Solve the system of linear equations using matrices.
2x+y+z=3
-x+y-6z=-24
x+6y+6z=-4
The solution is ____ (Type an exact answer in simplified form.)
Answers
Answer:
(x, y, z) = (2, -4, 3)
Step-by-step explanation:
It is convenient to let an appropriate calculator reduce the augmented matrix to reduced row-echelon form. The rightmost column in that form is the solution vector [x, y, z].
__
If you want to solve this by hand, you can perform the following row operations to reduce the augmented matrix as shown in the attachment.
r1 ← r2 +r3; r2 ← (r2 +r3)/7 . . . . use this matrix for the next row replacement
r3 ← (r3 -r1 -4·r2)/11 . . . . . . . . . . use this matrix for the next row replacement
r1 ← r1 -2·r2 +5·r3
__
r1, r2, r3 refer to rows 1, 2, 3, respectively. The indicated multiplication and division are scalar operations, operating on each individual term in the row.
_____
Additional comment
Most graphing calculators have matrix solving functions. Apps are available for phone and tablet that will do this, and there are online websites that will reduce an augmented matrix as well.
Related Questions
Can someone pls help me out with this the best I can do is 50 points
Answers
Sorry i cannot help you
Multiply: (3x + 2)(4x + 2)
7 x2 + 12 x + 4
12 x2 + 14 x + 4
3 x2 + 4 x + 2
12 x2 + 18 x + 2
Answers
Answer:
12x²+14x+4
Step-by-step explanation:
(3x+2)(4x+2)
you will coil, multiply first term from the first bracket with the 1st term of the second bracket, and again with the 2nd term of the second bracket
do the same with the 2nd term of the first bracket, you will get the following
12x²+6x+8x+4
12x²+14x+4
Your cousin opened a bank account with a deposit of $256 dollars. After one week, she had $280 in her account. After two weeks, she had $304, and after three weeks she had $328. If this pattern continues, how much money will your cousin have in her account after 18 weeks?
Answers
Answer:
dont waste your money... go and play free fire.. open play stire and downlod freefire. and waste your money in freefire by doing topup..
Select the geometric figure that correctly matches with the following formula:
A=LW
Answers
Answer:
Square because the area of a square is length times width.
The formula matches with square.
What is Geometry?A branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids
As,
First, Area of circle = πr²
Hence, it is not possible.
Second, square
Area of square = l * b = LW
Similarly for trapezium
Area= 1/2( a+ b)* h
Hence, the formula matches with square figure.
Learn more about geometry here:
https://brainly.com/question/12168921
#SPJ2
Identify this function
f (x) =x
Answers
Answer:
linear
Step-by-step explanation:
find the gcf of 27 and 3
Answers
Answer:
Step-by-step explanation:
27x3=81
Answer:
It's 3 hope it's help....
Intensive care units (ICUs) generally treat the sickest patients in a hospital. ICUs are often the most expensive department in a hospital because of the specialized equipment and extensive training required to be an ICU doctor or nurse. Therefore, it is important to use ICUs as efficiently as possible in a hospital. According to a 2017 large-scale study of elderly ICU patients, the average length of stay in the ICU is 3.4 days (Critical Care Medicine journal article). Assume that this length of stay in the ICU has an exponential distribution. Do not round intermediate calculations.
a. What is the probability that the length of stay in the ICU is one day or less (to 4 decimals)?
b. What is the probability that the length of stay in the ICU is between two and three days (to 4 decimals)?
c. What is the probability that the length of stay in the ICU is more than five days (to 4 decimals)?
Answers
Using the exponential distribution, it is found that there is a:
a) 0.2548 = 25.48% probability that the length of stay in the ICU is one day or less.
b) 0.1415 = 14.15% probability that the length of stay in the ICU is between two and three days.
c) 0.2298 = 22.98% probability that the length of stay in the ICU is more than five days.
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = e^{-\mu x}[/tex]
In this problem, the mean is of 3.4 days, hence, the decay parameter is:
[tex]\mu = \frac{1}{3.4}[/tex]
Item a:
[tex]P(X \leq 1) = 1 - e^{-\frac{1}{3.4}} = 0.2548[/tex]
0.2548 = 25.48% probability that the length of stay in the ICU is one day or less.
Item b:
[tex]P(X \leq 2) = 1 - e^{-\frac{2}{3.4}} = 0.4447[/tex]
[tex]P(X \leq 3) = 1 - e^{-\frac{3}{3.4}} = 0.5862[/tex]
[tex]P(2 \leq X \leq 3) = 0.5862 - 0.4447 = 0.1415[/tex]
0.1415 = 14.15% probability that the length of stay in the ICU is between two and three days.
Item c:
[tex]P(X > 5) = e^{-\frac{5}{3.4}} = 0.2298[/tex]
0.2298 = 22.98% probability that the length of stay in the ICU is more than five days.
A similar problem is given at https://brainly.com/question/17039711
Scores in the first and final round for a sample of 8 golfers who completed golf tournament as shown below. Golfer First Round Final Round 1 73 78 2 68 75 3 70 66 4 67 71 5 71 73 6 70 68 7 68 65 8 73 72 a. State any appropriate hypothesis that can be tested for the above data. Use 2% level of significance to test the stated hypothesis. Use p-value approach
Answers
Answer:
golfing is fun but not to fun
Step-by-step explanation:
(10 points!!!) AND I’LL MAKE YOU BRAINLEST
I ALREADY KNOW THE ANSWER I JUST WANT THE EXPLANATION!!
The answer is ( Jose, $901.31 more)
Janell deposits $2,000 and for 5 years leaves it in an account earning 3% annual interest, compounded quarterly. For 5 years, José saves and deposits $150 per quarter in an account earning 3% interest compounded quarterly. Who will have more money in the account after 5 years? How much more?
Use the table below to answer:
Answers
Answer:Jose will make 901.31 more
Step-by-step explana
Find the y-intercept of the following equation. Simplify your answer.
y = 9x - 3/7
y-intercept
Answers
Step-by-step explanation:
Find the slope? or what....
The circumference of a circle is 28.888 centimeters. What is the circle's radius?
Use 3.14 for pi
Answers
Answer:
4.6
Step-by-step explanation:
28.888 / 3.14 = 9.2
9.2 / 2 = 4.6
help me with number 9 please!!
Answers
Answer:
10
Step-by-step explanation:
just guessed
can this problem be solved using the unitary method?yes or no.An oven has a maximum temperature of 220°c.what will it be in 2 days time
Answers
Answer:
yes 25 :)
I'm sorry if I'm wrong
HURRY!
Which of the following is a geometric sequence?
1, 2, 4, 6, 8, 10, ..
-1, 0, 1, 2, 3, ...
2, -2, 2, -2, 2, -2, ...
5, 3, 1, -1, -3, ...
Answers
Answer:
C
Step-by-step explanation:
In a geometric sequence there is a common ratio. The common ratio is a number that you multiply each number of the sequence to get the next number.
A.
1, 2, 4, 6, 8, 10, ...
2/1 = 2
4/2 = 2
It looks like the common ratio is 2, but try the next division: 6/4 = 3/2
It is not 2, so there is no common ratio, and this is not a geometric sequence.
B.
-1, 0, 1, 2, 3, ...
0/-1 = 0
1/0 = undefined
There is no common ratio.
C.
-2/2 = -1
2/(-2) = -1
-2/2 = -1
The common ratio is -1.
This is a geometric sequence.
D.
3/5 = 3/5
1/3 = 1/3
No common ratio.
Answer: C
can some one help me solve this
Answers
Answer:
time = 0.4, height = 24.8mStep-by-step explanation:
We need to find the coordinates of the vertex of the parabola.
[tex]f(x)=ax^2+bx+c\\\\v(p,\ q)-\text{vertex}\\\\p=\dfrac{-b}{2a};\ q=f(p)[/tex]
We have
[tex]h(t)=24+4t-5t^2=-5t^2+4t+24\\\\a=-5,\ b=4;\ c=24\\\\p=\dfrac{-4}{2(-5)}=\dfrac{-2}{-5}=\dfrac{2}{5}=0.4\\\\q=h(0.4)=-5(0.4)^2+4(0.4)+24=-5(0.16)+1.6+24\\\\=-0.8+25.6=24.8[/tex]
Solve the inequality for u 20>u+8
Answers
Answer:
u < 12
Step-by-step explanation:
20 > u + 8 ( subtract 8 from both sides )
12 > u , then
u < 12
Answer:
See below:
Step-by-step explanation:
Hello! My name is Galaxy and I will be helping you today. I hope you are having a nice day!
We can solve this equation in one step, which is Algebra, I'll start solving the problem now.
Algebra
We can start by simplifying the problem, [tex]20>u+8[/tex], we can subtract by 8 on each side to simplify the equation. I'll explain why afterwards.
[tex]20>u+8\\12>u[/tex]
As you can see we've subtracted by 8 on both sides, the reason this works is because when we do something to one side, we must do it to the other, which keeps the equation balanced.
We can prove this works by picking a random number for [tex]u[/tex] from our simplified version. For this case, lets pick 11.
We can see that if we plug it in to the first unsimplified equation, it works perfectly fine:
[tex]20>11+8?\\20>19[/tex]
We've proven that its correct.
So our final answer is [tex]u<12[/tex].
Cheers!
What is the answer to this problem?
Answers
Answer:
infinitely many solutions
Step-by-step explanation:
3. Put your straightedge along this line. Draw this line as long as you can.
Why can't you make it longer?
Answers
The answer is 26 trust me I will be ur friend
Someone, please help me with this. I will give Brainliest
Answers
Explanation:
What we need to do here is to take the ratio of the distances of the planets to determine how much farther Neptune is from the sun compared to Mercury:
[tex]\dfrac{D_N}{D_M} = \dfrac{4.503×10^9\:\text{km}}{5.791×10^7\:\text{km}} = 7.776×10^1[/tex]
This means that Neptune is 77.76 times farther from the sun than Mercury is.
A company borrows $50,000 for 8 years at a simple interest rate of 13.5%. Find the interest paid on the loan and the total amount paid
The interest paid on the loan is $
The total amount paid is $
Answers
Answer:
13.5%×50000=6750
this is interest paid on loan 6750
50000+6750=56750
The total amount paid
The larger of 2 numbers is 2 more than five times the smaller number. if the sum of the two numbers is 80, find both numbers
Answers
Answer:
The larger number is 67 and the smaller number is 13
Step-by-step explanation:
y=5x+2
x+y=80
-5x+y=2
6x=78
x=13
y=65+2
y=67
15-3x when x = to -2
Answers
Answer:
21 is the answer
Step-by-step explanation:
Given:
x = -2Let's use the given clue to solve the problem.
15 - 3x = Solution
=> 15 - 3(-2) = Solution
=> 15 + 6 = Solution
=> 21 = Solution
After working on this problem, we can conclude that 21 is our answer.
- [tex]GenuisUser[/tex] -
Answer:
21
Step-by-step explanation:
So, when given a question like this, we must plug in the number give for "x" in the equation.
[tex]15-3x = 15-3(-2)[/tex]
Now, we can simplify using PEMDAS
[tex]15+6 = 21[/tex]
Dont forget that a negative times a negative equals a positive!
Jace is deciding between two landscaping companies for his place of business. Company A charges $50 per hour and a $250 equipment fee. Company B charges $75 per hour and a $150 equipment fee. Let A represent the amount Company A would charge for tt hours of landscaping, and let B represent the amount Company B would charge for tt hours of landscaping. Graph each function and determine the number of hours, t, that would make the cost of each company the same.
give me the corrdent plan point i need 2 for example
(5,2) and (4,1) like that on the graph
Answer: ________
dollars per hour
dollars
hours per dollar
hours
my graph is the y axis is 1000 and the x axis is 20
Answers
Answer:
hmmmm can you show your grapg
What's next in this sequence? 4,8,16,32,64 _?
Answers
Explanation: in order for 4 to go to 8 you have to times 2, 8 times 2 is 16, 16 times 2 is 32, so finally 64 times 2 would be 128.
i hope this helps!
Use technology to find the P-value for the hypothesis test described below.
The claim is that for a smartphone carrier's data speeds at airports, the mean is p = 19.00 Mbps. The sample size is n = 21 and the test statistic is t= 1.401
P-value = (Round to three decimal places as needed)
Answers
Using the t-distribution, it is found that the p-value is of 0.177.
At the null hypothesis, it is tested that for a smartphone carrier's data speeds at airports, the mean is 19 Mbps, that is:
[tex]H_0: \mu = 19[/tex]
At the alternative hypothesis, it is tested if the mean is different than 19 Mbps, that is:
[tex]H_1: \mu \neq 19[/tex]
We are testing if the mean is different from a value, hence it is a two-tailed test.The test statistic is t = 1.401.Sample size of n = 21, hence there are 21 - 1 = 20 df.Inputting this information into a calculator, the p-value is of 0.177.
A similar problem is given at https://brainly.com/question/13873630
you will receive a golden cookie and 30 points if you help me
Answers
Answer:
A: -5/4 ; B: -0.5 ; C: 2
Step-by-step explanation:
Its the number line which shows.
Answer:
B = -0.5
A= -5/4
C= 2
Brainlest
Step-by-step explanation:
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
A pair of kids and a pair of adults decided to compete in a three-legged race. The kids got to start 15 yards ahead of the adults, since they had shorter legs. When they were told to start, the kids hobbled forward at a rate of 1 yard per second, and the adults hobbled after them at a rate of 4 yards per second. Soon they were side-by-side. How long did that take? How far did the adults go?
It took seconds for the adults to go yards and catch up to the kids?
Answers
A system of equations is simply a system that contains related equations of multiply variables
It took 5 seconds for the adults to go 20 yards and catch up to the kids
Let x represents the time of the race
The kids started 15 yards ahead, and they raced at 1 yard per second.
So, the kids' equation is represented as: [tex]\mathbf{k =15 + x}[/tex]
The adults' raced at 4 yards per second.
So, the adults' equation is represented as: [tex]\mathbf{a =4x }[/tex]
When they are side by side, we have the following equivalent equation
[tex]\mathbf{4x = 15 + x}[/tex]
Subtract x from both sides
[tex]\mathbf{3x = 15}[/tex]
Divide both sides by 3
[tex]\mathbf{x = 5}[/tex]
It means that, it took the adults 5 seconds to catch up with the kids
Substitute 5 for x in any of the equations to calculate the distance travelled.
[tex]\mathbf{a =4 \times 5}[/tex]
[tex]\mathbf{a =20}[/tex]
It means that, the adults catch up with the kids at 20 yards
Read more about systems of equations at:
https://brainly.com/question/12895249
Answer:
The adults went 123 yards and caught up to the kids in 41 seconds
Step-by-step explanation:
ixl :)
Suppose the average price of the market basket for toddler toys was $737.75 in 1994 and $801.93 in 2000 for the same basket. Calculate the inflation rate over this period. (Round your answer to the nearest hundredth of a percent.)
Answers
Answer:
0.014
Step-by-step explanation:
Minused old price from New then divided the answer by the old price then divided that by 6 to get yearly inflation
Answer:
Knewton as of May 15, 2022 8.70%
Step-by-step explanation:
Owen paid $15 to download some of his favorite songs. He paid $2.50 per song. How many songs did he download?
The first step is to by a power of ten, so the divisor is a whole number.
The next step is to by figuring out how many times 250 goes into 1500.
Answers
Hope this helps
i will mark as brainliest PLZ HELPPPPPP
Answers
we know square gives maximum area.
so 8*8 =64
He could have gained 4 sq.ft