Write an augmented matrix of each system. Then, solve each system using matrix notation. Describe the solution set in vector notation.
Answers
Answer:
The answer is below
Step-by-step explanation:
Given the system of equations:
x + y + 2z = 9
2x + 4y - 3z = 1
3x + 6y - 5z = 0
This system of equation can be solved using matrix. This done by first representing the equations as matrix and then solving:
The matrix form is:
[tex]\left[\begin{array}{ccc}1&1&2\\2&4&-3\\3&6&-5\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}9\\1\\0\end{array}\right] \\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}1&1&2\\2&4&-3\\3&6&-5\end{array}\right] ^{-1} \left[\begin{array}{c}9\\1\\0\end{array}\right] \\\\\\[/tex]
[tex]\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}2&-17&11\\-1&11&-7\\0&3&-2\end{array}\right] \left[\begin{array}{c}9\\1\\0\end{array}\right] \\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}1\\2\\3\end{array}\right][/tex]
Related Questions
Zahraa made 4 pitchers of lemonade. Each pitcher holds ⅓ gallon. How many gallons of lemonade did she make? WHATS THE ANSWER??
Answers
Answer:
12 gallons
Step-by-step explanation:
If each pitcher can hold only a third of one of her makings. Think about it. Just pour the glasses in your mind. She fills it up a little bit, and then keeps doing it until 12 are full. or how else to explain it or really explain it at all.
Standard Error from a Formula and a Bootstrap Distribution Sample A has a count of 30 successes with and Sample B has a count of 50 successes with . Use StatKey or other technology to generate a bootstrap distribution of sample differences in proportions and find the standard error for that distribution. Compare the result to the value obtained using the formula for the standard error of a difference in proportions from this section.
Answers
Answer:
Using a formula, the standard error is: 0.052
Using bootstrap, the standard error is: 0.050
Comparison:
The calculated standard error using the formula is greater than the standard error using bootstrap
Step-by-step explanation:
Given
Sample A Sample B
[tex]x_A = 30[/tex] [tex]x_B = 50[/tex]
[tex]n_A = 100[/tex] [tex]n_B =250[/tex]
Solving (a): Standard error using formula
First, calculate the proportion of A
[tex]p_A = \frac{x_A}{n_A}[/tex]
[tex]p_A = \frac{30}{100}[/tex]
[tex]p_A = 0.30[/tex]
The proportion of B
[tex]p_B = \frac{x_B}{n_B}[/tex]
[tex]p_B = \frac{50}{250}[/tex]
[tex]p_B = 0.20[/tex]
The standard error is:
[tex]SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{\frac{0.30 * (1 - 0.30)}{100} + \frac{0.20* (1 - 0.20)}{250}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{\frac{0.30 * 0.70}{100} + \frac{0.20* 0.80}{250}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{\frac{0.21}{100} + \frac{0.16}{250}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{0.0021+ 0.00064}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{0.00274}[/tex]
[tex]SE_{p_A-p_B} = 0.052[/tex]
Solving (a): Standard error using bootstrapping.
Following the below steps.
Open StatkeyUnder Randomization Hypothesis Tests, select Test for Difference in ProportionsClick on Edit data, enter the appropriate data Click on ok to generate samplesClick on Generate 1000 samples ---- see attachment for the generated dataFrom the randomization sample, we have:
Sample A Sample B
[tex]x_A = 23[/tex] [tex]x_B = 57[/tex]
[tex]n_A = 100[/tex] [tex]n_B =250[/tex]
[tex]p_A = 0.230[/tex] [tex]p_A = 0.228[/tex]
So, we have:
[tex]SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{\frac{0.23 * (1 - 0.23)}{100} + \frac{0.228* (1 - 0.228)}{250}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{\frac{0.1771}{100} + \frac{0.176016}{250}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{0.001771 + 0.000704064}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{0.002475064}[/tex]
[tex]SE_{p_A-p_B} = 0.050[/tex]
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%
A restaurent pays a water R18 per hour in one week he worked a shift from 12h00 to 23h00 Calculate the number of hours the water works per shift
Answers
Answer:
Number of hour work per shift = 11 hour per day
Amount paid for one shift = Rs 198
Step-by-step explanation:
Given:
Amount pay per hour = Rs 18
Shift time = 12 h to 23 h
Find;
Number of hour work per shift
Amount paid for one shift
Computation:
Number of hour work per shift = 23:00 - 12:00
Number of hour work per shift = 11 hour per day
Amount paid for one shift = Number of hour work per shift x Amount pay per hour
Amount paid for one shift = 11 x 18
Amount paid for one shift = Rs 198
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:
Help Help Help it's in khan academy
Answers
Answer:
Step 1 is wrong
Step-by-step explanation:
[tex] \frac{1}{4} r+ 2 = 10[/tex]
[tex] \frac{r}{4} + 2 = 10[/tex]
[tex] \frac{r}{4} = 10 - 2[/tex]
[tex] \frac{r}{4} = 8[/tex]
[tex]r = 8 \times 2[/tex]
[tex]r = 32[/tex]
Hope it is helpful...Alex was trying to determine how much money he owed the bank. Since his checking account has a balance of -155 dollars, he thinks that he can find the absolute value of -155 to determine that he owes the bank 155 dollars. Is Alex correct?
Answers
Answer:
Alex is correct.
Step-by-step explanation:
In order for Alex to get to $0, meaning he owes the bank nothing, he has to add 155 dollars to negative 155 dollars, because this means he has no debt left. The absolute value of -155 is 155 and if Alex pays the 155 dollars, he will not have to pay anything else to the bank.
Need help ASAP!!!!!!
Answers
Answer:
I dont know for sure, but maybe try B
Step-by-step explanation:
Can someone help ASAP
Answers
the 2 count up 3 times and go to the right 2 times
Please help! Thank you!
Answers
Answer:
D: (2, -3)
Step-by-step explanation:
We have;
y = 3x - 9 - - - (1)
y = -2x + 1 - - - (2)
By substitution method, from eq 1, we see that: y = 3x - 9
Thus,let's put 3x - 9 for y in eq 2;
3x - 9 = -2x + 1
Rearranging to get;
3x + 2x = 9 + 1
5x = 10
x = 10/5
x = 2
Thus;
y = 3(2) - 9
y = 6 - 9
y = -3
Thus,the solution (x, y) = (2, - 3)
Which of the following is the point-slope form of the equation with slope 3 that goes through the point (4,2)?
Answers
Answer:
y–y1 =m (X–X1)
y–2=3(x–4)
y=3x–10
The
Slope
a line that goes
through the points (r, 6 ) and (4,2
is 4 find r
Answers
(2-6). -4
—— = ——-
(4-r). (This has to be -1 for the answer to be 4)
4-5=-1
So r=5
1. What must be added to 203 to get a number whose digits are reversed of the given number?
Answers
When we reverse the digits of 203,we get 302.
So we can form an equation out of these values:
203 + x = 302
x = 302-203
x = 99
This means that your answer is 99
PLEASE HELP ASAP!!! WILL MARK BRAINLIEST !!
Answers
Answer:
CA = LJ
Step-by-step explanation:
The third side
CA = LJ
Answer:
CA=LG is correct answer
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
Answer:
20 games are required to be play
What is the solution to -2(8x - 4) < 2x + 5?
Answers
Answer:
See image below:)
Step-by-step explanation:
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
What is the perimeter of the trapezoid? In unit
Answers
Answer:
20 units
Step-by-step explanation:
the perimeter = 7+4+4+5 = 20 units
The frequency table shows all but one score on a 5-point geography quiz. If the mode of the complete data set is 4, what is the unknown quiz score?
Answers
Answer:
(4)
Step-by-step explanation:
element =4
frequency=1
cumulative frequency-=1
relative frequency=1
cumulative relative frequency=1
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:
Which graph represents the function (x) = -1x - 21 - 1?
Answers
Answer:
Given in the graph
Step-by-step explanation:
In the figure below, which term best describes point R?
A. Orthocenter
B. Centroid
C. Incenter
D. Circumcenter
Answers
Orthocenter is the best term to describes point R in the triangle UVW.
What is orthocenter?" Orthocenter is defined as intersecting point of the altitudes of the sides of the acute angle triangle."
According to the given figure,
In triangle UVW,
Ray VR perpendicular to UW
Ray UR perpendicular to VW
Ray WR perpendicular to UV
Altitudes of side ( UV , VW, and WU) of triangle UVW intersect at
point R.
As per the definition of orthocenter , point R represents orthocenter.
Hence, orthocenter is the best term to describes point R in the triangle UVW.
Learn more about orthocenter here
https://brainly.com/question/19763099
#SPJ2
2. How many degrees has PRQ been rotated to make PRQ
Answers
Answer:
180 degree
Step-by-step explanation:
180 degee
......
......
.......
ayuda ÷18=40 que número falta
Answers
Para encontrar el número que falta,
multiplica 18 x 40.
18 x 40 = 720
Answer:
720
Step-by-step explanation:
x÷18=40
x=18•40
x=720
Anyone know this? Please help
Answers
C
Explanation
Because i said so
A model train is built at a scale of 1 to 60. If the model train is 10 inches long, how many feet long is the actual train?
Answers
Answer:
Step-by-step explanation:
um yes..!
The graph makes it appear that there are how many times as many students per teacher at North HS as there are at
West HS?
Student Teacher Ratios at Area High Schools
North RS
East HS
13
West HS
12
14
18
22
a.
b.
10
2 times
3 times
4 times
5 times
C.
d.
Answers
Answer:
5 times
Step-by-step explanation:
Using visual inspection, the bar of North HS is 5 times longer Than the bar of West HS.
The gtids are of equal size, West HS occupies one portion of the grid, while North HS occupies 5 portions of the grid
5 portions / 1 portion = 5
Hence, North HS according to the graph is 5 times West HS
Help (PLATO)
its Algebra
Answers
Answer: The answer is D
Step-by-step explanation:
You add z to the other side then it will cancel out which then it would be (w+z) and then you times it by 2 by both sides which would be 2(w+z) and then you would subtract x from both sides which will be 2(w+z)-x
Hopefully this helps
A box is filled with several party favors. It contains 12 hats, 15 noisemakers, 10 finger traps, and 5 bags of confetti. Let H = the event of getting a hat. Let N = the event of getting a noisemaker. Let F = the event of getting a finger trap. Let C = the event of getting a bag of confetti. Find P(N).
Answers
Answer:
P(N) = 5/14
Step-by-step explanation:
Find P(N) by finding the probability of getting a noisemaker.
There are 42 items in total, and 15 are noisemakers. Find the probability by dividing 15 by 42:
15/42
Simplify:
5/14
So, P(N) = 5/14
2×(4×2-10)³ How do you simplify powers in this?
Answers
Answer:
Step-by-step explanation:
first work what's in the brackets { 4 x 2 -10}^3
{4 x 2-1000}
4 x -998
Explication:
FYI: Use P.E.M.D.A.S
(Parentheses, exponent, multiply or divide, add or subtract)
2(4x2-10)^3
4x2=8
(8 - 10)
2(8-10)^3
8-10=-2
(-2)
2(-2)^3
-2^3=-8
2 (-8)
-16
