Solve a One-Step Matrix Equation
Solve the matrix equation:
[X1
X2]
+
[-2
5]
=
[8
15]
X1 =?
X2 =?
![Solve A One-Step Matrix EquationSolve The Matrix Equation:[X1X2]+[-25]=[815]X1 =?X2 =?](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/aO9tADd8xyy6HCVFWphJnLBNcnEOPIvc.png)
Answers
Answer: 10 , 10
Step-by-step explanation:
By solving one-step matrix equation, we get [tex]x_{1} =10[/tex], [tex]x_{2}=10[/tex].
What is one-step matrix equation?A matrix equation is an equation of the form Ax = b , where A is an m × n matrix, b is a vector in R m , and x is a vector whose coefficients x 1 , x 2 ,..., x n are unknown.
A one-step equation is an algebraic equation you can solve in only one step. You've solved the equation when you get the variable by itself, with no numbers in front of it, on one side of the equal sign.
Given one-step matrix equation
[tex]\left[\begin{array}{c}x_{1} &x_{2} \end{array}\right]+\left[\begin{array}{c}-2 &5 \end{array}\right] =\left[\begin{array}{c}8 &15 \end{array}\right][/tex]
By adding the matrix the respective equations are:
[tex]x_{1} +(-2)=8[/tex].....(1)
[tex]x_{2} +(5)=15[/tex].....(2)
By solving [tex]x_{1} +(-2)=8[/tex]
⇒ [tex]x_{1} -2=8[/tex]
Add 2 on the both sides of the equation
⇒ [tex]x_{1}-2+2 =8+2[/tex]
⇒ [tex]x_{1} =8+2[/tex]
⇒ [tex]x_{1} =10[/tex]
Solving equation 2
[tex]x_{2} +(5)=15[/tex]
⇒ [tex]x_{2} +5=15[/tex]
Subtract 5 on both sides of the equation
⇒ [tex]x_{2} +5-5=15-5[/tex]
⇒ [tex]x_{2}=10[/tex]
By solving one-step matrix equation, we get [tex]x_{1} =10[/tex], [tex]x_{2}=10[/tex].
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Related Questions
The amount of money in Mark's bank account after x months is given by the function
f(x) = 1000 - 200x. Select all the true statements.
Pick up to 2 answers.
A. The account began with $1000.
B. The account began with $200.
C. Mark withdraws $1000 each month.
D. Mark withdraws $200 each month.
E. Mark deposits $200 each month.
Answers
Mx is the rate of change
B is your starting point
Started with 1000, A
-200 is the rate of change, D
Help plz that would be great
Answers
Answer:
-8
Step-by-step explanation:
I got 8 from my calculations so im sure thats the anwser
PLEASEEEEE HELP ME IF YOU GET THIS QUESTION!!
Answers
Answer:
one and a quarter mile
please can i have brainliest
can someone please help me with this question??
Answers
Answer:
2nd one
Step-by-step explanation:
Use numerals instead of words.
The Smiths are sending out a batch of holiday cards. Emily signed 2/5 of the cards. Then Josh signed 1/9 of the remaining cards. Tatiana signed 20% of what Josh had left.
If there were 75 cards in all, how many cards are left to be signed?
There are
cards yet to be signed.
Answers
Answer:
25 because is the steep between card
Answer:
32
I hope this helps
The perimeter of a square is 52 cm.
Calculate the area of the square.
Answers
Answer:
A = 169cm²
Step-by-step explanation:
Answer:
A=169cm²
Or
A=26.2in²
or
A=0.18ft²
Step-by-step explanation:
Let v(t) = 1/π + sin(3t) represent the velocity of an object moving on a line. On the interval [π/2, π], what is the velocity when the acceleration is 3?
Answers
Answer:
[tex]\displaystyle \frac{1}{\pi}\approx0.318[/tex]
Step-by-step explanation:
The velocity of an object moving on a line is given by the function:
[tex]\displaystyle v(t)=\frac{1}{\pi}+\sin(3t),\; \frac{\pi}{2}\leq x\leq\pi[/tex]
And we want to determine the velocity of the object when its acceleration is 3.
So, we will need to determine our acceleration function. Remember that acceleration is simply the derivative of speed. Therefore, our acceleration function a(t) will be:
[tex]\displaystyle a(t)=v^\prime(t)=\frac{d}{dt}[\frac{1}{\pi}+\sin(3t)][/tex]
Differentiate. We will use the chain rule on the second part. Hence, our acceleration function is:
[tex]\displaystyle a(t)=3\cos(3t)[/tex]
We want to find the velocity when the acceleration is 3.
So, let’s set a(t) equal to 3 and determine at what time t our function equals 3. Hence:
[tex]3=3\cos(3t)[/tex]
Divide both sides by 3:
[tex]\cos(3t)=1[/tex]
Take the inverse cosine of both sides.
Remember that cosine is 1 for every 2π. Hence:
[tex]3t=2\pi n[/tex]
Where n is an integer.
Divide both sides by 3. Therefore, our solutions are:
[tex]\displaystyle t=\frac{2\pi n}{3}[/tex]
However, our domain was π/2≤x≤π.
Hence, we can test values of n such that it is within our domain.
Testing for n=0, 1, and 2, we see that:
[tex]\displaystyle t=0, \, t=\frac{2\pi}{3},\, t=\frac{4\pi}{3}...[/tex]
However, the only solution that is within our domain is the second solution.
Hence, the acceleration is 3 when the t is 2π/3.
Therefore, our velocity at that time t is:
[tex]\begin{aligned}\displaystyle v(\frac{2\pi}{3})&=\frac{1}{\pi}+\sin(3(\frac{2\pi}{3}))\\ &=\frac{1}{\pi}+\sin(2\pi)\\&=\frac{1}{\pi}+0\\&=\frac{1}{\pi}\approx 0.318\end{aligned}[/tex]
Please answer asap. thank you
A car drives 10 m/s. How long will it take the bus to drive 70 meters?
Answers
Answer:
7 Seconds
Step-by-step explanation:
Bruhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Answer:
It will take 7 seconds
Step-by-step explanation:
The answer is 7 because 10 multiplied by 7 is 70.
A barrel of 20 apples has 2 rotten apples and 18 good apples. 7 apples are selected at random from the barrel. What is the expected number of good apples selected
Answers
Answer:
Expected value = 7 x 0.9 = 6.3
Step-by-step explanation:
Probability of getting a good apple is 18/20 = 0.9
Probability of getting a bad apple is 2/20 = 0.1
This follows a binomial distribution because either you get a good apple or a bad apple.
The expected value of a binomial distribution is given as n*p where n is number of trials and p is the probability of success.
In this case our number of trials is 7 and the probability of success is 0.9, since the trials are for getting good apples.
Hence
n = 7
p = 0.9
Expected value = 7 x 0.9 = 6.3
Use the Distributive Property to write an equivalent expression. 20 + 24g A. 4 (5 + 6g) B. 20 (1 + 4g) C. 5 (4 + 6g)
Answers
Answer:
A.
Step-by-step explanation:
4(5+6g)
4*5+4*6g
20+24g
The equivalent expression for the given expression is 4(5+6g). Therefore, option A is the correct answer.
The given expression is 20+24g.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression can be simplified as follows:
20+24g
= 4(5+6g)
The equivalent expression for the given expression is 4(5+6g). Therefore, option A is the correct answer.
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I don’t get this please help me
Answers
Explanation
(Brand A)24 diapers is 0.29¢ per diaper
(Brand B) 50 diapers is 0.27¢ per diaper
I need help asappp!!!
Answers
The measurement of the complement of an angle is 40° more than the angle. What is the supplement for the angle?
Answers
convert 15 °C to Fahrenheit, use the formula F = 9/5 C + 32
Answers
Answer:
59
9/5(15)+32 =59
Step-by-step explanation:
A poll asked 325 people whether they would support a certain amendment to the state constitution. 58% of people said they would.
Write a 95% confidence statement.
Answers
In 2011, Japan experienced an intense earthquake with a magnitude of 9.1 on the Richter scale. In 2003, Japan experienced another intense earthquake that measured 8.3 on the Richter scale. Compare the intensities of the two earthquakes. Use a logarithmic model to solve. Round to the nearest whole number.
Answers
Answer:
The intensity of the 2011 earthquake was about 6 times the intensity of the 2003 earthquake.
Step-by-step explanation:
To compare the intensities, we first need to convert the magnitudes to intensities using the log formula. Then we will set up a ratio to compare the intensities.
Convert the magnitudes to intensities and write them in exponential form.
R=logI
2011 earthquake:
9.1I=logI=109.1
2003 earthquake:
8.3I=logI=108.3
Form a ratio of the intensities.
intensity for 2011intensity for 2003
Substitute in the values and divide by subtracting the exponents to find
109.1108.3100.8≈6.
The intensity of the 2011 earthquake was about 6 times the intensity of the 2003 earthquake.
Your answer:
The intensity of the 2011 earthquake was about 15 times the intensity of the 2003 earthquake.
The intensities of the two earthquakes will be 6.3095.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
In 2011, Japan encountered a serious quake with an extent of 9.1 on the Richter scale. In 2003, Japan encountered another extraordinary seismic tremor that deliberate 8.3 on the Richter scale.
The intensity of the earthquake is given as,
㏒ (I₁ / I₂) = M₁ - M₂
㏒ (I₁ / I₂) = 9.1 - 8.3
Simplify the equation, then we have
㏒ (I₁ / I₂) = 9.1 - 8.3
㏒ (I₁ / I₂) = 0.8
Take anti log, then we have
(I₁ / I₂) = 6.3095
The intensities of the two earthquakes will be 6.3095.
More about the Algebra link is given below.
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If f(x) = 3x + 2, what is f(5)?
Answers
Answer:
The 5 in the () is what the x is
Step-by-step explanation:
3(5)+2=17
Answer:
Step-by-step explanation:
Replace the X with 5
3(5)+2
Follow PEMDAS
so multiplication goes first
15+2
Then add
17
True or False
1. We find the x-intercepts of a function fby evaluating f(0).
2. The solutions of a function are the first coordinates of the
x-intercepts of the function.
3. We can use completing the square to solve any quadratic equation.
4. The function f(x)=-3(x+4)2-5 has a maximum value.
Answers
2. True
3. True
4. True
Help me please *an image is attached*
Answers
Answer:
the height it is at is 95 meters
How much warmer is 82 than -40?
Answers
Answer:
-42 degrees
Step-by-step explanation:
-40-82=-42
The owner of an apartment building can rent all 50 apartments if she charges $600 per month, but she rents one fewer apartment for each $20 increase in monthly rent. Identify the maximum revenue for this function?
Answers
Answer:
30,000
Step-by-step explanation:
If she gets all 50 at 600 per month, 50x600 is 30,000.
I hope this helped!
-25+t/z greater these or =to 50
Answers
Answer:
=to 50
Step-by-step explanation:
Find the area of the trapezoid below.
4 cm
3 cm
8 cm
Answers
Answer:
4 + 8 / 2 * 3 = 18
4 + 8 = 12
12 / 2 = 6
6 * 3 = 18
Step-by-step explanation:
*Hope this helps*
Is there anyone here who does Calvert or Odessy?
I was quite behind on my assignments, and, somehow, I go to catch up and they've been completed or something. It says I'm 100% on pace, and I know for a fact that I wasn't. What happened?
Answers
what happen is there is a glitch probably
yes this is what happened to me. if u get too far behind they will change the due dates to your "pace" and make it easier for you.
find the slope please help!
Answers
Answer:
-3/4
Step-by-step explanation:
Get the coordinates of the two points and use the slope formula to find the slope.
We'll call the points point A and point B.
Point A's coordinates are (-3,1) and point B's coordinates are (1,-2)
Now, plug the numbers into the slope formula
Slope formula is: y2-y1/x2-x1
-2-1/1--3
-3/4
GIVING BRAINLIEST PLEASE HELP!!!!!!!!!!!!!!!! Calculate the correlation coefficient of the following data: (1,1) (2,3) (3,6) (4,2) (7,9) (8,6) (10,7)
Answers
Answer:
The value of R is 0.7482.
Step-by-step explanation:
X Values
∑ = 35
Mean = 5
∑(X - Mx)2 = SSx = 68
Y Values
∑ = 34
Mean = 4.857
∑(Y - My)2 = SSy = 50.857
X and Y Combined
N = 7
∑(X - Mx)(Y - My) = 44
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = 44 / √((68)(50.857)) = 0.7482
r = 0.7482
Sorry if I get this wrong Because not for sure how you need the awnsers I dont know if this is the right way
Mx: 5.000
My: 4.857
Sum: 68.000
Sum: 50.857
sum: 44.000
X Values
∑ = 35
Mean = 5
∑(X - Mx)2 = SSx = 68
Y Values
∑ = 34
Mean = 4.857
∑(Y - My)2 = SSy = 50.857
X and Y Combined
N = 7
∑(X - Mx)(Y - My) = 44
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = 44 / √((68)(50.857)) = 0.7482
Meta Numerics (cross-check)
r = 0.7482
I need help, please
it is do tomorrow
Answers
Answer:
21 millimeters
Step-by-step explanation:
ummmm yes
14.
Find the sum of the expression: 87.75 – 7.25 =
A. 80.50
B. 79.25
C. 80.25
D. 80.80
Answers
Answer:
A
Step-by-step explanation:
87.75-7.25=80.50
Answer:
A. 80.50
Step-by-step explanation:
70% of the 30 sandcastles at Donatello Beach have moats. how many more moats are there
Answers
Answer:
21 moats
Step-by-step explanation:
.70 x 30 = 21
5) Tyra went to the movies and bought a coke for $1.25, popcorn for $4.25 and peanut butter M&Ms for $3. How much did Tyra spend in I