what is using cramer method x-y=-3
Answers
The Cramer's rule is a method used to solve a system of linear equations. Given a system of two linear equations in two variables:
a1x + b1y = c1
a2x + b2y = c2
where a1, b1, c1, a2, b2, and c2 are constants, and x and y are the variables we want to solve for, we can use Cramer's rule to find the values of x and y.
Cramer's rule states that the solution for x is given by:
x = (det(Ax)) / (det(A))
where Ax is the matrix obtained by replacing the x column in the coefficient matrix with the constants c1 and c2, and det(Ax) is the determinant of Ax.
Similarly, the solution for y is given by:
y = (det(Ay)) / (det(A))
where Ay is the matrix obtained by replacing the y column in the coefficient matrix with the constants c1 and c2, and det(Ay) is the determinant of Ay.
Now, let's apply Cramer's rule to the system of linear equations:
x - y = -3
We can rewrite this equation as:
x + (-1)y = -3
So, the coefficient matrix A and the constants matrix B are:
A = | 1 -1 |
| 0 0 |
B = | -3 |
| 0 |
The determinant of A is:
det(A) = (1 * 0) - (0 * -1) = 0
Since the determinant is zero, Cramer's rule cannot be applied to this system of equations. This means that either the system has no solution or it has infinitely many solutions. In this case, we can see that the equation x - y = -3 represents a line in the xy-plane with slope 1 and y-intercept -3. This line does not intersect with the y-axis, which means that there is no solution to the system of equations.
Therefore, the system of equations x - y = -3 has no solution.
Related Questions
If Charlie invested $1,000 in an account paying 10% compounded monthly, how much will be in the account at the end of 10 years?
Answers
Answer:
Compound Interest Formula: A = P (1 + R/100)^t
P = Principle ($1,000)R = Rate (10%)T = Time (10 years)A = 1000 (1 + 10/100)^10
A = $2593.74
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Select the correct answer.
Which triangles in the diagram are congruent?
70
triangle 1
triangle 2
70°
70
triangle 3
triangle 4
ОА triangle 1 and triangle 2
ОВ. triangle 1, triangle 2, and triangle 3
Ос
triangle 1 and triangle 3
OD. triangle 1, triangle 3, and triangle 4
Reset
Next
Answers
Answer:
triangle 1,3,4 are congruent by S.A.S axiom
write 600 as a product of it's primse factors
Answers
Answer:
2*2*2*3*5*5
or
2^3 *3* 5^2
Step-by-step explanation:
600 = 60*10
These are not prime so keep going, breaking 60 and 10 down
= 6*10 * 5*2
6 and 10 are not prime so keep going ( 5 and 2 are prime)
= 3*2 * 5*2 * 5*2
All of the numbers are prime, so we normally write them in order from smallest to largest
2*2*2*3*5*5
We can write with exponents
2^3 *3* 5^2
Complete the table and ploty = 3x- 1x=0x=1
Answers
Given the equation:
\(y=3x-1\)If x = 0, then:
\(\begin{gathered} x=0 \\ \Rightarrow y=3(0)-1=0-1=-1 \\ y=-1 \end{gathered}\)next, if x = 1, then:
\(\begin{gathered} x=1 \\ \Rightarrow y=3(1)-1=3-1=2 \\ y=2 \end{gathered}\)then, the table would be the following:
and the graph would be:
Please help me i need help.
Answers
Answer:
5x+7 > 17 matches with 3.
1+3x > -5 matches with 2.
2x+1 < 3 matches with 1.
5-3x > 11 matches with 4.
Step-by-step explanation:
(27ах³ – 9а²x) ÷ Зах
Answers
The following data represent the age (in weeks) at which 10 randomly selected babies crawled for the first time. 43, 44, 42, 31, 38, 45, 36, 39, 50, 52 Suppose that the data is a random sample from a population with a normal distribution. Construct a 90 confidence interval for the average age at which babies first crawl.
Answers
Answer:
\(42-1.833\frac{6.325}{\sqrt{10}}=38.334\)
\(42+1.833\frac{6.325}{\sqrt{10}}=45.666\)
The 90% confidence interval is given by \( 38.334 \leq \mu \leq 45.666\)
Step-by-step explanation:
Notation
\(\bar X\) represent the sample mean
\(\mu\) population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
\(\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}\) (1)
In order to calculate the mean and the sample deviation we can use the following formulas:
\(\bar X= \sum_{i=1}^n \frac{x_i}{n}\) (2)
\(s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}\) (3)
The mean calculated for this case is \(\bar X=42\)
The sample deviation calculated \(s=6.325\)
The degrees of freedom are given by:
\(df=n-1=10-1=9\)
The Confidence level is 0.90 or 90%, the significance is \(\alpha=0.1\) and \(\alpha/2 =0.05\), and the critical value would be \(t_{\alpha/2}=1.833\)
Replacing we got:
\(42-1.833\frac{6.325}{\sqrt{10}}=38.334\)
\(42+1.833\frac{6.325}{\sqrt{10}}=45.666\)
The 90% confidence interval is given by \( 38.334 \leq \mu \leq 45.666\)
Please help I am struggling bad with this question thank you all
Answers
b = speed of the boat in still water
c = speed of the current
when going Upstream, the boat is not really going "b" fast, is really going slower, is going "b - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "b" fast, is really going faster, is going "b + c", because the current is adding its speed to it.
Now, the boat goes Upstream 48 miles, so Downstream must be travelling the same 48 miles back.
\({\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&48&b-c&3\\ Downstream&48&b+c&2 \end{array}\hspace{5em} \begin{cases} 48=(b-c)(3)\\\\ 48=(b+c)(2) \end{cases} \\\\[-0.35em] ~\dotfill\)
\(\stackrel{\textit{using the 1st equation}}{48=(b-c)3}\implies \cfrac{48}{3}=b-c\implies 16=b-c\implies \boxed{16+c=b} \\\\\\ \stackrel{\textit{using the 2nd equation}}{48=(b+c)2}\implies \cfrac{48}{2}=b+c\implies 24=b+c\implies \stackrel{\textit{substituting}}{24=(16+c)+c} \\\\\\ 24=16+2c\implies 8=2c\implies \cfrac{8}{4}=c\implies \boxed{2=c}~\hfill~\stackrel{ 16~~ + ~~2 }{\boxed{b=18}}\)
In the Michigan State Lottery, a player wins the grand prize by correctly picking 6 different numbers
from 1 to 49. The numbers do not need to be selected in order. If a player buys one ticket, find the prob-
ability of winning the grand prize.
Answers
Answer:
e
Step-by-step explanation:
use a calculator online
The probability of winning the grand prize is 0.00101 if the In the Michigan State Lottery, a player wins the grand prize by correctly picking 6 different numbers from 1 to 49.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have a player wins the grand prize by correctly picking 6 different numbers from 1 to 49.
Total outcome = C(49, 6) (repetition not allowed)
= 13983816
Favourable outcomes = 49⁶
Probability of winning the grand prize:
= 13983816/49⁶
After calculating:
P = 0.00101
Thus, the probability of winning the grand prize is 0.00101 if the In the Michigan State Lottery, a player wins the grand prize by correctly picking 6 different numbers from 1 to 49.
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anyone know the answer to this ?
Answers
Write a fraction that is equivalent 3/4 to .
Answers
Answer:
6/8 OR 9/12
Step-by-step explanation:
please answer asap please
A piano mover uses a ramp to move a piano into a house. The doorway to the house is 2 feet above the ground and the ramp starts 7 feet from the doorway. Assuming the ground is level and is perpendicular to the side of the house, what is the approximate length of ramp? You must round your answer to two decimal places.
Answers
The time it takes for a planet to complete its orbit around a particular star is called the? planet's sidereal year. The sidereal year of a planet is related to the distance the planet is from the star. The accompanying data show the distances of the planets from a particular star and their sidereal years. Complete parts? (a) through? (e).
I figured out what
(a) is already.
(b) Determine the correlation between distance and sidereal year.
(c) Compute the? least-squares regression line.
(d) Plot the residuals against the distance from the star.
(e) Do you think the? least-squares regression line is a good? model?
Planet
Distance from the? Star, x?(millions of? miles)
Sidereal? Year, y
Planet 1
36
0.22
Planet 2
67
0.62
Planet 3
93
1.00
Planet 4
142
1.86
Planet 5
483
11.8
Planet 6
887
29.5
Planet 7
? 1,785
84.0
Planet 8
? 2,797
165.0
Planet 9
?3,675
248.0
Answers
Answer:
(a) See below
(b) r = 0.9879
(c) y = -12.629 + 0.0654x
(d) See below
(e) No.
Step-by-step explanation:
(a) Plot the data
I used Excel to plot your data and got the graph in Fig 1 below.
(b) Correlation coefficient
One formula for the correlation coefficient is
\(r = \dfrac{\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2} -\left (\sum{y}\right )^{2}\right]}}\)
The calculation is not difficult, but it is tedious.
(i) Calculate the intermediate numbers
We can display them in a table.
x y xy x² y²
36 0.22 7.92 1296 0.05
67 0.62 42.21 4489 0.40
93 1.00 93.00 20164 3.46
433 11.8 5699.4 233289 139.24
887 29.3 25989.1 786769 858.49
1785 82.0 146370 3186225 6724
2797 163.0 455911 7823209 26569
3675 248.0 911400 13505625 61504
9965 537.81 1545776.75 25569715 95799.63
(ii) Calculate the correlation coefficient
\(r = \dfrac{\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2} -\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{9\times 1545776.75 - 9965\times 537.81}{\sqrt{[9\times 25569715 -9965^{2}][9\times 95799.63 - 537.81^{2}]}} \approx \mathbf{0.9879}\)
(c) Regression line
The equation for the regression line is
y = a + bx where
\(a = \dfrac{\sum y \sum x^{2} - \sum x \sum xy}{n\sum x^{2}- \left (\sum x\right )^{2}}\\\\= \dfrac{537.81\times 25569715 - 9965 \times 1545776.75}{9\times 25569715 - 9965^{2}} \approx \mathbf{-12.629}\\\\b = \dfrac{n \sum xy - \sum x \sum y}{n\sum x^{2}- \left (\sum x\right )^{2}} - \dfrac{9\times 1545776.75 - 9965 \times 537.81}{9\times 25569715 - 9965^{2}} \approx\mathbf{0.0654}\\\\\\\text{The equation for the regression line is $\large \boxed{\mathbf{y = -12.629 + 0.0654x}}$}\)
(d) Residuals
Insert the values of x into the regression equation to get the estimated values of y.
Then take the difference between the actual and estimated values to get the residuals.
x y Estimated Residual
36 0.22 -10 10
67 0.62 -8 9
93 1.00 -7 8
142 1.86 -3 5
433 11.8 19 - 7
887 29.3 45 -16
1785 82.0 104 -22
2797 163.0 170 - 7
3675 248.0 228 20
(e) Suitability of regression line
A linear model would have the residuals scattered randomly above and below a horizontal line.
Instead, they appear to lie along a parabola (Fig. 2).
This suggests that linear regression is not a good model for the data.
Patrick had earned 125 points so far this year in math class. After the most recent assignment, Patrick now has 328 points. What was the percentage increase in points? Round your answer to the nearest
Answers
Answer: 162%.
Step-by-step explanation:
To find the percentage increase in points, we need to calculate the difference between the two values, divide it by the original value, and then multiply by 100 to get the percentage.
The difference between Patrick's old score and his new score is:
328 - 125 = 203
The percentage increase is:
203/125 x 100% = 162.4%
Rounded to the nearest whole number, the percentage increase is 162%.
What system of equations would you use to solve the problem below?
A test is worth 100 points. Multiple-choice questions are worth 3 points and
short-answer questions are worth 5 points. If the test has 28 questions, how
many multiple-choice questions are there?
Answers
The system of equations would be x + y = 28 and 3x + 5y = 100.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given;
A test is worth 100 points. Multiple-choice questions are worth 3 points and short-answer questions are worth 5 points.
If the test has 28 questions
Let x be multiple-choice questions
Let y be short-answer questions
The system of equations would be
x + y = 28
3x + 5y = 100
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An item on sale costs 40% of the original price if the original price was $25 what is the sale price
Answers
Answer: $10
Step-by-step explanation:
original price = 25
40% = 0.4
25 * 0.4= 10
Perform the indicated operation & simplify.
Answers
\((8-15i) +(11+24i) = 19+9i\\\\(8-15i)-(11+24i)=-3-39i=-3(1+13i)\)
Look at this set of 7 numbers:
8 2 5 1 8 2 2
By how much would the mean increase if the number 8 replaced the number 1 in the set?
Answers
Answer: 1
Explanation:
Current Mean:
8 + 2 + 5 + 1 + 8 + 2 + 2 = 28
28 / 7 = 4.
So 4 is the current mean.
If you replace 1 with 8:
8 + 2 + 5 + 8 + 8 + 2 + 2 = 35
35/7 = 5
So the new mean is 5.
5 - 4 = 1
What is the equation of the line that passes through (4, 3) and (-4, -1)?
Choices:
2x+1
y=2x+7
y=x/2 +1
y= -x/2 +7
Answers
The equation of the line that passes through (4, 3) and (-4, -1) is y = -x/2 + 5. So, correct option is A.
To find the equation of the line that passes through two given points, we use the slope-intercept form of a linear equation, which is:
y = mx + b
where m is the slope of the line and b is the y-intercept.
First, we need to find the slope of the line using the two given points. The formula for finding slope between two points is:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
Substituting the given points into the formula, we get:
m = (-1 - 3) / (-4 - 4) = -4/8 = -1/2
Now we know the slope, we can use one of the given points (4, 3) and substitute the slope into the slope-intercept form of the equation and solve for b.
y = mx + b
3 = (-1/2)(4) + b
3 = -2 + b
b = 5
Therefore, the equation of the line that passes through (4, 3) and (-4, -1) is:
y = -x/2 + 5
So, correct option is A.
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Complete question is:
What is the equation of the line that passes through (4, 3) and (-4, -1)?
Choices:
y = -x/2 + 5
y=2x+7
y=x/2 +1
y= -x/2 +7
WILL GIVE BRAINLEIST PLEASE HELP!
Answers
The solution of the given expression 2(x - 18) + 3x = 24 is,
⇒ x = 12
The given mathematical expression is,
2(x - 18) + 3x = 24
Now expand the given equation,
⇒ 2x - 36 + 3x = 24
We can write it as,
⇒ 5x - 36 = 24
Now add 36 both sides,
⇒ 5x - 36 + 36 = 24 + 36
⇒ 5x + 0 = 60
⇒ 5x = 60
Divide both sides by 5 we get,
⇒ x = 12
The required solution is,
⇒ x = 12
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Which statement best summarizes the relationship between investments and productivity?
A. Companies with high levels of productivity are the most likely to need investment.
B. Companies must choose between high levels of productivity and large investments. C. Companies use investments to pay for services that improve their productivity.
D. Companies use investments to avoid the need to increase overall productivity.
Answers
The relationship between investments and productivity is that investments can help improve productivity, which is the correct option (C).
What are investments?Investments can be used to acquire new equipment, hire additional workers, or implement new technologies that can enhance a company's productivity.
In general, corporations' major source of revenue is productivity, which is the economic outcome of the company's specific operations, such as the sale of a certain product, the rental of a certain item, the supply of a certain service, and so on.
By investing in these areas, companies can improve their efficiency, reduce costs, and increase output.
Therefore, the relationship between investments and productivity is that investments can help improve productivity.
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Write the set in set-builder notation.
{1, 3, 5, 7, 9, 11, ... , 47}
Answers
{1, 3, 5, 7, 9, 11, ... , 47}
To Write The Following in Set-builder notation
Solution\( \text{A} = \) {x : x ∈ N;x is an odd number, x ≤ 47}
Hope This Helps!!2x − 6y = 12
−x + 3y = 1
For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular:
Answers
We are given the following set of equations,
\(2x-6y=12 \\ -x+3y=1\)
and asked to determine whether they are parallel, perpendicular or neither. We first need to alter each equation and put into slope-intercept form, \(y=mx+b\) (m=slope/rate of change, b=y-intercept). Then we can follow the following basic guidelines,
\(\Rrightarrow\) Lines that are parallel will have slopes that are equal (\(m =m\)) .
\(\Rrightarrow\) Lines that are perpendicular will have slopes that are reciprocal, opposite signs (\(m \rightarrow -\frac{1}{m}\)).
\(\Rrightarrow\) Lines that are neither will have slopes that are NOT equal (\(m_{1} \neq m_{2}\)).
Taking the first equation, \(2x-6y=12\), and putting it in slope-int form.
\(\Longrightarrow2x-6y=12\)
\(\Longrightarrow-6y=12-2x\)
\(\Longrightarrow y=\frac{12}{-6} -\frac{2}{-6} x\)
\(\Longrightarrow y=-2+\frac{1}{3} x\)
\(\Longrightarrow y=\frac{1}{3} x -2\)
The slope of line 1 is \(\frac{1}{3}\).
Now taking the second equation, \(-x+3y=1\), and putting it in slope-int form.
\(\Longrightarrow -x+3y=1\)
\(\Longrightarrow 3y=1+x\)
\(\Longrightarrow y=\frac{1}{3} +\frac{x}{3}\)
\(\Longrightarrow y=\frac{1}{3}x +\frac{1}{3}\)
The slope of line 2 is \(\frac{1}{3}\).
Since the slopes of each line are equal, than the lines are parallel.
What is the slope of the line with equation y = - 3x + 4
Answers
Answer:
-3
Step-by-step explanation:
-3 is the slope y=mx + b m is -3
Answer:
m= -3
Step-by-step explanation:
\(y = - 3x + 4\\y = \:mx+b\\where \:m\:is\:slope\)
saloman was told the written paper on his science experiment should express measurements in liters. Which shows how to calculate the number of liters if he used 5 cups of water
Answers
Answer:
Step-by-step explanation:
Divide 5 by 4.22
Just took the test and this is the right answer
Answer: multiply 5 by 4.22
Step-by-step explanation:
social health is one component of the health tringal what are the other two components
Answers
Answer:
mental health and emotional health
What is the value of log0.5^16
Answers
Answer:
Step-by-step explanation:
log(0.5)^16=log(1/2)^16
=log(2^(-1))^16
=-16log(2)=-4.81647
Help with this :))))))))))))
Answers
Answer:
24
Step-by-step explanation:
120/6=20
300/15=20
360/18=20
480/20=24
Check:
480/24=20
Answer: 20???
Step-by-step explanation:
Malcolm has $50 gift card to a local car wash and order is the ultimate car wash each visit is $8.95
Answers
The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.
The correct answer choice is option B.
How much cheaper is the car washes Malcolm orders than the car washes Martha's order?Malcolm's gift card = $50.
Cost Malcolm's car wash per visit = $7
Martha's gift card = $180
Cost Martha's car wash per visit = Difference between gift card balance of first and second visit
= $180 - $160
= $20
How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7
= $13
Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13
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A basket had 15 mangoes. A monkey came and took
away two-fifths of the mangoes. How many mangoes
were left in the basket
Answers
explanation: 2/5x15= 6 which was taken so 15-6=9