To solve the system of linear equations, we can represent the given system in matrix form as:
A * X = B
where A is the coefficient matrix, X is the column vector of variables (x, y, z), and B is the column vector of constants on the right-hand side.
The coefficient matrix A is:
A = [tex]\left[\begin{array}{ccc}3&1&-1\\12&-3&1\\2&-1&-1\end{array}\right] \\[/tex]
The column vector B is:
B = [tex]\left[\begin{array}{ccc}4\\-4\\8\end{array}\right][/tex]
To find the inverse matrix A⁻¹, we can use the formula:
A⁻¹ = (1 / det(A)) * adj(A)
where det(A) is the determinant of matrix A, and adj(A) is the adjugate of matrix A.
The determinant of matrix A can be calculated as follows:
det(A) = 3 * (-3) * (-1) + 1 * 1 * 2 + (-1) * 12 * (-1) = -3 + 2 + 12 = 11
Next, we need to find the adjugate of matrix A:
adj(A) = [tex]\left[\begin{array}{ccc}-2&1&-3\\11&3&11\\11&-3&-3\end{array}\right][/tex]
Now, we can calculate the inverse matrix A⁻¹:
A⁻¹ = (1 / 11) * adj(A) = [tex]\left[\begin{array}{ccc}-2/11&1/11&-3/11\\11/11&3/11&11/11\\11/11&-3/11&-3/11\end{array}\right][/tex]
Finally, we can solve for X by multiplying both sides of the equation by A^-1:
X = A⁻¹ * B = [tex]\left[\begin{array}{ccc}-2/11&1/11&-3/11\\11/11&3/11&11/11\\11/11&-3/11&-3/11\end{array}\right] * \left[\begin{array}{ccc}4\\-4\\8\end{array}\right][/tex]\
Performing the matrix multiplication, we get:
X = [tex]\left[\begin{array}{ccc}1\\-1\\-3\end{array}\right][/tex]
Therefore, the solution to the given system of linear equations is:
x = 1
y = -1
z = -3
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Think about comparing a table to a graph. What steps would you take to determine which of the two has a greater rate of change?
Please help I need this for math!!!Thank you
Q1: What is the measure of angle one?
Answer:
34
Step-by-step explanation:
omg please don't listen to the other person it's 34 bc if you look at the angle under 2 it's 34 so that's your answer for one
Uhhh someone plz help me plz
Answer:
The number 3.97 is very close to the whole number 4. Therefore, the difference of 4.3 - 3.97 is about 0.33. So, the difference of 4.3 - 3.97 is less than 1.
Remember: The farther the number is to the right, the smaller it becomes.
Ex. 0.10 is greater than 0.100 since the number is shorter and closer to the ones/whole number spot.
Hope this Helps!:)
What is the measure of angle R? *
7 points
R
(10n + 19)"
(12n - 4)
S
Answer:
(10n + 19) (12n - 4)º ... The midsegment of a trapezoid is parallel to each base and its measure is one half the ...
Missing: pointsR( S
Step-by-step explanation:
A closed plain forgive with all sides congruent and all angles congruent is called a
Answer:
Polygon. A closed plane figure for which all sides are line segments. The name of a polygon describes the number of sides. A polygon which has all sides mutually congruent and all angles mutually congruent is called a regular polygon.
please help___________
What is the mean of the following data set?
25, 34, 33, 41, 19, 20, 25, 22, 30, 29, 34, 39
A: 29.5
B:29.25
C:29.75
Answer:
B
Step-by-step explanation:
After adding them all together, we end up with 351. There are 12 numbers, so we do 351/12, getting 29.25.
determine Sn given the series: 45 - 56 + 67 - 78 + 89
- 100 + ..... - 342
The given series is an alternating series with a pattern of adding and subtracting consecutive terms. To determine Sn, we need to find the sum of the first n terms of the series. Therefore, the sum of the series is -13,365.
In the given series, each term is obtained by adding 11 to the previous term and then changing its sign. We can observe that the first term is positive (45), the second term is negative (-56), the third term is positive (67), and so on.
To find Sn, we need to determine the number of terms in the series and then calculate the sum. The series ends with -342, so we need to find the position of -342 in the series.
To do this, we can subtract 45 from -342 and divide the result by 11 to find the number of terms. (-342 - 45) / 11 = -297 / 11 = -27. Therefore, the series consists of 27 terms.
To find the sum of the first 27 terms, we can use the formula for the sum of an arithmetic series: Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term.
Using the formula, we can calculate Sn as follows: Sn = (27/2)(45 - 342) = (27/2)(-297) = -13,365.
Therefore, the sum of the series is -13,365.
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5 x 2 y = 5 3 x - y = 14 which of the following equations is not a result of solving the system of equations by addition?
The equation "6x + y = 29" is not a result of solving the given system of equations by addition.
To solve a system of equations by addition, we aim to eliminate one variable by adding the equations together. Let's analyze the given system of equations:
Equation 1: 5x + 2y = 5
Equation 2: 3x - y = 14
To eliminate the y variable, we can multiply Equation 2 by 2 and add it to Equation 1:
2(3x - y) = 2(14)
6x - 2y = 28
Adding this modified Equation 2 to Equation 1, we get:
(5x + 2y) + (6x - 2y) = 5 + 28
11x = 33
x = 3
Substituting the value of x into either of the original equations, we find that y = -1. Therefore, the solution to the system of equations is x = 3 and y = -1.
Now, let's verify the options to see which equation is not a result of solving the system by addition:
A) 11x = 33 - This equation is derived from adding the two equations together.
B) 6x + y = 29 - This equation is derived from substituting the values of x and y into one of the original equations.
C) 2y = 2 - This equation is derived from isolating the variable y in Equation 1.
D) x = 3 - This equation is derived from solving for x.
Thus, the equation "6x + y = 29" is not a result of solving the system of equations by addition.
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Simplify 7 - 2(5 - 2x)
Answer:
4 − 3
Step-by-step explanation:
Skip count 89300 forward by 5000
HELPPPPPPPPP
What is the value of x in the figure at the right?
Answer:
x=30
HOPE THIS HELPS
-Todo <3
Step-by-step explanation:
60=2x
/2 /2
30=x
can someone please help me with this question?
Answer:
your answer will be 70 have a nice day:)
Step-by-step explanation:
43+27=70
Answer: 18
Step-by-step explanation:
To answer this question you have to add all the number and however many over 100 there is that how many like both of the teams so 27 + 48 + 43 = 118
then you take 100 away from 118 and you get 18
pls help i’m so confused omg!!
Answer:
C or B
Step-by-step explanation:
Answer:
Your answer is A.
Step-by-step explanation:
You can count the arrow lines as the 2s. Such as, 2, 4, 6, 8 and 10.
So, the line 'x' is being divided by how many lines touching it.
Therefore, it is 1.
Then you add x and 6, the number which the line is ending with.
Your final answer is, F(x) = 1
x+6
Hope this helped!
Thomas loaned $6,250 to Cameron at a simple interest rate of 4.12% p.a. for 2 years and 6 months. Calculate the amount of interest charged at the end of the term. Round to the nearest cent
The amount of interest charged at the end of the term is approximately $644.75.
To calculate the amount of interest charged at the end of the term, we can use the simple interest formula:
Interest = Principal * Rate * Time
Principal = $6,250
Rate = 4.12% = 0.0412 (decimal form)
Time = 2 years + 6 months = 2.5 years
Plugging in these values into the formula, we have:
Interest = $6,250 * 0.0412 * 2.5
Calculating this expression:
Interest = $6,250 * 0.0412 * 2.5 = $644.75
Therefore, the amount of interest charged at the end of the term is $644.75 (rounded to the nearest cent).
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For the following estimated CAPM (Capital Assets Pricing Model) model for stock XYZ, stock XYZ return = 0.003 + 1.38 (market return) what is the financial interpretation of 1.38 inn nauation of X and Y
In the Capital Asset Pricing Model (CAPM), the coefficient of the market return is known as the stock’s beta. Beta measures the stock’s systematic risk, or its sensitivity to market movements.
what is the financial interpretation of 1.38 inn nauation of X and YA beta of 1 indicates that the stock’s return moves with the market. A beta greater than 1 indicates that the stock is more volatile than the market, while a beta less than 1 indicates that the stock is less volatile than the market.
In this case, the estimated CAPM model for stock XYZ has a beta of 1.38. This means that stock XYZ is expected to be more volatile than the market. For every 1% increase in the market return, stock XYZ’s return is expected to increase by 1.38%. Conversely, for every 1% decrease in the market return, stock XYZ’s return is expected to decrease by 1.38%.
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help would be really nice here just a bit lost
Enteros 15+18 resultado
Is x = 5 a solution to the equation 19 - x = 14?
Answer:
Yes
Step-by-step explanation:
Test the equation by substituting 5 in for x:
19- 5 =14
14=14
TRUE
If I helped, a brainliest would be greatly appreciated!
Answer: If you replace x with 5 then 19-5=14
Step-by-step explanation:
X Kawika had to raise the flag this morning. The 15 ft flag pole casted at
shadow with the ground at a 35° angle. What is the length of the
shadow? (Round answers to the nearest tenth) *
Answer with JUST THE NUMBER, without writing out the unit after the number.
Someone please help me.
Answer:
with what life
Step-by-step explanation:
Emily is making a flag with the dimensions shown. What is the minimum amount of material needed for the flag?
9514 1404 393
Answer:
B 80 square inches
Step-by-step explanation:
The area of a parallelogram has the same formula as the area of a rectangle:
A = bh . . . . . b is the base; h is the height
A = (10 in)(8 in)
A = 80 in²
The minimum amount of material needed is 80 square inches.
Answer:
The answer is 80
Step-by-step explanation:
Hope this helps
Arthur is interested in the effects of sleep deprivation usage on number of calories consumed. He asks a group of 20 college students to spend the night in the sleep lab under one of these conditions: no sleep, 2 hours of sleep, 4 hours of sleep, 6 hours of sleep, or 8 hours of sleep. Arthur measures how many calories are consumed by the students in the sleep lab, which is stocked with various food items. After collecting these data, Arthur performs an ANOVA and finds that he can reject the null hypothesis. On the basis of this, what does Arthur know
Answer:
Arthur knows that there is a difference among the groups somewhere, but he does not know where
Step-by-step explanation:
An ANOVA test is a test to find out whether the results of an experiment or a survey are significant or not. ANOVA test helps the researcher or the experimenter to decide whether they reject the null hypothesis or accept the alternate hypothesis in the experiment. In ANOVA test, the experimenter wants to find if there is a difference between them or not.
In the context, Arthur is doing a study and he wishes to find out effect of a sleep deprivation on the number of the calories that people consumed. He collects some data from his subject group from the sleep lab and after running the ANOVA test, he finds out that he can reject the null hypothesis. So on this basis, Arthur knows that there is some basic difference among the members of the group somewhere, but he does not know where actually the difference is.
Seriously, somebody please help me! I've been asking all day, someone actually help me and not just halfassly answer it for points.
Answer:
9. A = Length by Width
Length = x
Width = 12x - 6y
A = x(12x - 6y)
A = 12x² - 6xy
10. A = ½bh
h = 2ab
A = ½(b)(2ab)
A = ab²
Solve for n. 2n+3/4n = 3/4
Answer: n=3/11
Step-by-step explanation:
1. You want to simplify both sides of the equation.
2n+3/4n=3/4.
(2n+3/4n)=3/4 (combine like terms).
11/4n=3/4.
2. Multiply both sides using 4/11.
(4/11)x(11/4n)=(4/11)x(3/4)
3. You get your answer which is n=3/11.
Hoped I help :)
Find –(–14).
–14
–4
4
14
Answer:
bhjtijo3
Step-by-step explanation:
Answer:
Step-by-step explanation:
D. 14
HELP WILL MARK BRAINLIEST
Multiplication and division questions that equal -8?
And another one for -15?
Pls and thank u <3
For negative 8
1. -4 x 2
2. -48 ÷ 8
For negative 15
1. -5 x 3
2. -60 ÷ 4
( Sorry if they aren't complex enough)
If 40% of a number is 14, find 20% of that number.
Answer:
7
Step-by-step explanation:
Because half of 40% is 20%
So 14%2 = 7
WORTH 25 POINTS! HELP PLZZZZZZ
Answer:
I pretty sure its A
Step-by-step explanation:
Answer:
The answer on the top, 32 * __ = 3616
Step-by-step explanation:
3616/32 = __
multiply by 32
3616 = 32 * __ or 32 * __ = 3616