The inverse matrix of the given matrix using Gauss-Jordan elimination method is:
[-7, 4, 0 ]
[-1, 0.5, 0 ]
[-0.5, 0.25, 0.5 ]
To find the inverse matrix using Gauss-Jordan elimination, we augment the given matrix with an identity matrix of the same size:
[1, -2, 0 | 1, 0, 0]
[2, -6, 4 | 0, 1, 0]
[0, -1, 3 | 0, 0, 1]
Next, we perform row operations to transform the left side of the augmented matrix into an identity matrix. We start by performing row operations to create zeros below the diagonal entries:
[1, -2, 0 | 1, 0, 0]
[0, 2, 4 | -2, 1, 0]
[0, -1, 3 | 0, 0, 1]
Next, we use row operations to create zeros above the diagonal entries:
[1, 0, 8 | -7, 4, 0]
[0, 1, 2 | -1, 0.5, 0]
[0, 0, 2 | -1, 0.5, 1]
At this point, the left side of the augmented matrix has been transformed into an identity matrix, while the right side has become the inverse matrix:
[1, 0, 0 | -7, 4, 0]
[0, 1, 0 | -1, 0.5, 0]
[0, 0, 1 | -0.5, 0.25, 0.5]
Therefore, the inverse matrix of the given matrix is:
[-7, 4, 0 ]
[-1, 0.5, 0 ]
[-0.5, 0.25, 0.5 ]
By performing the necessary row operations using the Gauss-Jordan elimination method, we have successfully obtained the inverse matrix. The inverse matrix is a useful tool in various mathematical operations, such as solving linear equations and computing transformations.
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The Stock Market Alexander is a stockbroker. He earns 14% commission each week. Last week,
he sold $4,500 worth of stocks. How much did he make last week in commission? If he averages
that same amount each week, how much did he make in commission in 2011?
Por un tubo de 2.5 cm de diámetro fluye agua con una repidez de 20 cm/s ¿Cuál es el valor del flujo y el gasto del agua?
Answer:
El flujo y gasto de agua es aproximadamente 98.175 centímetros cúbicos por segundo.
Step-by-step explanation:
El gasto del agua ([tex]Q[/tex]), medido en centímetros cúbicos por segundo, es el flujo que pasa a través del tubo. La ecuación para determinar el gasto es:
[tex]Q = \frac{\pi}{4}\cdot D^{2}\cdot v[/tex] (1)
Donde:
[tex]D[/tex] - Diámetro del tubo, medido en centímetros.
[tex]v[/tex] - Velocidad del flujo, medida en centímetros por segundo.
Si sabemos que [tex]D = 2.5\,cm[/tex] y [tex]v = 20\,\frac{cm}{s}[/tex], entonces el flujo y gasto del agua es:
[tex]Q = \frac{\pi}{4}\cdot (2.5\,cm)^{2}\cdot \left(20\,\frac{cm}{s} \right)[/tex]
[tex]Q \approx 98.175\,\frac{cm^{3}}{s}[/tex]
El flujo y gasto de agua es aproximadamente 98.175 centímetros cúbicos por segundo.
Jordan bought 3 bags of chips and 4 bars of chocolate and paid $7.25. Diego bought 2 bags of chips and 3 bars of chocolate and paid $5.25. What is the cost of a bag of chips and a bar of chocolate?
Answer:
Step-by-step explanation:
Choose ALL the angles with a measure less that 90 degrees.
Answer:
Top left Top middle Bottom Left Bottom right
Step-by-step explanation
If the angle makes an "L" it is a 90 degrees angle or a right angle
If the angle makes a "V" it is less than 90 degrees or an acute angle
If the angle makes a "Stretched out V" it is more than 90 degrees or an obtuse angle
The option that represents the acute angle will be option A, option B, option D, and option F.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
The types of angles are as follows:
If the angle is less than 90° then the angle is known as an acute angle.If the angle is equal to 90° then the angle is known as a right angle.If the angle is more than 90° then the angle is known as an obtuse angle.Then the option that represents the acute angle will be option A, option B, option D, and option F.
More about the angled link is given below.
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Solve the equation. 8| n | − 1 = 15
A.n=2
B.n=2 or n=-2
C.n=8 or n=-8
D. No solution
Answer:
8n=15+1
8n=18
divide both sides by 8
n=2 A
Hello
I have to write at least 20 words to say hi.
Exponent shown below
[tex]tan(0)=\frac{5\sqrt{20} }{11}[/tex]
Answer:
0.035°
Step-by-step explanation:
We need to find the value of [tex]\theta[/tex] for the given expression. So,
[tex]\tan\theta=\dfrac{5\sqrt{20}}{11}[/tex]
or
[tex]\theta=\tan^{-1}\tan\left(\frac{5\sqrt{20}}{11}\right)\\\\=-2.0083\ radian[/tex]
Or we can write as :
[tex]\theta=0.035^{\circ}[/tex]
So, the value of [tex]\theta[/tex] is equal to 0.035°.
This is a short answer question.
Describe what the graph and equation look like for each of the parent functions.
Answer:
there you go there's your answers
Step-by-step explanation:
→A parent function is the simplest function of a family of functions. of this form is y = x2. The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II.
€xample→For example, you can simplify "y=2*sin(x+2)" to "y=sin(x)" or "y=|3x+2|" to "y=|x|." Graph the result. This is the parent function. For example, the parent function for "y=x^+x+1" is just "y=x^2," also known as the quadratic function.
Help Please is the answer zero? I’m not good with algebra
Answer:
should be 0 because it isnt increasing or decreasing
A population numbers 15,500 and grows at 3.75% per year. Write an exponential model for the growth of this population.
Answer: [tex]f(x)=15500(1.0375)^x[/tex]
Step-by-step explanation:
The exponential model for growth is given by :-
[tex]f(x)=A(1+r)^x[/tex], where A = initial value , r = growth rate (in decimal), x = time (in years).
Given: A= 15,500 r= 3.75% = 0.0375
The exponential model for the growth of this population will be :
[tex]f(x)=15500(1+0.0375)^x\\\\\Rightarrow\ f(x)=15500(1.0375)^x[/tex]
hence, the required model: [tex]f(x)=15500(1.0375)^x[/tex]
The range for the set of data represented by the following box-and-whisker plot is 8.
Answer:
TrueStep-by-step explanation:
The range is the difference between the lowest and the highest values of the set:
19 - 11 = 8The answer is TRUE
Answer:
true
Step-by-step explanation:
The price of a plain bowl plus the price
of
extra ingredients equals $
Answer:3,13
Step-by-step explanation:the price of the bowl is 10$ then you add 3 extra ingredients for a dollar each 10+3=13
Answer:
3,13
Step-by-step explanation:
Mr. Berger assigned the following system of equations to be solved for homework.
2 x minus 3 y = negative 12. 4 x + y = negative 10.
Which is the x-coordinate of the correct solution?
x = negative 3
x = negative one-fifth
x = StartFraction 9 Over 7 EndFraction
x = 2
Answer:
x=-3
Step-by-step explanation:
2 x - 3 y = -12.
4 x + y = -10.
Answer:
X=3
Step-by-step explanation:
Trust me ;))
Pls help FAST I’m giving brainliest
Please help..........
Maybe try
[tex] \frac{z - y}{x} [/tex]
If that doesn't work, tell me.
An eagle is flying at an altitude of 280 feet. The angle of depression from the eagle to a mouse on the ground is 15º. What is the direct line distance from the eagle to the mouse? Round answer to the nearest thousandth
Answer:
Step-by-step explanation:
X = distance between eagle and mouse.
sin(15°) = 280/x
X = 280/sin(15°) = 1,081.837 ft
Tyrone went to a basketball game and brought a jersey that was on sale at a 30% discount. He also bought a hat that cost $37.89. Tyrone spent a total of $83.39.
Help me please :)....
Answer:
a = 6, b = 12, c = 18, d = 12
Step-by-step explanation:
What is the value of x? 5 + 1/5x = 5
Answer:
x = 0
Step-by-step explanation:
5 + 1/5x = 5
Subtract 5 from both sides.
1/5x = 0
Divide both sides by 1/5
x = 0
I hope this helps!
can someone answer this for me please and thank you !!
Answer:
gfcdxgstez5xdyrfctugv-
_=+86545
Step-b57645745y-step explanation:
uygtf57d4ftv
The price of a television is $567.31. The state sales tax rate is 8.3%.
What is the total cost of the television?
that in the image could be your answer but i rlly dont know thats the way I was taught
PLEASE HELP WILL MARK BRAINLIEST!!!
Select all that are equivalent to sin∠GFH
Answer:
I think sin<GEJ IS equivalent to sin∠GFH
All that are equivalent to sin∠GFH is
D) cos(<EGJ)
"Corresponding angles"sin(<GEJ)cos(<FGH)cos(<EGJ)
From the image JE and HF are parallel.
So angle GFH and angle GEJ are corresponding angles.
So they are equal.
so, sin(<GFH) = sin(<GEJ).
From triangle GFH, <GFH+<FGH = 90.
So, sin(<GFH) =cos(<FGH).
Again <FGH = <EGJ.
So, sin(<GFH) =cos(<EGJ)
All that are equivalent to sin∠GFH is cos(<EGJ).
Thus, the correct answer is D.
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The cactus grill has decided to run a special on Wednesday night where every table gets 10% off their bill find the total for this table
What is a numerical expression? Give an example.
Answer:
Step-by-step explanation:
The term numerical expression is made up of two words, numerical meaning numbers, and expression meaning phrase. ... A numerical expression in mathematics can be a combination of numbers, integers combined using mathematical operators such as addition, subtraction, multiplication, or division.
is 3+5(9+2n)equal to48+5n
Mike's car holds 14 2/5 g of gas, averages 20mpg. About how far can Mike's travel if his tank is 1/4 full?
Solution :
It is given that :
The car of Mike's can hold = [tex]$14 \frac{2}{5}$[/tex] g of gas.
[tex]$=\frac{72}{5}$[/tex] g of gas
∴ [tex]$=\frac{1}{4} $[/tex] th of [tex]$\frac{72}{5}$[/tex] g of gas is [tex]$=\frac{1}{4} \times \frac{72}{5}$[/tex]
[tex]$=\frac{18}{5}$[/tex] g of gas
The average distance that the car can travel when the tank is full is = 20 mpg
∴ In [tex]$\frac{72}{5}$[/tex] g of gas, the car travels = 20 mpg
In 1 g of gas, the car travels = [tex]$20 \times \frac{5}{72} $[/tex] mpg
So in [tex]$\frac{18}{5}$[/tex] g of gas, the car travels = [tex]$20 \times \frac{5}{72} \times \frac{18}{5} $[/tex] mpg
= 5 mpg
(3x +7x² + 2x + 3) + (x + 1)
Answer:
=7x2+6x+4
Step-by-step explanation:
3x+7x2+2x+3+x+1
Combine Like Terms:
=3x+7x2+2x+3+x+1
=(7x2)+(3x+2x+x)+(3+1)
=7x2+6x+4
Answer:
=7x2+6x+4
The mid point of a given line segment must lie on the given line segment
true or false
in a week 13 hens laid 78 eggs what is the unit rate for eggs per hen?
Answer:
6 eggs per hen
Step-by-step explanation:
78/13=6 eggs per hen