Ax=b has a solution for infinitely many b in R3, but Ax=b does not have a solution for all b in R3.
Consider the matrix A:
```
A = [1 2 3;
4 5 6;
7 8 9]
```
To find the solutions of Ax=b, we need to solve the system of linear equations:
```
x1 + 2x2 + 3x3 = b1
4x1 + 5x2 + 6x3 = b2
7x1 + 8x2 + 9x3 = b3
```
We can rewrite this system as:
```
x1 + 2x2 + 3x3 - b1 = 0
4x1 + 5x2 + 6x3 - b2 = 0
7x1 + 8x2 + 9x3 - b3 = 0
```
This is an homogeneous system of linear equations, and we can solve it using Gaussian elimination. We find that the rank of A is 2, since the third row is a linear combination of the first two rows. Therefore, the system has either one or infinitely many solutions.
If we solve for x1, x2, and x3 in terms of b1, b2, and b3 using Gaussian elimination, we get:
```
x1 = -b1 + 2b2 - b3
x2 = b1 - b2
x3 = (1/3)b1 - (2/3)b2 + (1/3)b3
```
These expressions show that the solution of Ax=b depends on the values of b1, b2, and b3. If we choose b1 = 1, b2 = 0, and b3 = 0, then we find that Ax=b has a solution. Similarly, if we choose b1 = 0, b2 = 1, and b3 = 0, then we find that Ax=b has a solution. In fact, for any values of b1, b2, and b3 such that b1 - b2 + b3 = 0, the system Ax=b has a solution.
However, if we choose b1 = 1, b2 = 1, and b3 = 1, then we find that Ax=b does not have a solution, since the equation b1 - b2 + b3 = 1 - 1 + 1 = 1 is not satisfied. Therefore, Ax=b has a solution for infinitely many b in R3, but Ax=b does not have a solution for all b in R3.
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Please help me I have been doing this forever.
Which are corresponding pairs
Answer:
pandn
Step-by-step explanation:
jsubeuodoqok1kwnebhxhhw
emdndiiwjwkd
d
ddnjd
A man walks a certain distance due North and then the same distance plus a further 7 km due East. If the final distance from the starting point 17 km, find the distances he walks North and East
Step-by-step explanation:
in a triangle, if the hipotenus is 17, the other edges' lenghts are multiples of 8 and 15.
so the Man walked 23km.
subtract 7km
16km left
so he goes 8km north and 15km east
Please help!!! Factorise this expression
Answer:
Step-by-step explanation:
Let's solve the equation:
3m² + 22m + 7 = 0
Discriminant:
D = b² - 4·a·c = 22² - 4·3·7 = 400
√ D = √ 400 = 20
m₁,₂ = ( - b ± √ D) / (2·a)
m₁ = ( - 22 + 20) / (2·3) = - 2/6 = - 1 / 3
m₂ = ( - 22 - 20) / (2·3) = - 42/6 = - 7
3m² + 22m + 7 = 3·(m - (-1/3))·((m - (-7)) =
= (3m + 1)·(m + 7)
3m² + 22m + 7 = (3m + 1)·(m + 7)
if i get a 100 you get brainliest and a thanks, please help
Suppose the volume of air inhaled by a person during respiration is given by V(t) = 3/5 pi(1 - cos pi t/2) liters at a time t (in seconds). When is the volume of inhaled air at a maximum? - t = 1, 2, 3, ... - t = 1, 4, 7, ... - t = 2, 4, 6, ... - t = 1, 3, 5, ... - t = 2, 6, 10, ...
The volume of inhaled air at a maximum at t = 2, 4, 6, ...
The volume of inhaled air is at a maximum when the function V(t) is at a maximum. This occurs when the derivative of V(t) is equal to zero.
The derivative of V(t) is:
V'(t) = (3/5) pi * (pi/2) * sin(pi t/2)
Setting this equal to zero gives:
(pi/2) * sin(pi t/2) = 0
This occurs when pi t/2 is equal to a multiple of pi. This means that t/2 is equal to a multiple of 1, or t is equal to a multiple of 2. Therefore, the volume of inhaled air is at a maximum when t = 2, 4, 6, ...
The correct answer is: t = 2, 4, 6, ...
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Which graph is correct?
The graph of the inequality y ≥ (1/2)x - 1 and x - y > 1 is attached. Shannon's graph is correct.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
Inequalities are used for the non equal comparison of numbers and variables.
Given the inequalities:
y ≥ (1/2)x - 1 (1)
and
x - y > 1 (2)
The graph of the inequality is attached. Shannon's graph is correct.
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Which number should be added to
both sides of this quadratic equation
to complete the square?
(-3/2)² + 1 = x² − 3x + (-3/2)²
Answer:
9/4
Step-by-step explanation:
You want to know the value required to complete the square in the equation 1 = x² -3x.
PictureYour picture shows the required value: (-3/2)² = 9/4.
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there are 18 major sea islands in the queen elizabeth islands of canada. there are 15 major lakes in saskatchewan, canada. (a) if you are planning a trip to visit one of these islands, followed by one of these lakes, how many different trips could you make? (b) if you plan to visit either one of these lakes or one of these islands, how many different visits could you make?
(a) Total number of trips = 270
(b) There are 33 different visits that could make.
We have the information:
There are 18 major sea islands in the queen Elizabeth islands of Canada. There are 15 major lakes in Saskatchewan, Canada.
Let us say that A indicates the major sea Islands and B indicates the major lakes.
Taking both the cases as events, we will use multiplication principle.
Based on the information, the event A occurs in m ways and the event B will occur in n ways. So, the two events will occur in m×n ways.
(a) A × B = 18 × 15
Total number of trips = 270
(b) |A| = 18
|B| = 15
A ∩B = θ (as we cannot visit both an island and lake)
Addition Principle: There are |A| + |B| ways to choose an element form
A ∪ B , when A and B are the finite sets with A ∩B = θ
|A ∪ B| = |A| + |B| = 18 + 15 = 33
Thus, There are 33 different visits that could make.
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if 24x - 8 = ab + ac what is the value of a?
Therefore:
\(a=\frac{24x-8}{b+c}\)find an equation of the slant asymptote. do not sketch the curve. y = x2 + 4 x + 4
To find the slant asymptote of the function y = x^2 + 4x + 4, we need to perform polynomial long division. In this case, we will divide the function by y = x.
1. Divide the function y = x^2 + 4x + 4 by y = x using polynomial long division.
2. x goes into x^2 x times. Write x on top.
3. Multiply x by x, which is x^2. Write x^2 under x^2 in the dividend and subtract it.
4. Bring down 4x from the dividend.
5. x goes into 4x, 4 times. Write 4 next to x on top.
6. Multiply 4 by x, which is 4x. Write 4x under 4x in the dividend and subtract it.
7. Bring down the constant term 4 from the dividend.
8. Since the degree of the remaining dividend (constant term) is lower than the divisor's degree (x), we stop dividing.
After performing polynomial long division, we get the quotient y = x + 4, which is the equation of the slant asymptote for the given function.
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a relief fund is set up to collect donations. a random sample of 400 people shows that 28% of those 200 who were contacted by telephone actually made contributions compared to only 18% of the 200 who received mail requests. is there a difference between the proportions of people who make donations when contacted by telephone or mail? use the 0.05 level of significance
At the 0.05 significance level,
the lower limit of confidence interval is approx. 0.018 and upper limit of confidence interval is approx.0.182...
A relief fund is set up to collect donations.
first Sample size, n₁ = 200
Second sample, n₂ = 200
28% of those 200 people's who contacted by telephone , p₁-cap = 28% = 0.28
18% of the 200 who received mail requests, p₂-cap = 0.18
significance level, α = 0.05
S.E for difference between proportions
= √(p₁-cap(1-(p₁-cap))/n₁ + p₂-cap(1-(p₂-cap))/n₂)
= √0.28(1-0.28)/200 + 0.18(1-0.18)/200
= √0.28(0.72)/200 + 0.18(0.82)/200
= 0.04178 ~ 0.0418
the z-value for significance level 0.05, Zα/2 = Z₀.₀₂₅ = 1.96 (from Z-table)
Margin of error = α/2 ( S.Eₚ₁ ₋ₚ₂)
= 1.96× 0.0418 = 0.08189
CI is given by (p₁-cap - p₂-cap) +- Zα/2 ( S.E )
Lower limit = (0.28-0.18)+ 0.08189
=0.01818 ~ 0.018
Upper limit = (0.28-0.18) - 0.08189
= 0.18189~0.182
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help asap please :)
which of the following expressions is equal to -x^2-36?
A: (-x+6i)(x-6i)
B: (x+6i)(x-6i)
C: (-x-6i)(x+6i)
D: (-x-6i)(x-6i)
\( - x {}^{2} - 36 \\ - (x {}^{2} + 36) \\ - (x {}^{2} - (6i) {}^{2} ) \\ - (x - 6i)(x + 6i) \\ ( - x + 6i)(x + 6i) \: \: or \: \: (x - 6i)( - x - 6i)\)
Answer: DAnswer:
D: (-x-6i)(x-6i)
Step-by-step explanation:
(-x-6i) (x-6i)
-x^2 +6ix -6ix -36
-x^2 -36
So, D is the correct
A company orders 25 boxed lunches from a deli for $185. If each boxed lunch costs the same amount, what is the unit cost of each boxed lunch?
Answer:
you have to divide the total cost by the amount of lunches bought so that equation would be 185÷25. according to my calculator that would be seven dollars and forty cents or $7.40
in its simplest form, kanban consists of a whiteboard divided into multiple columns. what are they titled?
The correct option for whiteboard of the Kanban are-
b) Planned; e) Done; f) WIP
Explain the term Kanbanboard?The work that needs to be done, that work that is being done, and the work that has been finished are all displayed on a Kanban Board.
It's a graphic representation of a person's, a team's, or a department's value stream, which has been diagrammed on a board, a wall, or specifically designed Kanban software.The purpose of the Kanban technique applied to knowledge management is the same as it was in manufacturing even though it was developed as a stock management tool in Toyota manufacturing: better visualize work, restrict work progress, optimize flow, and uncover improvement opportunities.Thus, the more visible a Kanban board is, the better; optimum outcomes are likely to be achieved when a team can always see it.
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The complete question is-
In its simplest form, Kanban consists of a whiteboard divided into multiple columns. What are they titled?
a) In Queue
b) Planned
c) Opened Ticket
d) Delayed
e) Done
f) WIP
plz help me with this question plz it's requested plz
Step-by-step explanation:
Answer above
if you have any doubts ask in comments
Answer:
sorry didi I am study in 6 so I didn't understand
sorry
Find 51% of the number 93.
Answer:
47.43
Step-by-step explanation:
To find 51% of the number 93, multiply the latter by 0.51:
0.51(93) = 47.43
Answer:
47.43
Step-by-step explanation:
51% of 93
\(\frac{51}{100}\times \frac{93}{1}\)
\(=\frac{4743}{100\times \:1}\)
\(=\frac{4743}{100}\)
What is the volume of the rectangular prism?
^answer:^
~10 cubic feet~
^step by step explanation:^
first, calculate the volume of the front “panel” of the shape. (5 cubic centimeters because 5 times 3 is 15 and 15 times 1/3 is 5. 5 times 2 is 10.
Which of the relations given by the following sets of ordered pairs is not a function?
HELPPPPP :((((( IF YOU SEND LINK I WILL REPORT YOU
Answer:
Hi, there your answer will be C.
Step-by-step explanation:
The reason why is because X(Input) can not be repeated the same
for example the coordiante( 1,3) and (1,4). See there are two ones which make them not function
Also, if you're having trouble with Functions and nonfunctions
REMEMBER THS
Function: X and y has to be separarte and can't have the same X
NON-FUNCTION- WHEN X REPEATS ITSELF
Hope this helps :)
30 POINTS PLEASE HELP!!
Answer:
㏑ [a² / y^4]
Step-by-step explanation:
2 ㏑a = ㏑ a²
4 ㏑ y = ㏑ y^4
so, 2 ㏑ a - 4 ㏑ y
= ㏑a² - ㏑y^4
= ㏑ [a² / y^4]
1. A box contains 3 shoes, 7 pants and 10 shirts. If an item is drawn from the box randomly, what is the probability of getting shirts?
The probability of getting shirts is 1/2 or 0.5 if the box contains 3 shoes, 7 pants and 10 shirts.
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 box contains 3 shoes, 7 pants and 10 shirts.
Total number of outcomes = 3+7+10 = 20
Total number of shirts(favourable outcomes) = 10
Probability = 10/20 = 1/2 = 0.5
Thus, the probability of getting shirts is 1/2 or 0.5 if the box contains 3 shoes, 7 pants and 10 shirts.
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Write the standard form of the equation of the line through the given point with the given slope. point (-1.0); slope -2/3
Answer:
Step-by-step explanation:
When given a point and a slope, the best equation to use is the point-slope formula, y - k = m(x - h)
which here becomes:
y - 0 = m(x + 1), or y = (-2/3)(x + 1), or y = (-2/3)x - 2/3
If you want this in standard form, first clear the fractions by multiplying all terms by 3: 3y = -2x - 2
Now add 2x to both sides, obtaining: 2x + 3y = -2 (in "standard form."
If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?
I. 1/8
II. 1/9
III. 1/10
A. None
B. I only
C. III only
D. II and III only
E. I, II, and III
Sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, lies between 1/10 and 1/9
1/10 < S < 1/9
The correct option is C.
From the question, we have the following information is:
If S is the sum of the reciprocals of the consecutive integers from 91 to 100.
Now, we have to find the which of the following is less than S?
Now, According to the question:
There are 10 consecutive integers from 91 to 100 , inclusive
If all 10 integers be 90 , then sum of the reciprocals of the consecutive integers :
=> \((\frac{1}{90} )10 =\frac{1}{9}\)
If all the 10 integers be 100, then sum of the reciprocals of the consecutive integers:
=> \((\frac{1}{100} )10 =\frac{1}{10}\)
This means, sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, lies between 1/10 and 1/9
1/10 < S < 1/9
Hence, 1/10 is less than S
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Giải phương trình: 3x^2 + 3x - 6 = 0
Answer:
x=1
x=-2
Step-by-step explanation:
(3x-3)(x+2)
x=1
x=-2
Describe the long run behavior of f(x)=5(2)x+1:
As x→−[infinity], f(x) =
As x→[infinity], f(x) =
The long run behavior of the function f(x)=5(2)x+1 is that it approaches 1 as x approaches negative infinity and it approaches infinity as x approaches positive infinity.
The long-term behavior of the function f(x)=5(2)x+1 can be discovered by examining how the function behaves as x gets closer to negative and positive infinity.
As x→−[infinity], f(x) = 5(2)^ -∞+1 = 5(0)+1 = 1
As x approaches negative infinity, the value of the function approaches 1.
As x→[infinity], f(x) = 5(2)^ ∞+1 = 5(∞)+1 = ∞
As x approaches positive infinity, the value of the function approaches infinity.
As a result, the function f(x)=5(2)x+1 behaves in the long run in such a way that it approaches 1 as x approaches negative infinity and infinity as x approaches positive infinity.
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Make x the subject of the formula
х
+b=
a
Answer:
x = a(c - b)
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesStep-by-step explanation:
Step 1: Define Equation
x/a + b = c
Step 2: Solve for x
Subtract b on both sides: x/a = c - bMultiply a on both sides: x = a(c - b)Solve this equation 3/5 (x-10) = 18 - 4x - 1
Answer:
x=5
Step-by-step explanation:
Good luck
Determine if each are true or false. True f(2)=5 True f(-6)-f(-3)=6 False The domain is (-6,2] False f(-1)=-3 False The range is [-1,5)
The statements are: True, True, False, False, False.
1. The statement f(2) = 5 is true if the function f evaluates to 5 when the input is \(2\).
2. The statement f(-6) - f(-3) = 6 is true if the difference between the values of f at -6 and -3 is 6.
3. The domain refers to the set of all possible input values for the function. The statement that the domain is (-6,2] is false because it should include all real numbers from -6 to 2, including -6 and 2. The correct notation would be [-6,2].
4. The statement f(-1) = -3 is false if the value of the function at -1 is not equal to -3.
5. The range refers to the set of all possible output values of the function. The statement that the range is [-1,5) is false if there is at least one value outside of that interval included in the range.
To determine the truth or falsehood of these statements, you would need the specific function definition or additional information about the function's behavior.
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The equation says x - 0.8 divided by 1.2 = 6 This is a multi step with decimals find the x equation
The value of x in the equation (x – 0.8) / 1.2 = 6 is 8.
Given,
The equation = (x – 0.8) / 1.2 = 6
We have to expand this equation and find x.
That is,
(x – 0.8) / 1.2 = 6
Multiply 1.2 both sides.
(x – 0.8) x (1.2) / 1.2 = 6 x 1.2
(x – 0.8) = 6 x 1.2
(x – 0.8) = 7.2
Shift 0.8 to right hand side
Then we get,
x = 7.2 + 0.8
x = 8
Therefore, the value of x in the equation (x – 0.8) / 1.2 = 6 is 8.
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Suppose you borrowed $45,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you owe in the first year? Select the correct answer. a. $7,594.46 b. $7,600.46 c. $7,618.46 d. $7,612.46 e. $7,606.46
The correct answer is option a. $7,594.46.
To calculate the amount you would reduce the amount you owe in the first year, we can use the formula for the equal installment of a loan. The formula is:
Installment = Principal / Number of Installments + (Principal - Total Repaid) * Interest Rate
In this case, the principal is $45,000, the number of installments is 5, and the interest rate is 8.5%.
Let's calculate the amount you would reduce the amount you owe in the first year:
Installment = $45,000 / 5 + ($45,000 - $0) * 0.085Installment = $9,000 + $3,825
Installment = $12,825
Therefore, you would reduce the amount you owe by $12,825 in the first year.The correct answer is option a. $7,594.46.
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