

L ➡️ L’ (-1,9)

K ➡️ K’ (2,6)

J ➡️ J’ (-1,3)

M ➡️ M’ (-6,6)

Anyone know this? Please help

Answers

Answer:
C
Explanation
Because i said so

find the mesure of angle b

Answers

Answer:

It's C

Step-by-step explanation:

because there is a 90 degrees sigh behind it and those two angles need to add up to 90

Answer:

31

Step-by-step explanation:

b+59=90

b=90-59

b=31

hope it helps

PLEASE HELP

Libby flips a quarter 2 times in a row.
What is the probability of the quarter landing on heads at least 1 time?

A. 1/4
B. 1/3
C. 3/4
D. 1/2

Answers

D.1/2 it’s easy lol here

Jenny made $35,000 in taxable income last year suppose the income tax rate is 10% for the first 9000+16% for the amount over 9000 how much money is jenny pay in income tax for last year

Answers

Answer:

for the first 9000 $ tax rate is 10%

so tax = 10% of 9000 = 900

rest of the amount = 35000-9000 =26000

tax rate is 16%

tax on 26000 =  16% of 26000 = 3900

total tax Debra has to pay for last year = 900 + 3900 = $4800

Step-by-step explanation:

Answer:

900+3900=$4800

#CarryOnLearning

work out 8^1/3
^1/3 = power

Answers

Answer:

8/9 (decimal: 0.888889)

Answer:

[tex]2[/tex]

Two is the answer.

Step-by-step explanation:

simple explanation is; when you go through your two times table.. in order to arrive at eight, (8), you have to mention or go through 3 numbers

Or .... cube root of 8 is two..

PLEASE MARK ME BRAINIEST

Sum of all edges of all shape

Answers

Answer:

Infinient amount buddy. They are infinent amounts of polygons, as a polygon is a shape with more then 3 sides and closed. This means as long as a number is bigger then 3, there will be a shape for it, so infinent sides

Step-by-step explanation:

3
Solve for x.
X =
8
20
35

Answers

Answer:

x=00

Step-by-step explanation:l

nnm

How many different ways may a set of 4 books be arraged side by side on a shell?

Answers

Answer:

24

Step-by-step explanation:

4 * 3 * 2 * 1 = 24

If the ratio of paintings to paintbrushes is 11:9, what percent of the items are paintbrushes. A.30% B. 35% C.40% D.45%

Answers

Answer:

D. 45%

Step-by-step explanation:

there are 11 paintings and 9 paintbrushes, added together you have a total of 20 items. There are 9 paintbrushes and 20 items in total which is 9/20. 9/20 as a percentage is 45%

Can any one help?

Solve the following equations:

Answers

Answer:

2- x=16/3 or 5.3

4- x=8

Step-by-step explanation:

yeah

Five minivans and three trucks are traveling on a 3.0 mile circular track and complete a full lap in 98.0, 108.0, 113.0, 108.0, 102.0, 101.0, 85.0, and 95.0 seconds, respectively. Assuming all vehicles are traveling at constant speeds, what is the time-mean speed of the minivans

Answers

Answer:

The time-mean speed of the minivans is of 105.8 seconds.

Step-by-step explanation:

Mean of a data-set:

The mean of a data-set is the sum of all values in the data-set divided by the number of values.

Five minivans, times of: 98.0, 108.0, 113.0, 108.0, 102.0, in seconds.

Thus, the mean is:

[tex]M = \frac{98 + 108 + 113 + 108 + 102}{5} = 105.8[/tex]

The time-mean speed of the minivans is of 105.8 seconds.

Help me fast 50 points!!!!!!!!

Answers

Answer:

30

Step-by-step explanation:

There are 14 data points on the plot

The median is the middle value, which is between the 7th and 8th data points

Since it is even, we find the average of the 7th and 8th data points

Add the 7th and 8Th data points values and divide by 2

( 30+30)/2 = 60/2 = 30

The median is 30

Answer:

30

Step-by-step explanation:

Middle numbers are 30 and 30 so you add them and then divide by two:

[tex]\frac{30 + 30}{2}[/tex] = [tex]\frac{60}{2}[/tex]= 30

Question 6. * The number of likes a social media post has generated has been tracked as a function of the number of min since it was posted. The data is shown in the table below, where t is the number of minutes and I is the number of likes. If an exponential model was used to fit this data, which of the following would be closest to its prediction for the number of likes after one hour

Answers

Answer:

Step-by-step explanation:

yes

My mom is making me do prayice and i need the answer for this thanks very much

Answers

4 is an even number

A study of college football games shows that the number of holding penalties assessed has a mean of penalties per game and a standard deviation of penalties per game. What is the probability that, for a sample of college games to be played next week, the mean number of holding penalties will be penalties per game or less

Answers

Answer:

The probability that the mean number of holding penalties per game is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean number of penalties per game, [tex]\sigma[/tex] is the standard deviation and n is the number of games that will be sampled.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

We have that:

The mean number of penalties per game is [tex]\mu[/tex] and the standard deviation is [tex]\sigma[/tex].

Sample of n games:

This means that [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

What is the probability that, for a sample of college games to be played next week, the mean number of holding penalties will be X penalties per game or less?

The probability that the mean number of holding penalties per game is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean number of penalties per game, [tex]\sigma[/tex] is the standard deviation and n is the number of games that will be sampled.

What is the slope of the line that contains the points (-1,-1) and (3, 15)?
O A.
1
4
B. 4
O C. -
4
D. -4

Answers

Answer:

its b

Step-by-step explanation:

The
Slope
a line that goes
through the points (r, 6 ) and (4,2
is 4 find r​

Answers

R= 5
(2-6). -4
—— = ——-
(4-r). (This has to be -1 for the answer to be 4)
4-5=-1
So r=5

The base of a solid is a circular disk with radius 4. Parallel cross sections perpendicular to the base are squares. Find the volume of the solid.

Answers

Answer:

the volume of the solid is 1024/3 cubic unit

Step-by-step explanation:

Given the data in the question,

radius of the circular disk = 4

Now if the center is at ( 0,0 ), the equation of the circle will be;

x² + y² = 4²

x² + y² = 16

we solve for y

y² = 16 - x²

y = ±√( 16 - x² )

{ positive is for the top while the negative is for the bottom position }

A = b²

b = 2√( 16 - x² )           { parallel cross section }

A = [2√( 16 - x² )]²

A = 4( 16 - x² )

Now,

VOLUME = [tex]\int\limits^r -rA dx[/tex]

= [tex]\int\limits^4_4 {-4(16-x^2)} \, dx[/tex]

= 4[ 16x - (x³)/3 ]           { from -4 to 4 }

= 4[ ( 64 - 64/3 ) - (-64 = 64/3 0 ]

= 4[ 64 - 64/3 + 64 - 64/3 ]

= 4[ (192 - 64 + 192 - 64 ) / 3 ]

= 4[ 256 / 3 ]

= 1024/3 cubic unit

Therefore,  the volume of the solid is 1024/3 cubic unit

Five schools are going to send their baseball teams to a tournament, in which each team must play each other team exactly once. How many games are required

Answers

20 one team plays four other teams

Answer:

20 games are required to be play

A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?

f(x) = 1500(1.15)x
f(x) = 1500(115)x
f(x) = 1500(2.15)x
f(x) = 1500(215)x

Answers

Answer:

C) f(x) = 1500(2.15)x

Step-by-step explanation:

Got it right on Edge :)

You have 3 five dollar bills and 4 ten dollar bills in your pocket. If you pull out 2 bills, what is the probability they are both tens?

Answers

Answer: I think its 4%

Step-by-step explanation: 3+4=7 7/2=3.5

Answer:

1/14

Step-by-step explanation:

(b) A telemarketing supervisor tells a new worker that the odds of making a sale on a single call are 4 to 19. What is the probability of a successful call

Answers

Answer:

0.1739 = 17.39% probability of a successful call.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The odds of making a sale on a single call are 4 to 19.

This means that in 4 + 19 = 23 calls, 4 are successful.

What is the probability of a successful call?

[tex]p = \frac{4}{23} = 0.1739[/tex]

0.1739 = 17.39% probability of a successful call.

Find the point on the terminal side of θ = three pi divided by four that has a y coordinate of 1. Show your work for full credit.

Answers

Answer:

Remember that tan=y/x from your notes from module 4.

Step-by-step explanation:

Refer to the unit circle to see the relationship between x and y at that angle, it is -1. Now you can set up your equation of tan=1/x and solve for x.

For all the problems in this section you can set up an equation where tan=y/x, sin = y/h, and cos=x/h. Then using your equation you can solve for whatever number is missing.

Answer:

-1/1

Step-by-step explanation:

Consider the following data. 15,−4,−10,8,14,−10,−2,−11

Step 1 of 3: Determine the mean of the given data
Step 2 of 3: Determine the median of the given data.
Step 3 of 3: Determine if the data set is unimodal, bimodal, multimodal, or has no mode. Identify the mode(s), if any exist.

Answers

Answer:

(a) The mean is 0

(b) The median is -30

(c) The mode is unimodal

Step-by-step explanation:

Given

[tex]Data: 15,-4,-10,8,14,-10,-2,-11[/tex]

Solving (a): The mean.

This is calculated using:

[tex]\bar x = \frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x =\frac{15-4-10+8+14-10-2-11}{8}[/tex]

[tex]\bar x =\frac{0}{8}[/tex]

[tex]\bar x =0[/tex]

Solving (b): The median

First, arrange the data

[tex]Sorted: -11,-10, -10, -4, -2,8,14,15[/tex]

There are 4 elements in the dataset. So, the median is the mean of the 4th and 5th item.

[tex]Median = \frac{-4-2}{2}[/tex]

[tex]Median = \frac{-6}{2}[/tex]

[tex]Median = -3[/tex]

Solving (c): The mode

The item that has occurs most is -10.

Hence, the mode is -10. The dataset is unimodal because it has only 1 mode (-10).

3. Find the value of:
a) 9²
b) 15²
c) (0.2)²
d) (0.7)​

Answers

Answer:

Step-by-step explanation:

9^2

=9*9

=81

15^2

=15*15

=225

(0.2)^2

=0.2 * 0.2

=0.04

(0.7)

=0.7

Researchers at a medical school conducted a study to test the effectiveness of a new drug for lowering cholesterol. The 52 subjects who volunteered for the study were each given a randomly generated number. Subjects with an odd number were given the new drug, while those with an even number were given a placebo. Cholesterol levels before and after the treatment were measured for each subject, and the differences were computed.

This study is an example of ______________ study. The difference in cholesterol level is _____________ the variable. The treatment with drug or placebo is the ____________ variable.

Answers

Answer:

1. An Experimental

2. Dependent

3. Independent

Step-by-step explanation:

Considering the description of how the research was carried out, it can be concluded that This study is an example of AN EXPERIMENTAL study. This because the researcher is trying to study the effectiveness of a new drug for lowering cholesterol

The difference in cholesterol level is the DEPENDENT variable. This is because the difference in cholesterol level is what the researcher wants to determine.

The treatment with a drug or placebo is the INDEPENDENT variable. This is because this is what the researcher manipulates to determine the difference in cholesterol level which is the dependent variable in this experimental study.

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