Answer:
These techniques for elimination are preferred for 3rd order systems and higher. They use "Row-Reduction" techniques/pivoting and many subtle math tricks to reduce a matrix to either a solvable form or perhaps provide an inverse of a matrix (A-1)of linear equation AX=b. Solving systems of linear equations (n>2) by elimination is a topic unto itself and is the preferred method. As the system of equations increases, the "condition" of a matrix becomes extremely important. Some of this may sound completely alien to you. Don't worry about these topics until Linear Algebra when systems of linear equations (Rank 'n') become larger than 2.
Step-by-step explanation:
Just to add a bit more information, "Elimination" Can have a variety of other interpretations. Elimination techniques typically refer to 'row reduction' to achieve 'row echelon form.' Do not worry if you have not heard of these terms. They are used in Linear Algebra when referring to "Elimination techniques"
Gaussian Elimination
Gauss-Jordan Elimination
LU-Decomposition
QR-Decomposition
These techniques for elimination are preferred for 3rd order systems and higher. They use "Row-Reduction" techniques/pivoting and many subtle math tricks to reduce a matrix to either a solvable form or perhaps provide an inverse of a matrix (A-1)of linear equation AX=b. Solving systems of linear equations (n>2) by elimination is a topic unto itself and is the preferred method. As the system of equations increases, the "condition" of a matrix becomes extremely important. Some of this may sound completely alien to you. Don't worry about these topics until Linear Algebra when systems of linear equations (Rank 'n') become larger than 2.
Substitution is the preferred method for 2 equations in 2 unknowns. The constants are unimportant other than having a non-zero determinant. It is always easy to find multiplicative factors using LCMs of one variable or the other to allow substitution into the other equation:
Example:
4X + 5Y = 9
5X - 4Y = 1
Notice that 20 is a LCM of either the X or Y variable. So multiply the first by 4 and the second by 5 and then adding the two (Y's will drop out allowing for substitution)
4(4X + 5Y = 9)
5(5X - 4Y = 1)
Multiplying to produce the LCM factors:
16X + 20Y = 36
25X - 20Y = 5
Adding the equations
41X = 41
X = 1
Substitution into either equation yields
Y = 1
Elimination techniques are preferred for Rank-n>3
Answer:
I like the view
I need Unit 3 parallel and perpendicular lines Homework 5 slope of lines it’s due today!
14. Slope (m) of PQ = -4
Slope (m) of RS = 1/4
The lines are perpendicular.
15. mPQ = -3
mRS = 3
They are neither perpendicular nor parallel lines.
16. mPQ = 0
mRS = 0
The lines are parallel.
17. x = -6
18. x = -2
What are the Slopes of Parallel and Perpendicular Lines?If two lines have the same slope (m), then both lines are parallel to one another. On the other hand, if the slopes of two lines are negative reciprocals to each other, then both lines are regarded as perpendicular lines because the product of their slopes is equal to -1.
Slope (m) = change in y / change in x
14. Slope (m) of PQ = (-3 - 17) / (1 -(-4))
Slope (m) of PQ = -20/5 = -4
Slope (m) of RS = (4 - 3) / (-5 -(-9))
Slope (m) of RS = 1/4
(1/4)(-4) = -1, therefore, the lines are perpendicular.
15. Slope (m) of PQ = (-1 - 14) / (2 -(-3))
Slope (m) of PQ = -15/5 = -3
Slope (m) of RS = (-10 - 8) / (-2 - 4)
Slope (m) of RS = -18/-6 = 3
They are neither perpendicular nor parallel lines.
16. Slope (m) of PQ = (-1 - (-1)) / (-3 - 2)
Slope (m) of PQ = -0/-5 = 0
Slope (m) of RS = (9 - 9) / (-7 -(-11))
Slope (m) of RS = 0/4 = 0
The lines are parallel.
17. If CD║EF, their slope will be equal. Therefore:
Slope of CD = slope of EF
(-4 - 16)/(2 - x) = (4 - 14)/(-2 -(-6))
-20/(2 - x) = -10/4
-20/(2 - x) = -5/2
Cross multiply
-20(2) = -5(2 - x)
-40 = -10 + 5x
-40 + 10 = 5x
-30 = 5x
-30/5 = x
-6 = x
x = -6
18. Slope of JK = slope of l
(-5 -(-8))/(-1 - x) = 6/2
3/(-1 - x) = 3
3(-1 - x) = 3
-3 - 3x = 3
-3x = 3 + 3
-3x = 6
-3x/-3 = 6/-3
x = -2
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Can someone help me understand this pls? (Provide an explanation)
Question:
Is triangle AFD congruent to triangle BEC?
Answer: is not congruent
To be congruent, it has to be same size and shape. It can face in any directions. Both the shapes have to be equal in all side lengths and equal angles.
Looking at the triangle you can understand that it is not congruent as the triangles have a size difference of being big and small. But if you still desire detailed explanation then here:
There is four rules for a triangle to be congruent. If one of these rule matches then you can say the triangle is congruent.
1. The three sides are equal
2. Two angles are the same and a corresponding side is the same
3. Two sides are equal and the angle between the two sides is equal
4. Two angles are equal and the side between them is equal
There are no angles, so find if all the three sides are equal. Even if one side is not equal, you can say it is not congruent. So if you just measure any side length of the smaller and big triangle, the length is not equal. None of the side lengths in either of the triangle is equal.
What proportion of US women have a height between 62 and 67 inches?
Answer:
short ppl
Step-by-step explanation:
if u 62 inches u short as hell
Help find initial value for graph PLSSSSSS the dotted points are (0,8) and (16,20)
Answer:8
Step-by-step explanation:
The initial value, or y-intercept, is the output value when the input of a linear function is zero, as you've already pointed out, the function crosses the y- axis at (0,8)
27.if 2 lbs of rice is $3. How much will 15 lbs of rice be?
Answer:
2 lbs rice= $3
15 lbs rice= x
x= 15×3/2
=45/2=22.5For $22.5 will be 15 lbs of rice .
8 + 2 + (1/2) + (1/8) +...... Find the sum of the infinite series.
HOLA necesito ayuda... como puedo combertir 50% en fraccion y decimal. Y como combertir 25% en fraccion y decimal
Answer:
Step-by-step explanation:
50/100 = 1/2 or 0.5
25/100 = 1/4 or 0.25
Find profit or loss percent if CP-Rs 900 and loss =Rs 360
loss%=loss/CP×100%
=Rs.360/Rs.900×100%
=Rs. 360/9
loss% =40% ans
HEPL!! due in 2 hours so please help or attempt! I came up with 5 different answers and don't know which one is the actual answer!!
Answer:
Original Price = $23
Step-by-step explanation:
$5.75 is the price after a discount of 75%
Let the original price be x and x is 100% of the price
5.75 = 100%x - 75%x
5.75 = 25%x
The new price is 25% of the original because you are subtracting 75%
25% is also written as 0.25
5.75 = 0.25x
x = 5.75/0.25
x = 23
The original price is 23
-Chetan K
what is the equation of the line that passes through the point (0, -2) with a slope of 2
Answer:
Step-by-step explanation:
You can use a fill in the blank formula called "point-slope" formula because you were given a point and the slope. But there's an even easier way because they gave you a special point. The point (0, -2) is on the y-axis. So it actually IS the y-intercept. So just in this case, you can use the slope-intercept formula as a fill-in-the-blank formula bc you were actually given the slope (we always use m for slope) and the y-intercept.
This is y = mx + b... fill in the given slope for the m, fill in the y-intercept for the b, then you're done!
y = 2x -2
Explain why the square root of a number is defined to be equal to that number to the 1/2 power
Answer:
Because square root is essentially the same thing as the power to a half
sqrt(x) is the same as (x)^1/2
What is an equation of the line that passes through the points (6, 2)( and (−6,−8)
By which reason can it be proven that triangles DAB and DAC are congruent?
AAS
SSS
SSA
AAA
Answer:
AAS
Step-by-step explanation:
Answer:
AAS
Step-by-step explanation:
(5z+5)+(7z+4) what is this confused ?
Answer:
U have to solve this equation[tex](5z + 5) \: + \: (7z + 4)[/tex]
[tex]5z + 5 - 7z - 4[/tex]
[tex]5z - 7z + 5 - 4[/tex]
[tex]2z + 1[/tex]
hope this helps you !!What is the range of possible sizes for side x?
Answer:
x = 3.96
Step-by-step explanation:
apply the pitagoras theorem
x =
[tex] \sqrt{ {2.8}^{2} + {2.8 }^{2} } [/tex]
If the distance between A(0, 4) and B(3,a) is 5 units then find the value of a.
Answer:
Step-by-step explanation:
a = 0
So that AOB makes a right triangle with sides 3-4-5
Answer:
a = 8
Step-by-step explanation:
Calculate AB using the distance formula and equate to 5
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A (0, 4 ) and (x₂, y₂ ) = B (3, a )
d = [tex]\sqrt{(3-0)^2+(a-4)^2}[/tex]
= [tex]\sqrt{3^2+(a-4)^2}[/tex]
= [tex]\sqrt{9+(a-4)^2}[/tex] , then
[tex]\sqrt{9+(a-4)^2}[/tex] = 5 ( square both sides )
9 + (a - 4)² = 5² = 25 ( subtract 9 from both sides )
(a - 4)² = 16 ( take square root of both sides )
a - 4 = 4 ( add 4 to both sides )
a = 8
Katie works as a waitress and records her monthly tips in the table shown below. If Katie decided not to work the month of November, how would her five month average compare to her six month average for monthly tips? June July August Septemper October November $133. 45 $235. 31 $239. 45 $258. 87 $298. 45 $115. 67 a. Her monthly average would have decreased by $19. 57. B. Her monthly average would have increased by $19. 57. C. Her monthly average would have increased by $2. 7. D. Her monthly average would have decreased by $2. 7. Please select the best answer from the choices provided A B C D.
Her monthly average would have decreased by $19.57 and it can be determined by using taking the average value of every month.
Given that,Katie works as a waitress and records her monthly tips in the table shown below.
June, July, August, September, October, November
$133.45, $235.31, $239.45, $258.87, $298.45, $115.67
If Katie decided not to work the month of November,
We have to determine,How would her five-month average compare to her six-month average for monthly tips?
According to the question,Katie works as a waitress and records her monthly tips in the table below.
June, July, August, September, October, November
$133.45, $235.31, $239.45, $258.87, $298.45, $115.67
To find out how not working in November would affect the average of Katie's tips.
The average of her working June until October only.
[tex]\rm Average = \dfrac{133.45 + 235.31 +239.45 + 258.87 + 298.45}{5}\\\\Average =\dfrac{ 1165.53 }{ 5}\\\\Average = 233.10[/tex]
Then, The average is with the month of November is,
[tex]\rm Average = \dfrac{133.45 + 235.31 +239.45 + 258.87 + 298.45 + 115.67}{6}\\\\Average =\dfrac{ 1281.2 }{ 6}\\\\Average = 213.53[/tex]
Therefore,
On comparing the average of her five-month average to her six-month average for monthly tips is,
[tex]233.10 - 213.53 = 19.57[/tex]
The average will decrease because 213.53 is less than 233.10.
Therefore, Her average will decrease by $19.57.
Hence, Her monthly average would have decreased by $19.57.
For more details about the Average value refer to the link given below.
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Answer:
b
Step-by-step explanation:
1.(01.01)
Evaluate -6 - (-1). (1 point)
5
-5
6
Answer:
I don't understand the question. Write it again & briefly.
Which number sentence is true?
OA) 5.6 > |-8.91
OB) |-5.6] < |-8.91
OC) -5.6 > 1-8.91
OD 15.6] > 1-8.91
The first one (when simplify) is
5.6>8.91
Which is not true if you plot it on a number line
The second one (when simplify) is
5.6<-8.91
which is not true because it is the same thing as number 1
The third one (when simplify) is
-5.6>8.91
which is obviously not true since negatives are way smaller than positives
So that leaves us the last one
Thefore the answer is OD.
I hope this helped!!
(BRAINLIEST TO THE PERSON WHO HELPS ME WITH THESE FOUR QUESTIONS)
Cheryl writes 7 fewer posts than Kevin on a social media site.
Answer the questions to write an algebraic expression. Then evaluate the expression for the given value.
1. Choose a variable to represent the number of posts Kevin writes. Explain why you chose this variable.
2. Which operation (addition, subtraction, multiplication, or division) applies to this situation? Justify your choice.
3. Use your variable and the operation you identified to write an expression for the number of posts Cheryl wrote
4. If Kevin wrote 21 posts, how many did Cheryl write?
Answer:
Cheryl's posts + 7 posts =Kevin Posts
K-C=7 or C+7+K I use them because C is Cheryl and K is Kevin
Operation=subtraction or addition because it could be K-C=7 or C+7+K
Cheryl wrote K-7=C posts
6x² = 7xy + 20y² where x ˃ 0 and y ˃ 0
Find the ratio x : y
Convert 45 mi/hr to feet per minute
Answer:
3960
Step-by-step explanation:
multiply 45 by the amount of feet in a mile (5280)
take that answer and divide in by how many minutes are in an hour
25% of the seniors class has blue eyes of the blue student 60% are females. What is the probability that seniors selected randomly is a blue eyed female.
A) 15%
B) 85%
C)60%
D)35
Explanation:
Let's say this school has 1000 seniors.
25% of this count is 0.25*1000 = 250 to indicate there are 250 seniors with blue eyes. Of this smaller count, 60% of them are girls with blue eyes. So there are 0.60*250 = 150 female seniors with blue eyes.
Divide that last number over the original value: 150/1000 = 0.15 = 15%
The probability that the senior selected randomly is a blue-eyed female is 15%.
It is given that 25% of the seniors class has blue eyes of the blue student 60% are females.
What is the probability?Probability refers to the occurrence of random events. Basically, it is the possibility to predict how likely events are to happen.
Probability of event = Number of favorable outcomes / Total number of outcomes.
Let's consider this school has 1000 seniors.
25% of this count
0.25 × 1000 = 250
Which shows that there are 250 seniors with blue eyes.
Similarly, 60% of them are girls with blue eyes.
So, there are 0.60 × 250 = 150
there are 150 female seniors with blue eyes.
Here, the probability that seniors selected randomly is a blue-eyed female
150/1000 = 0.15
= 15%
Therefore, the probability that the senior selected randomly is a blue-eyed female is 15%.
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Juliet needs to rewrite 3 (x 2) = 6 y in slope-intercept form so she can easily graph it. Which step would be correct to start the process? She could combine the x and 2 to get 3 (2 x) = 6 y. She could divide both sides by 3 to get x 2 = 2 y. She could distribute the 3 to get 3 x 2 = 6 y. She could subtract the 6y to get Negative 6 y = 3 (x 2).
The step that would be correct to start the process is she could distribute the 3 to get 3x+2=6y
Note that the standard equation of a line in slope-intercept form is expressed as y = mx + b
m is the slopeb is the y-interceptGiven the function 3(x+2)=6y, for Juliet to write in slope-intercept form, the best approach is to first divide both equations by 6 as shown:
[tex]3(x+2)=6y \\\frac{3(x+2)}{6} =\frac{6y}{6} \\\frac{x+2}{6}=y[/tex]
Swap sides
[tex]y=\frac{x+2}{6}\\y=\frac{1}{6}x +\frac{1}{3}[/tex]
She could as well distribute the 3 over x + 2 to have:
3(x + 2) = 6y
3x + 3(2) = 6y
3x + 6 = 6y
Hence based on the option, the step that would be correct to start the process is she could distribute the 3 to get 3x+2=6y
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Answer:
Its C
Nevermind Its Not its A or B
Step-by-step explanation:
:)
Joan purchased a refrigerator for $1,200. She made a down payment of $65 and paid
$121 a month for 11 months. Find the total installment price of the refrigerator.
The total installment price is $1331.
What is an installment?Installment means adding the total principal of the loan and the total interest on the principal together and then dividing the sum by the number of installment payments.
For the given situation,
The purchase price of the refrigerator = $1200
Down payment = $65
Monthly installment = $121
Installment period = 11 months
Total installment price = [tex](121)(11)[/tex]
⇒ [tex]\$1331[/tex]
Hence we can conclude that the total installment price is $1331.
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Costco is selling boxes of pomegranates for $18.99. if a box contains 6 pomegranates, what is the cost of one pomegranate?
Answer:
$113.94
18.99 multiplied by 6 is 113.94
in the figure given alongside if X=3y find the sizes of angles represented by a and b
Answer:
Step-by-step explanation:
x = 3y
x + y = 180°
3y + y = 180° ⇒ y = 45° = a
x = 3( 45° ) ⇒ x = 135° = b
The sizes of angles represented by a and b are 45 and 135 degrees.
How does an angle form?An angle requires two straight line/ line segments/rays, such that they're connected on one of their endpoints.
The point of their joint is called vertex of that angle.
Those two line segments forming it are called arms of that angle.
The angle is the degree of rotation that it will take for the moving side to go from initial side to the position it is currently on.
We are given that
x = 3y
Since we know that the linear pair is
x + y = 180°
Therefore, 3y + y = 180°
y = 45° = a
x = 3( 45° )
x = 135° = b
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Sam has a piece of rope that is 3. feet long. He cuts the rope so that one piece
is 13 feet long. How long is the other piece?
2 feet
2 feet
27 feet
12 feet
Done
Answer:
1.11 feet
Step-by-step explanation:
i assume you meant inches not feet so you will just multiply 3 feet by 12 to change it into 36 inches do 36-13 get 33 dived by 12 get 1 with a remainder of 11 so 1.11
what is 2 2/3 - (-3 2/6)
Answer:
6
Step-by-step explanation:
7x - 4 = -18?
please give an answer.
Answer:
x=-2
Step-by-step explanation:
7x - 4 = -18
+ 4. +4
7x = -14
÷7. ÷7
x=-2
Answer:
x = -2Step-by-step explanation:
7x - 4 = -18?
7x - 4 = -18
7x = -18 + 4
7x = -14
x = -14 : 7
x = -2
-----------------
check
7 * (-2) - 4 = -18
-14 - 4 = -18
-18 = -18
the answer is good