If the equation Hx=c is inconsistent for some c in Rn,what can you say about the equation Hx=0? Why?
Answers
To summarize, if the equation Hx = c is inconsistent for some c in ℝⁿ, the equation Hx = 0 is consistent because it always has at least one solution, x = 0.
If the equation Hx=c is inconsistent for some c in Rn, then it means that there is no solution for that particular value of c. However, this does not necessarily mean that the equation Hx=0 is also inconsistent. In fact, it is possible for Hx=0 to have a solution, even if Hx=c does not. This is because the equation Hx=0 represents a homogeneous system of linear equations, while Hx=c represents a non-homogeneous system. Homogeneous systems always have at least one solution (x=0), while non-homogeneous systems may or may not have a solution depending on the specific values of the constants involved.
If the equation Hx = c is inconsistent for some c in ℝⁿ, it means that there is no solution for that specific c value.
Now let's analyze the equation Hx = 0.
An equation is inconsistent if it has no solution. On the other hand, if an equation has at least one solution, it is considered consistent.
Since Hx = c is inconsistent for some c in ℝⁿ, it indicates that the rows of the matrix H do not span the entire space of ℝⁿ. In this case, the equation Hx = 0 will always have at least one solution (x = 0), making it a consistent equation. This is because when you substitute x = 0 into the equation Hx = 0, you get 0 = 0, which is always true.
Therefore, we cannot make any conclusions about the consistency of the equation Hx=0 based on the inconsistency of the equation Hx=c.
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Related Questions
helppppif fd = 20 units and de = 52 units, what is the value of b? round the solution to the nearest hundredth.
Answers
Answer: The value of b is 22.62
Step-by-step explanation: 20 is the opposite of b, 52 is the hypotenuse. Because we're given the opposite and hypotenuse, we have to use sine. So....
sin b=20/52
sin b = 0.38461538461
then using inverse of sine, the equation would be sin^-1(0.38461538461)
by putting that into the calculator you get 22.61986495 (aka 22.62)
Based on the triangle inequality theorem, if fd = 20 units and de = 52 units, the value of b is approximately 71 units.
To find the value of b, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
In this case, we have fd = 20 units and de = 52 units. Let's assume that b is the length of the remaining side.
Using the triangle inequality theorem, we can write the following inequality:
fd + de > b
Substituting the given values, we get:
20 + 52 > b
72 > b
Therefore, the value of b must be less than 72 units.
To round the solution to the nearest hundredth, we can round down to the nearest whole number, which is 71.
So, the value of b is approximately 71 units.
In conclusion, based on the triangle inequality theorem, if fd = 20 units and de = 52 units, the value of b is approximately 71 units.
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someone help me!!! please
Answers
Answer:
124568
865421
Step-by-step explanation:
please give 5 stars then i will say the rest
Simplify The Expression 12g + 3 - g^2 + 2 g=4
Answers
Given:
\(12g+3-g^2+2\)Where, g = 4
To simplify the expression, substitute g for 4 and evaluate.
We have:
\(\begin{gathered} 12g+3-g^2+2 \\ \\ 12(4)+3-4^2+2 \\ \\ 48+3-16+2 \\ \\ 51-16+2 \\ \\ =37 \end{gathered}\)ANSWER:
37
Each morning, Sleepwell Hotel offers its guests a free continental breakfast with pastries and orange juice. The hotel served 820 gallons of orange juice last year. This year, the hotel served 8.4% less orange juice than it did the previous year. How much was served this year? Round your answer to the nearest tenth.
Answers
Proportionately, since the Sleepwell Hotel served 8.4% less orange juice than it did the previous year, the total number it served this year is 751 gallons.
What is proportion?Proportion involves the equation of two ratios or values.
Proportion is a fractional value like ratios and is depicted in percentages, decimals, or fractions.
The quantity of orange juice served last year = 820 gallons
The percentage served this current year = 91.6% (1 - 8.4%)
Proportionately, the current year's quantity = 751 gallons (820 x 91.6%)
Thus, we can conclude that proportionately, the hotel served 751 gallons, which is 8.4% less than last year's.
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(14) (55, 42, 32, 48, 55, x), mean = 49
Answers
Answer:
78
Step-by-step explanation:
Add all the numbers given =256 then take the mean and multiply it with 7 =334 then take 334_256=78 and done
The area and perimeter
Answers
Answer:
N/A
Step-by-step explanation:
the area and perimeter for what exactly?
How many reflectional symmetries does this figure have?Enter your answer in the boxreflectional symmetriesHow many rotational symmetries does this figure have?Enter your answer in the boxrotational symmetnes
Answers
The capital letter H has 2 reflectional symmetry and 2 rotational symmetry.
A figure has reflectional symmetry if it can be reflected across a line and still look the same. For the capital letter H, there is two lines of symmetry, which is the vertical line and horizontal line that divides the letter into two equal halves. Reflecting the letter across this line produces the same letter. So, the H has only 2 reflectional symmetries.
A figure has rotational symmetry if it can be rotated by some angle and still look the same. For the capital letter H, if we rotate it 180 degrees and 360 degrees about the center point of the letter, it will look the same. There is no other angle of rotation that produces the same letter. Therefore, the H has only 2 rotational symmetries.
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--The question is incomplete, answering to the question below--
"How many reflectional symmetries does this figure have?
Enter your answer
___ reflectional symmetries
How many rotational symmetries does this figure have?
Enter your answer
___ rotational symmetries"
A circle divided into 6 parts. 1 part is shaded.
Which best describes the fraction represented by the shaded portion of the circle?
Since 1 of the 6 equal parts is shaded, the shaded portion represents One-sixth.
Since 1 of the equal parts is shaded and 5 are not shaded, the shaded portion represents One-fifth.
Since 5 of the 6 equal parts are unshaded, the shaded portion represents Five-sixths.
Since 5 of the equal parts are unshaded, the shaded portion represents Five-fifths.
Answers
Answer:
5/6
Step-by-step explanation:
Since 1 of the 6 equal parts is shaded, the shaded portion represents One-sixth.
Since 1 of the equal parts is shaded and 5 are not shaded, the shaded portion represents One-fifth.
Since 5 of the 6 equal parts are unshaded, the shaded portion represents Five-sixths.
Since 5 of the equal parts are unshaded, the shaded portion represents Five-fifths.
Answer:
1/6
Step-by-step explanation:
Since 1 part of the 6 parts is shaded then by fraction the shaded portion is 1/6 while the unshaded portion is 5/6.
A triangle has coordinates A(-3,5), B(-3,8)
and C(2,5). The triangle was dilated
By a scale factor of 3. What are the
coordinates of the new triangles?
Answers
Answer:
A(-9,15); B(-9,24); C(6,15)
Step-by-step explanation:
multiply each number in the coordinates by 3
What is the product?
2x(x-4)
O 2x² - 4
O zx²-8
2x?- 4x
2x² – 8x
Answers
which series of transformations shows that paralelogram abcd is congruent to parallelogram abcd by superimposing one onto the other
Answers
The series of transformations that shows that parallelogram ABCD is congruent to parallelogram A'B'C'D' by superimposing one onto the other is a combination of translation and rotation that involves 150 degrees. A transformation refers to the process of changing an object's position, size, or shape.
Translation, reflection, rotation, dilation, and skew are the five basic transformation types that modify an object.In geometry, congruent shapes have the same shape and size. To superimpose one shape onto another means to make them coincide with each other.
The following series of transformations would show that parallelogram ABCD is congruent to parallelogram A'B'C'D' by superimposing one onto the other: Step 1: Translation. Translate the parallelogram ABCD by 5 units to the right and 6 units down to obtain parallelogram A1B1C1D1.Step 2: Rotation. Rotate parallelogram A1B1C1D1 by 150 degrees counterclockwise around point A1 to obtain parallelogram A2B2C2D2.Step 3: Translation. Translate parallelogram A2B2C2D2 by 8 units to the right and 3 units up to obtain parallelogram A'B'C'D'.Thus, the series of transformations that shows that parallelogram ABCD is congruent to parallelogram A'B'C'D' by superimposing one onto the other involves translation and rotation, with a rotation of 150 degrees.
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Please help me!
"Explain why this graph shows a function."
Answers
Answer:
This graph shows a function because no vertical line passes through more than one point on the graph.
Step-by-step explanation:
How do you prove csc^4 x - cot^4 x = csc^2 x + cot^2 x
Answers
To prove the equation csc^4(x) - cot^4(x) = csc^2(x) + cot^2(x), we can start by expressing the trigonometric functions csc(x) and cot(x) in terms of sine and cosine:
csc(x) = 1/sin(x)
cot(x) = cos(x)/sin(x)
Substituting these expressions into the equation, we get:
(1/sin(x))^4 - (cos(x)/sin(x))^4 = (1/sin(x))^2 + (cos(x)/sin(x))^2
Next, we simplify each term separately:
(1/sin(x))^4 = 1/sin^4(x)
(cos(x)/sin(x))^4 = cos^4(x)/sin^4(x)
Expanding the powers, we have:
1/sin^4(x) - cos^4(x)/sin^4(x) = 1/sin^2(x) + cos^2(x)/sin^2(x)
Combining the fractions on the left side:
(1 - cos^4(x))/sin^4(x) = (1 + cos^2(x))/sin^2(x)
Now, let's simplify the left side:
1 - cos^4(x) = sin^4(x)
Using the identity sin^2(x) + cos^2(x) = 1, we can rewrite the equation as:
sin^4(x) = sin^4(x)
The equation simplifies to an identity, showing that the original equation csc^4(x) - cot^4(x) = csc^2(x) + cot^2(x) is true for all values of x.
Therefore, we have proved the given equation.
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The table shows the possible outcomes of spinning the given
spinner and tossing a fair coin. find the probability of spinning a 1 and tossing a
head.
5
3
4
1 2 3 4 5
h1,
h2,h 3, 4, 5,h
t 1, 2, 3, t4, t5,t
the probability of spinning a 1 and tossing a head is
Answers
Spinning the spinner and tossing the coin is an illustration of probability
The probability of spinning a 1 and tossing a head is 0.10
How to determine the probability?From the table, we have the following parameters:
Total outcomes, n = 10
A 1 and a head, n(H1) = 1
So, the probability of spinning a 1 and tossing a head is:
P(H1) = n(H1)/n
Substitute known values
P(H1) = 1/10
Evaluate the quotient
P(H1) = 0.10
Hence, the probability of spinning a 1 and tossing a head is 0.10
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Brad and Allison have three girls. Brad tells Allison that he would like one more child because they are due to have a boy. What do you think of​ Brad's logic?
Answers
Brad's logic is flawed and does not hold any scientific basis. The gender of a child is determined by the combination of genetic factors from both parents
. Each pregnancy is an independent event, and the probability of having a boy or a girl is not influenced by the gender of the previous children. The belief that having a certain number of children of one gender increases the likelihood of having a child of the opposite gender is known as the "gamblers fallacy" or "Monte Carlo fallacy." In reality, the probability of having a boy or a girl remains approximately 50% for each pregnancy, regardless of the gender composition of the existing children.
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Graph 0.25 on the number line.
Answers
Answer: dude its the line after the 0
Step-by-step explanation:
Answer: The first line to the right to the 0
Step-by-step explanation:
The right of the graph is: 0.25, .50, .75 and 1
You invest $500 in an account that pays 6% interest compounded continuously. How
much will be in the account after 6 years?
Answers
=====================================================
Explanation:
We'll apply this formula
A = P*e^(r*t)
where,
A = account balance after t yearsP = initial deposit, aka principale = special constant roughly equal to 2.718 but it goes on forever without a pattern; it's better to let the calculator handle this value rather than type the decimal digits in.r = annual interest rate in decimal formt = number of yearsIn this case, we have
P = 500r = 0.06t = 6Again we won't type "2.718..." for 'e', and we'll just type it into the calculator as shown below. That way the calculator can handle the digits instead.
So...
A = P*e^(r*t)
A = 500*e^(0.06*6)
A = 716.66470728026
A = 716.66 dollars is the final answer
line k in the xy-plane has slope the negative of the fraction 2 p over 5 and y-intercept the point with coordinates 0 comma p, where p is a positive constant. what is the x-coordinate of the x-intercept of line k ?
Answers
The x-coordinate of the x-intercept of line k is -5/2.
Since this point lies on the x-axis, its y-coordinate is 0.
Given that the line has a y-intercept at the point (0, p), where p is a positive constant. This means that when x = 0, y = p.
As we know that the equation of the line can be written as y = mx + b, where m is the slope and b is the y-intercept.
Here, the slope is the negative of the fraction 2p/5, so the equation of line k is y = -2p/5 x + p.
Substitute y = 0 into the equation and solve for x:
0 = -2p/5 x + p
Subtract p from both sides and then multiply by 5/(-2p):
-2p/5 x = -p
x = (-p)(5/2p)
x = -5/2
Therefore, the x-coordinate of the x-intercept of line k is -5/2.
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Suppose that you use a pair of chopsticks
and apply a force of 1 are
N over a distance of 0.01 m. How much
work do you do? If the output force of the
chopsticks is only 0.5 N, how far do the tips
of the chopsticks move?
Answers
0.01 N of work is to be done to move the chopsticks to a distance of 0.01 m
0.02m far the tips of the chopsticks move.
What is work done?
Every time a force pushes something over a distance, work is done. By multiplying the force by the distance moved in the force's direction, you may determine the energy transferred, or work done. Energy transmitted equals work done, which is force times the distance travelled in the force's direction.
1. WD = F×d
= 1×0.01
= 0.01 N
2. d = WD/F
= 0.01/(0⋅5)
= 0.02m
0.02m far the tips of the chopsticks move.
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what is the answer to b²-17b-38
Answers
Answer:
Step-by-step explanation:
I hope this helps you
\(4x+2y=12\\-4x+y=-18\)
Answers
Answer:
(4, - 2 )
Step-by-step explanation:
4x + 2y = 12 → (1)
- 4x + y = - 18 → (2)
adding the 2 equations term by term will eliminate x
(4x - 4x) + (2y + y) = 12 - 18
0 + 3y = - 6
3y = - 6 ( divide both sides by 3 )
y = - 2
substitute y = - 2 into either of the 2 equations and solve for x
substituting into (1)
4x + 2(- 2) = 12
4x - 4 = 12 ( add 4 to both sides )
4x = 16 ( divide both sides by 4 )
x = 4
solution is (4, - 2 )
brainliest!!!!!!!!! sjshdd
Answers
Answer:
a. a = 6
b. b = 1
c. c = 0
d. d₁ = -7, d₂ = 7
e. f = -1
I really need help I will give you 5 stars and alike.
Answers
Answer:
the area is 935 square inches, and the perimeter is 39 inches
Step-by-step explanation:
Hey there!
In order to find the perimeter and area of the board, we must first list out the information we already know
----------------------------------------------------------------------------------------------------------
- The original board has a length of 44 - The original board has an area of 1496- The original board has a perimeter of 156- The new board has a length of 11----------------------------------------------------------------------------------------------------------
There is a tiny pattern in here:
The original board has a length of 44 while the new one has the length of 11
This means that, the original board had dimensions 4 times the length of the new board
In order to find the area or perimeter, we need to know the width of the new board
To do this, we divide 1496 by 44
That gets us 34
This means that the width of the old board is 34
Now we divide 34 by 4 which gets us 8.5
This means, 8.5 is the width of the new board
Now that we know this, we can easily find the area and the perimeter of the new board
8.5 + 8.5 + 11 + 11 = 39
This means, the perimeter is 39
8.5 x 11 = 935
This means, the area is 935
This brings us to the conclusion that the area is 935 square inches, and the perimeter is 39 inches!
Assuming that the long-run demand for oranges is the same as the short-run demand, you would expect a binding price ceiling to result in a________ that is_________in the long run than in the short run.(Surplus/Shortage) (Larger/Smaller)
Answers
If the long-term demand for oranges is the same as the short-term demand, a binding price ceiling will result in a shortage that is larger in long-run demand than the short-run demand. So the answers are shortage and larger.
A shortage occurs when there is a difference between the quantity that is supplied and the quantity that is required of a product, service, or resource. Surplus is a term used to describe situations where there is more supply than demand for a product, service, or resource.
So when the long-run demand is the same as the short-run demand, binding price ceilings typically result in a shortage when there is a lack of supply of products. And, the result will be larger in the case of the long run compared to the short run. Therefore, the first blank can be filled with shortage and the second blank with larger.
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What is the y-intercept of the line graphed below?
Answers
Answer:
I think it's -3 if I'm right
Answer:4
Step-by-step explanation:
I did it it’s right
Guys i need help! Its for my final! ! What is 1+1?
Answers
Answer:
1 + 1 = 2
Step-by-step explanation:
You add
1
+
1
=
2
HELP ILL GIVE BRAINLIEST what’s the shape of the
Base?
Answers
Answer:
circle
Step-by-step explanation:
In your own words, why will rigid transformations always produce congruent figures? Could non-rigid transformations also produce congruent figures?
Answers
Rigid transformation are transformation that preserve the shape and size hence producing congruent figures such as translation, reflection and rotation.
Dilation is a non rigid transformation and does not produce congruent figures.
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation are transformation that preserve the shape and size hence producing congruent figures such as translation, reflection and rotation.
Dilation is a non rigid transformation and does not produce congruent figures.
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A package of poster board usually sells for $8.40. This week the package is on sale for $6.30. What is the percent of discount?
A.
25%
B.
33.3%
C.
15%
D.
21%
Answers
Answer:
A. 25%
Step-by-step explanation:
\((8.40-6.30)/8.40\)\(2.10/8.40\)\(1/4\)\(0.25\)In 2017 there were enough renewable energy sources to supply a total of 9309 megawatts of electricity in a country. This graph shows the proportions that the different renewable energy sources could supply. Approximately how many megawatts of electricity could be supplied by Hydropower in 2017?
700
1700
2300
7000
Answers
Approximately 1700 megawatts of electricity could be supplied by Hydropower in 2017. Option B is correct.
Given that,
In 2017 there were enough renewable energy sources to supply a total of 9309 megawatts of electricity in a country. The graph shows the proportions that the different renewable energy sources could supply.
the percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here, from the graph contribution of the hydropower is 18.2%.
So the electricity produced through hydropower is,
= 9309 * 18.2%
= 9309 * 18.2/100
= 1694.23
≈ 1700 megawatts
Thus, approximately 1700 megawatts of electricity could be supplied by Hydropower in 2017.
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