Solve the following system of equations using an inverse matrix. You must also indicate the inverse matrix, A^−1, that was used to solve the system. You may optionally write the inverse matrix with a scalar coefficient.
x−6y=−1
−2x+9y=5
Answers
The solution to the system of equations is x = −7 and y = −1.
Step-by-step explanation:
To solve the given system of equations using an inverse matrix, we can represent the system in matrix form, Ax=B, then find the inverse of matrix A to solve for 'x'.
Given matrix:
\(\left\{\begin{array}{ccc}x-6y=-1\\-2x+9y=5\end{array}\right\)
\(\hrulefill\)
Step 1: Represent the System of Equations in Matrix Form\(\hrulefill\)First, we rewrite the system of equations in matrix for, Ax=B:
\(A = \left[\begin{array}{cc}1&-6\\-2&9\\\end{array}\right], \ x = \left[\begin{array}{cc}x\\y\\\end{array}\right], \ B = \left[\begin{array}{cc}-1\\5\\\end{array}\right]\)
So, Ax=B can be written as:
\(\Longrightarrow \left[\begin{array}{cc}1&-6\\-2&9\\\end{array}\right] \left[\begin{array}{cc}x\\y\\\end{array}\right] = \left[\begin{array}{cc}-1\\5\\\end{array}\right]\)
\(\hrulefill\)
Step 2: Find the Inverse of Matrix A\(\hrulefill\)\(\boxed{\left\begin{array}{ccc}\text{The inverse of a 2x2 matrix,} \ \left(\begin{array}{ccc}a&b\\c&d\end{array}\right), \ \text{is given by:}\\\\\\A^{-1}= \dfrac{1}{ad-bc}\left(\begin{array}{ccc}d&-b\\-c&a\end{array}\right)\end{array}\right}\)
Here,
\(\Longrightarrow A = \left[\begin{array}{cc}1&-6\\-2&9\\\end{array}\right]\)
The determinant ∣A∣ is:
\(\Longrightarrow |A|=(1)(9)-(-6)(-2)=9-12\\\\\\\\\therefore |A|=-3\)
Since the determinant is not zero, A has an inverse, which can be calculated as:
\(\Longrightarrow A^{-1}= \dfrac{1}{-3}\left(\begin{array}{ccc}9&6\\2&1\end{array}\right)\\\\\\\\\therefore A^{-1}=\left(\begin{array}{ccc}-3&-2\\-2/3&-1/3\end{array}\right)\)
\(\hrulefill\)
Step 3: Solve for 'x'\(\hrulefill\)We can solve for 'x' using x=A⁻¹B:
\(\Longrightarrow x = \left(\begin{array}{ccc}-3&-2\\-2/3&-1/3\end{array}\right)\left(\begin{array}{cc}-1\\5\\\end{array}\right)\)
Upon multiplication, we get:
\(\Longrightarrow x = \left(\begin{array}{cc}(-3)(-1)+(-2)(5)\\(-2/3)(-1)+(-1/3)(5)\\\end{array}\right)\\\\\\\\\Longrightarrow x = \left(\begin{array}{cc}3-10\\2/3-5/3\\\end{array}\right)\\\\\\\\\Longrightarrow x = \left(\begin{array}{cc}-7\\-3/3\\\end{array}\right)\\\\\\\\\therefore \boxed{\boxed{x=\left(\begin{array}{cc}-7\\-1\\\end{array}\right)}}\)
Thus, the solution to the system of equations is x = −7 and y = −1.
Related Questions
What is the velocity of the plane that travels 3000km in 5 hours?
Answers
Answer:
600km/h
546.807 fps
0.1666667 km/s
Step-by-step explanation:
Use which ever unit youd want to in this scenereo, I'd use 600km/h
3000 / 5 = 600
Rosa correctly solved 275 = 5. Enter numbers in the boxes to show the equations she could use to solve the problem.
(200 -
) + (50 =
+ (25:
What is 275 /5? Enter the answer in the box.
Answers
275 ÷ 5 = 55 is the equation which correctly represents the division.
To solve 275 divided by 5, Rosa could use the following equations:
275 ÷ 5 = 55
or
275 ÷ 5 = 55 r 0
In the first equation, Rosa directly divides 275 by 5 to get the quotient of 55.
In the second equation, Rosa divides 275 by 5 to get the quotient of 55, with no remainder (represented by the "r 0").
Both equations correctly represent the division of 275 by 5.
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a retailer sold a shirt for rupees 1000 and he made a profit of 25% find the purchased price of a shirt
Answers
Answer:
750 rupees is used to make shirt
250 rupees is profit
Step-by-step explanation:
If the retailer sold the shirt for 1000 rupees and got 25% profit then that means 1/4 is profit and 3/4 is how much the retailer spent to make the shirt.
So 1000 times 3/4 is 750 which is how much the shirt really cost and
1000 times 1/4 is 250 and that is the retailers profit.
Pleaseeee helppp????
Answers
Answer:
1-2
Step-by-step explanation:
ILL GIVE BRAINLIEST TO WHOEVER IS FIRST At the beginning of the week, Paloma opened a new box of 225 coffee creamers. Sixty-four coffee creamers were used during the week. Which equation could be used to find x, the number of coffee creamers left at the end of the week?
A. 64x = 225
B. x + 64 = 225
C. x - 64 = 225
D. 64 - 225 = x
Answers
It wouldn’t be d because the answer would be negative!
A baseball team plays the same opponent six times in a season. The set {0,1,2,3,4,5,6} describes the possible number of wins for the six games.
Set A contains the number of wins when exactly four games are won.
Set B contains the number of wins when at least four games are won.
Which of these statements are true? Choose all that are correct.
The union of set A and B is an empty set
The complement of the union of set A and B is {0,1,2,3} set A
The complement of set B is {0,1,2,3}
The intersection of set A and set B is an empty set
The complement of set B is {1,2,3}
Answers
- The complement of set B is {0,1,2,3}
- The complement of set B is {1,2,3}
Determine the end behavior of f(x) x^3-2x^2-x+2n
Answers
Here, we want to determine the end behavior of the given polynomial
To do this, we need to know the leading coefficient sign and the degree of the polynomial (if even or odd)
As we can see, the leading coefficient is a positive number while the degree of the polynomial is odd
So, we need to evaluate the behavior of a polynomial with a positive leading coefficient and an odd degree
The correct answer here is that;
\(\begin{gathered} As\text{ x }\Rightarrow-\infty\text{ , f(x) }\Rightarrow-\infty \\ \text{and;} \\ as\text{ x}\Rightarrow+\infty\text{ , f(x) }\Rightarrow+\infty \end{gathered}\)Answer:
B trustttttttt
Step-by-step explanation:
Instructions: Find the measure of the indicated angle to the nearest degree.
Answers
Step-by-step explanation:
I don't have a calculator with me right now but I can give you the equation to work out your answer.
cos-1(35/38)
There should be a function of "cos-1" on you're calculator, not just "cos"
hope it helps :)
a factory manufacturing tennis balls determines that the probability that a single can of three balls will contain at least one defective ball is 0.025. what is the probability that a case of 48 cans will contain at least two cans with a defective ball?
Answers
There is about a 33.7% probability that a case of 48 cans will contain at least two cans with a defective ball.
To solve this problem, we can use the binomial distribution. Let's define "success" as getting a can with no defective ball and "failure" as getting a can with at least one defective ball.
The probability of success in one can is:
P(success) = 1 - P(failure) = 1 - 0.025 = 0.975
The probability of failure in one can is:
P(failure) = 0.025
Now, let's define X as the number of cans in a case of 48 that have at least one defective ball. We want to find the probability that X is greater than or equal to 2.
We can use the binomial distribution formula to calculate this probability:
P(X ≥ 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)
P(X = 0) = (0.975)^48 ≈ 0.223
P(X = 1) = 48C1 (0.975)^47 (0.025)^1 ≈ 0.44
where 48C1 is the number of ways to choose one can out of 48.
Therefore, the probability that a case of 48 cans will contain at least two cans with a defective ball is:
P(X ≥ 2) ≈ 1 - 0.223 - 0.44 ≈ 0.337
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pls help
How does 8 × 2 13 compare to 8? Responses
A Greater than 8 because you are multiplying by a number greater than 1.Greater than 8 because you are multiplying by a number greater than 1.
B Greater than 8 because you are multiplying by a number less than 1.Greater than 8 because you are multiplying by a number less than 1.
C Less than 8 because you are multiplying by number less than 1.Less than 8 because you are multiplying by number less than 1.
D Less than 8 because you are multiplying by a number greater than 1.Less than 8 because you are multiplying by a number greater than 1.
Skip to navigation
Answers
A Greater than 8 because you are multiplying by a number Greater than 1.
The expression 8 × 2 13 can be simplified using the order of operations (PEMDAS/BODMAS) which states that we should perform the multiplication before the exponentiation. Let's simplify the expression:
8 × 2 13 = 8 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
Now, we can calculate the value of the expression:
8 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 8 × 8192 = 65536
So, the expression 8 × 2 13 simplifies to 65536.
Comparing this value to 8, we can see that 65536 is much greater than 8. Therefore, the correct response is:
A Greater than 8 because you are multiplying by a number greater than 1.
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Seven years ago, I invested $2,509 in the stock of Salamanca Sleep Systems. Today that investment is worth $10,845. Find the compound annual growth rate for this investment.
Answers
The compound annual growth rate for this investment is approximately 23.259% per year.
What is the compound annual growth rate for this investment?To find the compound annual growth rate (CAGR) for this investment, we use the derived formula from compound interest.
CAGR = (FV/PV)^(1/n) - 1
Where:
FV is the future value of the investment (i.e., the value today) = $10,845PV is the present value of the investment (i.e., the initial investment) = $2,509n is the number of years over which the investment has grown = 7 yearsWe can substitute these values into the above formula:
CAGR = (FV/PV)^(1/n) - 1
CAGR = ( $10,845 / $2,509)^(1/7) - 1
Simplifying the expression inside the parentheses, we get:
CAGR = ( $10,845 / $2,509)^(1/7) - 1
CAGR = 0.232589
Then convert r to R as a percentage
R = r × 100%
R = 0.232589 × 100%
R = 23.259% per year
Therefore, the compound annual growth rate is 23.259% per year.
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Y’all in need help. I can’t not finger it out
Answers
9514 1404 393
Answer:
E, D, A, C, B
Step-by-step explanation:
It is all about rounding.
To estimate the product, round each value to 1 significant figure. For example, 46.7 rounds to 50, and 31.7 rounds to 30. The estimate of the product will be the product of these rounded values: 50·30 = 1500.
__
Top to bottom, the appropriate estimates are ...
E, D, A, C, B
where the right-side choices are given letters A-E, top to bottom.
1,030 at 4% compounded semiannually for 2 years
Answers
Answer: $1114.91
Step-by-step explanation:
The formula for compound interest is
\(A= P(1+\frac{r}{n})^{nt} \\\)
Where
A = final amount
P = initial principal balance (1030 for this)
r = interest rate (0.04 for this)
n = number of times interest applied per time period (2 for this)
t = number of time periods elapsed (2 for this)
\(A= 1030(1+\frac{.04}{2})^{(2)(2)} \\\\A= 1030(1+0.02)^{4} \\A=1030(1.02)^4\\A=1114.905125\)
This rounds up to $1114.91
Classes: are the categories by which data are grouped.true or false
Answers
True. For simpler amount analysis and management, data can be grouped into classes that represent related categories.
Data can be grouped into groups in order to identify patterns, trends, and similarities that can then be utilised to influence decisions. As classes may be used to organise and make data easier to interpret, this can be very helpful when working with huge datasets. Classes can also be used to find outliers and abnormalities in data, which can improve results and offer more precise insights. With classes, data can be processed and analysed more quickly and correctly, enabling more effective decision-making.For simpler analysis and management, data can be grouped into classes that represent related categories. With the process of categorising, data can be divided into smaller, easier-to-manage chunks for easier analysis.
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suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than 97% good parts (h0:and ha:). the test results in a p-value of 0.122. unknown to the manufacturer, the machine is actually producing 99% good parts. what probably happens as a result of the testing?
Answers
As a result of the testing, we end up making a Type II error, by failing to reject H0.
Detailed instructions to reach the conclusion are as follows:
H0: H0: Null Hypothesis: p = 0.97 p > 0.97, alternative hypothesis.
The P-value is 0.102 if 0.05. hence, P-value is greater. As a result, we were unable to rule out the null hypothesis H0.
According to the following rule, if we reject H0, H0 is true for the Type I mistake and Ha is true for the right choice. When H0 is not rejected, Ha is true for a Type II error and H0 is true for the correct judgment.
Type II error is the failure to reject a false null hypothesis, resulting in a Type II error, based on the above and having failed to reject a false null hypothesis. We end up making a Type II error, by failing to reject H0.
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Suppose we are sampling from a population with population mean equal to μ and population standard deviation equal to σ. For large samples (at least 30 observations), the sampling distribution of the sample mean, X¯, has a population mean (i.e., μX¯) equal to
Group of answer choices
σ2n
t
z
μ
σn
Answers
For large samples (at least 30 observations), the sampling distribution of the sample mean, X¯, has a population mean (μX¯) equal to the population mean (μ).
This property is known as the central limit theorem. According to the central limit theorem, when the sample size is sufficiently large, the distribution of sample means will be approximately normal, regardless of the shape of the population distribution. The mean of the sampling distribution of the sample mean will be equal to the population mean.
The formula mentioned in the answer options, σ/√n, represents the standard deviation of the sampling distribution of the sample mean. It is worth noting that the standard deviation of the sampling distribution (σ/√n) decreases as the sample size (n) increases. This means that larger sample sizes tend to result in sample means that are closer to the population mean, indicating greater precision in estimating the population mean.
For large samples (at least 30 observations), the sampling distribution of the sample mean, X¯, has a population mean (μX¯) equal to the population mean (μ). This property is a result of the central limit theorem, which states that the sampling distribution of the sample mean becomes approximately normal with a mean equal to the population mean when the sample size is sufficiently large. The standard deviation of the sampling distribution is given by σ/√n, which decreases as the sample size increases, leading to more accurate estimates of the population mean.
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A company wants to identify which of two production methods has the smaller completion time. One sample of workers is randomly selected and each worker first uses one method and then uses the other method. The sampling procedure being used to collect completion time data is based on _____ samples.
Answers
The sampling procedure being used to collect completion time data in this scenario is based on paired samples or dependent samples.
In paired samples, each observation in one sample is uniquely linked or paired with an observation in the other sample. In this case, the workers are randomly selected, and each worker is assigned to use both production methods, one after the other. The completion time for each worker is measured under both methods, creating paired or dependent observations.
By using paired samples, the company can compare the completion times of the same workers using different production methods. This approach helps eliminate individual differences and other sources of variability among workers, focusing solely on the comparison between the two methods.
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Describe the transformation of f(x) to g(x).
(answers and graph in picture) PLSSSS HELP
Answers
Answer: b
Step-by-step explanation:
becuz now brainliest
The transformation of a function may involve any change. The correct option is A.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k × f(x)Horizontal stretch by a factor k: y = f(x/k)Given the function of f(x) as sin(x), Now it can be seen the graph of the two functions is parallel, but the function f(x) has a y-intercept of 0, while h(x) has a y-intercept of 1. Therefore, we can write,
h(x) = f(x) + 1
The function is shifted up by 1 unit.
Hence, the transformation of the function is correctly described in the first option.
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A student wrote, “if 2 and 8 are factors of a number, then 16 is also a factor of that number.” Is the student correct? Explain your answer.
Answers
No. An example might be 8. 2 and 8 are its factors, but not 16.
The answer is:
No, the student is not correct.
Work/explanation:
If 2 and 8 are factors of a number, then 16 is also a factor of that number.
This statement is not always true. Just because a number is divisible by 2 and 8 doesn't mean it is divisible by 16 as well.
I will use 24 as an example.
24 is divisible by 2 and 8, but it is not divisible by 16.
In the addition problem shown, each letter represents a different digit. If GOD=605, what number does MOVED represent?
Answers
The number does MOVED represent 1110.
How determine what number does MOVED represent?Since GOD=605, we know that D=5. We can now substitute this value of D into the addition problem to get:
GOD+ DOG = MOVED
605+ 506 = 1111
Since M cannot be 0 (otherwise it wouldn't be a 4-digit number), we know that M=1.
We can now subtract 1 from both sides of the equation to get:
604+ 506 = 1110
Now we can see that E+4=10, so E=6. We can also see that O+0=0, so O=0. Finally, we can see that G+D=1, so G=6 and D=5.
Therefore, MOVED = 1110.
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im trying to raise up my grade help plz
Answers
Answer:
Step-by-step explanation:
2x + 2 + 5x + 3 = 180
7x + 5 = 180
7x = 175
x = 25
54÷3² + (2 x 6)-4
Show your solution...
Answers
Step-by-step explanation:
54÷9+12-4
=6+12-4
=14//
Statistics from the past ten years predict that the chance of rain on any single day in April in Asha’s hometown is 41%. If Asha’s birthday is April 10, what is the chance of it not raining on Asha’s birthday?
Answers
Answer:
59% chance
Step-by-step explanation:
Statistics from the past ten years predict that the chance of rain on any single day in April in Asha’s hometown is 41%. If Asha’s birthday is April 10, what is the chance of it not raining on Asha’s birthday?
Asha's birthday in in April. The chance of rain on any single day in April is 41%. So, there is a 41% chance of rain.
But, that's not what the problem is asking for. The problem is asking for the chance of not raining. To solve for this, we use simple algebra.
100%(all of the time) - 41%(how much it happens) = 59%
The 59% is the chance of it not raining on Asha's birthday.
Hope this helps! Happy birthday, Asha!
Solve the system by substitution y=5x-9
-3x+7y=1
Answers
Answer:
{ 62/45,19/9}
Step-by-step explanation:
A researcher selects a sample of 32 participants who are assigned to participate in a study with one group. What are the degrees of freedom for this test
Answers
the degrees of freedom for this test Women found this trait to be important, and this result was significant, t(15)=8.00, p<.05
What is degrees of freedom?Various amounts of data or information can be used to estimate statistical parameters. The degrees of freedom refers to the quantity of independent data points used to estimate a parameter. The number of independent scores that are utilized in an estimate of a parameter, minus the number of parameters used as intermediary stages in the estimation of the parameter itself, is generally considered to be the measure of the degree of freedom of the estimate. The degrees of freedom, for instance, are equal to the number of independent scores (N) minus the number of parameters calculated as intermediary steps, or N 1, if the variance is to be estimated from a random sample of N independent scores.
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if you flew a kite at 2;20 and ended at 3;14 . how many minutes did you fly the kite ?
Answers
Answer:
Step-by-step explanation:
54 minutes
Answer:
54 minutes
Step-by-step explanation:
20+ 40 = 60
40+ 14 = 54 minutes
You flew for 54 minutes.
o please help meeeeeee
Answers
Answer:
20m would be right and correct
What is the completely factored form of this polynomial? 7x4 14x3 − 168x2
Answers
The completely factored form of the polynomial is 7x² (x + 6) (x - 4)
Given,
The polynomial ; 7x⁴ + 14x³ - 168x²
We have to find the complete factored form of this polynomial;
Polynomial;
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Here,
The polynomial is 7x⁴ + 14x³ - 168x²
Now,
Factorize the polynomial using common factors;
That is,
7x⁴ + 14x³ - 168x²
7x² (x² + 2x - 24)
Solve x² + 2x - 24 using quadratic formula;
That is,
\(\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}\) = \(\frac{-2(+-)\sqrt{2^{2} -4*1*-24} }{2*1}\) = \(\frac{-2(+-)\sqrt{4-96} }{2}\) = -2±√-92 / 2
Now,
Solve
-2 + √-92 / 2 = 3.79 ≈ 4
Solve
-2 - √-92 / 2 = -5.79 ≈ -6
Then,
The factors will be (x - 4) and (x + 6)
So,
7x² (x + 6) (x - 4) will be the factored form of the polynomial.
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Ms. Yamato's gross pay is $2644. Her deductions total $548.30.
What percent of her gross pay is take-home pay?
A. 84%
B. 79%
C. 21%
D. 18%
Answers
Thus, the correct Percent response is B) 79%.
what is a percent?Percentage refers to a portion of every hundred. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, it is frequently shown using the percent sign, "%".
If you have 100 apples and distribute 10 of them, for instance, you have distributed 10% of your total apple supply.
We deduct Ms. Yamato's deductions from her gross income to determine her take-home pay:
$2644 - $548.30 = $2095.702.
By dividing her take-home pay by her gross pay and multiplying the result by 100%, we can determine what proportion of her gross pay is taken home:
($2095.70 / $2644) * 100% = 79%
Thus, the correct response is B) 79%.
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mL1 = 26°
and
mL3 = 53°
What is
mL4
Answers
Answer:
53 + 26
=79 is righttherefore m angle 4 is 79