Answers
The solution of the system of linear equations by using the solving method based on the inverse matrix method is x ≈ 0.032, y ≈ 2.458 and z ≈ 1.531.
How to solve a system of linear equations by using matrices
Any system of linear equations can be described by the following linear algebra formula:
[tex]\vec A \cdot \vec X = \vec B[/tex] (1)
Where:
[tex]\vec A[/tex] - Matrix of dependent coefficients.[tex]\vec X[/tex] - Vector column of variables.[tex]\vec B[/tex] - Vector column of independent coefficients.A solution exists if and only if the determinant of the matrix of dependent coefficients does not equals to zero, that is to say:
[tex]det(\vec A) \neq 0[/tex] (2)
If (2) is observed, then the solution of the system is defined by:
[tex]\vec X = (\vec A)^{-1}\cdot \vec B[/tex] (3)
Where [tex](\vec A)^{-1}[/tex] is the inverse of the matrix of dependent coefficients.
Now we proceed to solve the system given:
[tex]\det (\vec A) =-123[/tex]
[tex]\left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}\frac{12}{41} &-\frac{1}{41} &-\frac{9}{41} \\-\frac{7}{123} &\frac{4}{123} &\frac{12}{41} \\-\frac{28}{123} &\frac{16}{123} &\frac{7}{41} \end{array}\right]\cdot \left[\begin{array}{c}7.5\\14\\8.3\end{array}\right][/tex]
[tex]\left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}\frac{13}{410} \\\frac{3023}{1230} \\\frac{1883}{1230} \end{array}\right][/tex]
Therefore, the solution of the system of linear equations by using the solving method based on the inverse matrix method is x ≈ 0.032, y ≈ 2.458 and z ≈ 1.531.
To learn more on inverse matrices, we kindly invite to check this: https://brainly.com/question/4017205
#SPJ2
Related Questions
Work out the mean for the data set below: 207, 208 Give your answer as a decimal.
Answers
Answer:
207.5 is the answer.
Step-by-step explanation:
Add up the numbers (207 + 208) = 415.
Then divide how many numbers, since the problem gives us 2 numbers, you divide 415 by 2.
That is how you find the mean.
the sum of three consecutive multiples of 7 is 44. Find the multiples.
Answers
Answer:
here's the Answer...see that
Step-by-step explanation:
write the slop intercept form of the equations below.
1. slope= 1/4,y intercept = 4
2. y-5=-4(x+1)
Answers
2 is y=x+1
Step-by-step explanation:
Given :-
1. slope= 1/4,y intercept = 42. y-5=-4(x+1)And we need to find the slope intercept form of the line . The slope intercept form of a line is y = mx + c , where m is the slope and c is the y intercept. Substitute respective values ,
Solution 1 :-
[tex]:\implies[/tex] y = mx + c
[tex]:\implies[/tex] y = 1/4 x + 4
[tex]:\implies[/tex] 4y = x + 16
[tex]:\implies[/tex] x - 4y + 16 = 0
Solution 2 :-
[tex]:\implies[/tex] y - 5 = -4( x +1)
[tex]:\implies[/tex] y -5 = -4x -4
[tex]:\implies[/tex] y = -4x +1
Find the slope of the line
Answers
Answer:
Slope = [tex]-\frac{3}{14}[/tex]
Step-by-step explanation:
We know that:
X₁ = -3
Y₁ = 5
X₂ = 11
Y₂ = 2
And the formula of the slope is:
Slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Therefore:
Slope = [tex]\frac{2-5}{11-(-3)}[/tex]
Slope = [tex]-\frac{3}{14}[/tex]
Hope this helps!
Answer:
B, [tex]-\frac{3}{14}[/tex]
Step-by-step explanation:
Use the equation below:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
Insert the values, with the first equation being equation 1 and the second equation being equation 2.
[tex]\frac{2-5}{11-(-3)}\\[/tex]
[tex]\frac{-3}{14}\\[/tex]
[tex]-\frac{3}{14}[/tex]
Find the slope of the lines shown in the graph
Answers
Blue: 4/2
Black: 1/3
please help me and use laws of exponents
Answers
Answer:
1/8*1/3^3
1/8*1/27
1/216
Step-by-step explanation:
just bring 3^-3 down then it will be positive.when u do so it will be1/3^3 .
the cost of a movie ticket depends on your age . the piecewise function below gives the cost of a movie ticket for children , adults , senior citizens .
a) how much does a ticket cost of a movie goer is 22 years old
b) find c(8) and explain it's meaning in context .
Answers
Answer:
8.50
Step-by-step explanation:
The points plotted below are on the graph of a polynomial. Which of the
following x-values is the best approximation of a root of the polynomial?
Check all that apply.
Answers
Answer: -1.1 , 2.4 , 1.51
Step-by-step explanation:
A company manufactures aluminum mailboxes in the shape of a box with a half-cylinder top. The company will make 1863 mailboxes this week. If each mailbox has dimensions as shown in the figure below, how many square meters of aluminum will be needed to make these mailboxes? In your calculations, use the value for , and round up your answer to the next square meter.
Answers
9514 1404 393
Answer:
3433 m^2
Step-by-step explanation:
The total surface area is the sum of the end areas and the lateral area.
The end areas together are a circle of diameter 0.4 m and two rectangles that are 0.4 m by 0.55 m.
End areas = πr^2 + 2LW = 3.14(0.2 m)^2 + 2(0.4 m)(0.55 m)
= 0.1256 m^2 +0.44 m^2 = 0.5656 m^2
The perimeter of the end piece is half the circumference of a 0.4 m circle and three sides of a 0.4 m by 0.55 m rectangle.
P = (1/2)πd + 2L +W = 1/2·3.14·0.4 m + 2(0.55 m) + 0.4 m = 2.128 m
The lateral area of the mailbox is the product of its length and the perimeter of the end piece:
LA = PL = (2.128 m)(0.6 m) = 1.2768 m^2
Then the total surface area of the mailbox is ...
0.5656 m^2 + 1.2768 m^2 = 1.8424 m^2
__
The area of aluminum required for 1863 mailboxes is ...
1863 × 1.8424 m^2 ≈ 3433 m^2
About 3433 square meters of aluminum are needed to make these mailboxes.
last year Patrick paid £2534 for his annual train ticket this year he has to pay £2612 for his annual train ticket. work out the percentage increase in the cost of his train ticket. give your answer correct to 3 significant figures.
Answers
Answer:
Percentage increase in the cost of his train ticket = 3% (Approx.)
Step-by-step explanation:
Given:
Cost of annual ticket paid by Patrick last year = £2,534
Cost of annual ticket paid by Patrick current year = £2,612
Find:
Percentage increase in the cost of his train ticket
Computation:
Percentage increase = [(Current - Base) / Base]100
Percentage increase in the cost of his train ticket = [(2,612 - 2,534) / 2,534]100
Percentage increase in the cost of his train ticket = [(78) / 2,534]100
Percentage increase in the cost of his train ticket = [0.03078]100
Percentage increase in the cost of his train ticket = 3.078
Percentage increase in the cost of his train ticket = 3% (Approx.)
list the reactants when limestone reacts to produce calcium chloride,water and carbondioxide
Answers
Answer:
The completed reaction is
CaCO3 + 2 HCl → (Ca+2 + 2 Cl-)aq + H2O + CO2↑
Help—
Natalie is having a birthday party and it's time to cut
the cake.
Unfortunately she doesn't know how far she needs to
cut from the center to the edge of the cake.
She remembered the baker told her that the
circumference is 46 inches.
How far should Natalie cut?
**NO spaces
**Include units
**Round to the nearest hundredths
Answers
Answer:
7.32 inches
Step-by-step explanation:
The circumference of the circle is 46 inches, and you just have to find the radius... you do the 2xpixr=C backwards. So 2xpixr=46 simplify the expression; 6.28xr=46 then divide... r=46/6.28... Which rounds to 7.32 inches as the radius.
(And yes you are finding the radius if you are finding a line from the middle of the circle to an edge)
I hope this helps :))
Find the greatest common factor of 30 and 105.
1.30
2.15
3. 3
4.5
Answers
What is the median of the data set shown below? {2,4,4, 6, 6, 8, 10, 11, 11, 11} OA) 7 OB) 7.3 OC) 9 OD) 11
Answers
Answer:
The median is going to be 7
The answer choices are:
-17
-8
-2
2
5
8
15
Answers
Answer:
-8, 2, 15
Step-by-step explanation:
For a function each input value can have one and only one output value
Therefor -17, -2, 5, 8 cannot be input values because they already have output values other than 9
Valid inputs are
-8, 2, 15
Find the final amount of money in an account if
$
6
,
700
is deposited at
7
%
interest compounded weekly and the money is left for
10
years.
Answers
Answer:
7064
Step-by-step explanation:
Can someone help me
Answers
Answer:
8
Step-by-step explanation:
If DEF has 2 bottom pieces that are both 6 which is equal to 12 then you just add 4+4 because both of the pieces on ABC are 4 and so 8 is your answer.
Find the mean proportion between 28 and 63.
Answers
Answer:45.5
Step-by-step explanation:
A zoning board in Pine County is interested in estimating the proportion of its residents in favor of larger school zones in that county. A random sample of Pine County residents was selected. All the selected residents were asked, "Are you in favor of larger school zones in your county?" A 95% confidence interval for the proportion of residents in favor of larger school zones in that county was calculated to be 0.48 ± 0.02. Which of the following statements is correct?
A) At the 95% confidence level, the majority of area residents is in favor of larger school zones in that county.
B) In repeated sampling, 95% of sample proportions will fall in the interval (0.46, 0.50).
C) At the 95% confidence level, the estimate of 0.48 is within 0.02 of the true proportion of county residents in favor of larger school zones in that county.
D)In repeated sampling, the true proportion of county residents in favor of larger school zones in that county will fall in the interval (0.46, 0.50).
E) In repeated sampling, 95% of the time, the true proportion of county residents in favor of larger school zones in that county will be equal to 0.48.
Answers
Answer:
C) At the 95% confidence level, the estimate of 0.48 is within 0.02 of the true proportion of county residents in favor of larger school zones in that county.
Step-by-step explanation:
x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.
In this question:
95% CI between 0.48 - 0.02 = 0.46 and 0.48+0.02 = 0.5.
The interpretation is that we are 95% sure that the true population proportion is in this interval, that is, with 95% confidence, the estimate is within 0.02 of the true proportion, and so the correct answer is given by option C.
What two reactants are needed to undergo the process of cellular respiration?
Answers
Answer:
Cellular respiration is the process responsible for converting chemical energy, and the reactants/products involved in cellular respiration are oxygen, glucose (sugar), carbon dioxide, and water. While the exact steps involved in cellular respiration may vary from species to species, all living organisms perform some type of cellular respiration.
Step-by-step explanation:
Suppose that a farmworker was making a banner for a march that has a length of 5x + 1 and a
width of 3 feet. If the area of the banner is equal to 33 square feet, what is the length of the
banner in meters? Round your answer to the nearest hundredth of a meter.
Answers
Answer:
The length of the banner would be 11.00 meters.
Step-by-step explanation:
A student in wildlife management studied trout habitat in the upper Shavers Fork watershed in West Virginia. The springtime water pH of 29 randomly selected tributary sample sites were found to have the following values:
6.2 6.3 5.0 5.8 4.6 4.7 4.7 5.4 6.2 6.0 5.4 5.9 6.2 6.1 6.0 6.3 6.2 5.8 6.2 6.3 6.3 6.3 6.4 6.5 6.6 6.1 6.3 4.4 6.7
Do the data of Exercise 17.8 (above) give good reason to think that the springtime water the tributary water basin around the Shavers Fork watershed is not neutral. (A neutral pH is the pH of pure water, pH 7.)
Step 1:
STATE: Is there evidence that the springtime water pH of the Shavers Fork watershed is not neutral (pH 7)?
FORMULATE: State hypotheses to be tested.
A. H 0 : μ = 7 vs. Ha : μ > 7
B. H 0 : μ = 7 vs. Ha : μ < 7
C. H 0 : μ = 7 vs. Ha : μ ≠ 7
D. H 0 : μ ≠ 7 vs. Ha : μ < 7
Answers
Answer:
C. H 0 : μ = 7 vs. Ha : μ ≠ 7
Since the calculated value of t = -9.462 falls in the critical region t ≤-2.048
We conclude that the springtime water the tributary water basin around the Shavers Fork watershed is not neutral. We accept our alternate hypothesis and reject the null hypothesis.
Step-by-step explanation:
The null hypothesis the usually the test to be performed. Here we want to check whether the water is neutral or not. Neutral water must have a pH of 7 . This can be stated as the null hypothesis. And the claim is treated as the alternate hypothesis that water in not neutral or not having pH= 7
In symbols it will be written as
H0: : μ = 7 vs. Ha : μ ≠ 7
So choice C is the best option for this hypothesis testing.
Let the significance level be 0.05
The degrees of freedom = n-1= 29-1 = 28
The critical value is t ≥ 2.048 and t ≤ - 2.048 for 0.05 two tailed test with 28 df.
The test statistic to use is t- test
t= x- u/ s/√n
The total sum is 170.9 and mean = x= 5.893
The u = 7
And the sample standard deviation is =s= 0.63
Putting the values
t= 5.893-7/0.63/√29
t= - 1.107/0.11699
t= -9.4623
Since the calculated value of t = -9.462 falls in the critical region t ≤-2.048
We conclude that the springtime water the tributary water basin around the Shavers Fork watershed is not neutral. We accept our alternate hypothesis and reject the null hypothesis.
Solve the system of linear equations by substitution 12x+y=−4 y=2x+16
Answers
Answer:
Your solution is (-10/7, 92/7)
Step-by-step explanation:
12x + y = -4
y = 2x + 16
To use substitution, we want to plug one variable's equation into the other equation.
We can see that y is already solved for us. Plug y into the first equation.
12x + y = -4
12x + (2x + 16) = -4
Combine like terms.
14x + 16 = -4
Subtract 16 from both sides.
14x = -20
Divide both sides by 14.
x = -20/14
x = -10/7
Now that we know x, we will plug it into one of the other equations.
y = 2x + 16
y = 2(-10/7) + 16
Multiply.
y = -20/7 + 16
Add.
y = -20/7 + 112/7
y = 92/7
Your solution is (-10/7, 92/7)
Hope this helps!
Find the approximate values of real numbers up-to-three decimal places.
Answers
9514 1404 393
Answer:
√51 ≈ 7.1411313/9900 ≈ 0.133∛971 ≈ 9.902Step-by-step explanation:
The usual rules of rounding apply. If the digit in the 4th decimal place is 5 or more, then 1 is added in the 3rd decimal place. The roots are found using your calculator. The first 4 digits of the repeating decimal are clearly visible already.
a) √51 ≈ 7.141428... ≈ 7.141
b) 0.1326_26 ≈ 0.133
c) ∛971 ≈ 9.90238... ≈ 9.902
_____
Additional comment
The repeating decimal is equivalent to the fraction 1313/9900.
Find the circumference use 3.1; for pie
Answers
Answer:
12.56 m
Step-by-step explanation:
If the radius is 2, the the diameter will be 4 since the diameter = 2 radius. Next, you will multiply 3.14 * 4 to get your answer:
12.56 m
10 cm
a
8 cm
What is the length of the missing leg?
Answers
Answer:
Could it be 9cm? There isnt enough info here to solve the problem.
Step-by-step explanation:
need help with this
Answers
(A) delta h(t) = 32
Step-by-step explanation:
Average rate of change delta h(t) is given by
[tex]delta \: h(t) = \frac{h(b) - h(a)}{b - a} [/tex]
at t = 0, h(0) = 80
at t = 2, h(2) = -16(4) + 64(2) + 80 = 144
Plugging in the numbers
delta h(t) = (144 - 80)/(2 - 0)
= 32
which graph represents this exponential function?
f(x) = 3(2)x -4
Answers
Answer:
show a graph?
Step-by-step explanation:
Help me :) with this i will give brainliest
Answers
Vision: If I lacked my vision it would affect my everyday day life because if I can not see then I won't be able to do everyday day things. For example if I go shopping I wouldn't be able to see the color or style of what it looks like.
Smell: If I lacked smell it wouldn't really affect me but if I were to buy a perfume I wouldn't know if it smells good then if it doesn't I would be the one who would end up smelling bad.
Touch: If I weren't able to pick things up anything my live would be extremely hard because I wouldn't be able to pick up anything.
Taste: If I lost my taste it wouldn't affect me at all I would just be mad I can't taste all my favorite foods.
Hearing: If I couldn't hear it would be hard because if someone were to shout out because a car is coming etc. I wouldn't know and get hit and I don't want that so it would be really hard to not hear.
Hope this helps :)
95/100 can be written as
19/20
13/20
19/10
Answers
Answer:
I quite strongly believe that the first option is the correct one since the following applies,
19/20
20*5=100
and
19*5=95
which in the end is equivalent to 95/100