8. (a) For A in Exercise 6, part (b) and b-[30, 30, 20], if Ax - b has the given solution x' [10, 10, 0, 0], find the family of all solutions to Ax - b. (b) Find a solution to Ax = b in part (a) with x = 5
Answers
(a) The family of all solutions to Ax - b can be represented as x = x' + N(A). (b) A solution to Ax = b in part (a) with x = 5 is Ax = 0.
To find the family of all solutions to the equation Ax - b and a specific solution with x = 5.
(a) We know that Ax - b has the given solution x' = [10, 10, 0, 0]. This solution is also referred to as a particular solution. To find the family of all solutions, we need to find the general solution by adding the particular solution to the null space of matrix A. The null space contains all the solutions to the equation Ax = 0. Let's denote the null space vectors as N(A).
After finding the appropriate combination of null space vectors, add it to the particular solution x' to obtain the required solution with x = 5.
(b) To find a solution with x = 5, we need to find a suitable combination of vectors in the null space N(A) that, when added to the particular solution x', results in a new vector whose first component is 5. Keep in mind that the null space vectors are obtained from the equation Ax = 0, and their linear combinations represent the possible transformations of the particular solution.
Please note that without the specific matrix A and vector b, it's impossible to provide exact solutions. However, the method described above should guide you in solving this type of problem.
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Related Questions
Convert the given from of the function into the other two forms
Answers
Step 1: Standard form to vertex form of rows 1 and 2:
\(\begin{gathered} S\tan dard\text{ form} \\ y=ax^2\text{ + bx + c} \\ \text{Vertex form } \\ y\text{ = }a(x-h)^2\text{ + k} \end{gathered}\)Standard form of row 1 to vertex form
\(\begin{gathered} y=x^2\text{ - 2x - 3} \\ y=x^2-2x+1^2-3-1^2 \\ \text{y = (x -1 )}^2\text{ - 3 - 1} \\ y=(x-1)^2\text{ - }4 \end{gathered}\)Intercept form of row 3 to vertex form.
\(\begin{gathered} y\text{ = (}x\text{ + 2)(x - 3)} \\ y=x^2\text{ - 3x + 2x - 6} \\ y=x^2\text{ - x - 6} \\ y=x^2\text{ - x + (}\frac{1}{2})^2\text{ - 6 - (}\frac{1}{2})^2 \\ y\text{ = (x - }\frac{1}{2})^2\text{ - 6 - }\frac{1}{4} \\ y\text{ = (x - }\frac{1}{2})^2\text{ - }\frac{25}{4} \end{gathered}\)Standard form to intercept form row 1
\(\begin{gathered} y=x^2\text{ - 2x - 3} \\ \text{method: factorize} \\ y=x^2\text{ - 3x + x - 3} \\ y\text{ = x(x - 3) +1( x - 3)} \\ y\text{ = (x + 1)(x - 3)} \end{gathered}\)Intercept form to standard form row 3
\(\begin{gathered} y\text{ = (x + 2)(x - 3)} \\ y\text{ = x(x - 3) + 2(x - 3) by distribution} \\ y=x^2\text{ - 3x + 2x - 6} \\ y=x^2\text{ - x - 6} \end{gathered}\)Vertice form to intercept fomr
Round 42.268 to the nearest tenth. f)
Answers
Answer:
Step-by-step explanation:
The rule is that whatever accuracy you want, you round that digit up if the one to the right is greater than 5 and not rounded up if it is 4 or less.
42.26 the 6 is greater than 5, so 2 will be rounded up.
42.3
Answer:
42.27
Step-by-step explanation:
The hundredths place digit is 5 or greater which means you round up,...
Chow,...!
What is the equation of the quadratic function represented by this table?
x 5 6 7 8 9 10
f(x) -4 5 8 5 -4 -19
Type the correct answer in each box. Use numerals instead of words. f(x) = (x − )2 +
Answers
Answer: f(x) = -3(x-7)^2+8
Step-by-step explanation:
-3, 7, 8
f(x)= -3
(x- 7)^2+
8
So the answer is -3, 7, 8
Step-by-step explanation: Got it right on Edmentum
charles owns a catering business. the amount his 10 most recent clients spent is shown in the histogram below. a bar graph is entitled cost per event. the event cost is on the x-axis and the number of events is on the y-axis. there are 2 events with a cost of 1,000-1,499; 4 with a cost of 1,500 to 1,999; 3 with a cost of 2,000 to 2,499; 1 with a cost of 3,000 to 3,499. why is the graph misleading?
Answers
The graph is misleading because the x-axis scale shows that the given data is more clustered than it actually is.
What is a misleading graph?
A misleading graph, sometimes referred to as a distorted graph, misrepresents data, amounts to statistical abuse, and may lead to the drawing of an inaccurate conclusion.
What is a data set?
A data set is a grouping of connected, discrete pieces of connected data that can be viewed separately, together, or handled as a single unit. A data structure of some kind is used to arrange a data set.
Here, we have
2 events with a cost of 1,000-1,499;
4 events with a cost of 1,500 to 1,999;
3 events with a cost of 2,000 to 2,499;
1 event with a cost of 3,000 to 3,499
We concluded from the given dataset that the cost of the event is plotted on the x-axis.
In a given dataset, the entry from 2500 to 2599 is missing.
The graph generates a point cluster that isn't actually displayed on the data components because of the missing item.
Hence, the graph is misleading because the x-axis scale shows that the given data is more clustered than it actually is.
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For the data in the table, tell whether y varies directly with x. If it does, write an equation for the direct variation. x y 3 5.4 7 12.6 12 21.6
Answers
The required expression of the proportionality is given as y = 1.8x.
Given,
The data
x = 3, 7, 12
y = 5.4, 12.6, 21.6
We have to write an equation for the direct variation.
What is proportionality?
The relationship between two or more sets of values—whether they are directly proportional or inversely proportional to one another—is referred to as proportionality.
Here,
If y is proportional to x,
y ∝ x
y = k x
k = y/x
Then,
k = 5.4/3 = 12.6/7 = 21.6/12 = 1.8
So put k in the proportionality equation,
y = 1.8k
Thus, the required expression of the proportionality is given as y = 1.8x.
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I. THE SET OF POINTS ON A PLANE THAT ARE THE SAME DISTANCE FROM A CENTER POINT.
A)Circle
B)Diameter
C)Radius
Answers
The vertex of f(x) = 2x² + 12x + 36
Answers
Answer:
vertex = (-3, 18)
Step-by-step explanation:
Rewrite in vertex form and use this form to find the vertex (h,k).
Step-by-step explanation:
You can graph it to find the vertex or massage this equation into vertex form. Thirdly , if you know calculus, you can take the first derivative and set it = 0 .
y = 2x^2 + 12x + 36 Arrange to vertex form by completing the square
2 ( x^2 + 6x) + 36
2 ( x+3)^2 -18 + 36
2 (x+3)^2 + 18 <====vertex fom Vertex is -3,18
By graphing: see image
By calculus
derivative 4x + 12 = 0
x = -3 use this value in the original equation to find y = 18
(-3,18)
Describe and correct the error
Answers
Answer:
ok
Step-by-step explanation:
Seven less than twice a
number is negative five.
What is the number?
Answers
Answer:
n = 1
Step-by-step explanation:
Represent the number by n. Then "seven less than twice a number is -5 becomes 2n - 7 = -5
Next we must solve for n. Adding 7 to both sides yields 2n = 2, so that
n = 1
How do you find the diameter of a quarter circle?
Answers
Answer:
um 1/4
Step-by-step explanation:
What is the value of x in the solution to this system of equations?
3 x - 5 y = 22
y = -5 x + 32
Answers
2) x=-y/5 + 32/5
The average of 2, 3, and what number is 10?
Answers
Answer:
the average number of 2 and 3 is 2.5 and 10 is an integer
Step-by-step explanation:
g(x)=x-6
If the opposite of g(x) is -g(x),
then -g(x) =
Answers
x-6=0
The answer is x=6
A carpenter needs to build a box to hold his wood screws. He has a sheet of wood that measures 18 inches by 12 inches. He then cuts equal squares from each corner. (a) Write an expression for the length, width, and height for the open box. (b) Write a function for the volume (use factored form).
Answers
The expressions for the length, width, and height are 18 - 2x, 12 - 2x, and x while the volume function is V = (12 - 2x)(18 - 2x)x
(a) How to determine the expression for the length, width, and heightFrom the question, we have the following parameters:
Dimension of sheet = 8 inches by 12 inches
Also from the question, we understand that:
He cuts equal squares from each corner.
The cut-out length from the sheet would represent the height of the box
Represent this cut-out length with x
So, we have
Height = x
The width and the length are then represented as
Width = Initial width - 2x
Length = Initial length - 2x
So, we have
Width = 12 - 2x
Length = 18 - 2x
(b) Write a function for the volumeThe volume of a box is the product of its dimensions
In this case, we have
Width = 12 - 2x
Length = 18 - 2x
Height = x
So, we have
Volume = Width * Length * Height
Substitute the known values in the above equation So, we have the following equation
V = (12 - 2x)(18 - 2x)x
So, the volume function is V = (12 - 2x)(18 - 2x)x
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Consider the following: x 29 62 75 99 108 y 215 225 173 129 111 1) what is slope of the regression line predicting y from x,rounded to 2 decimal places?
Answers
The slope of the regression line predicting y from x is 0.30.
Given that,
x y
29 215
62 225
75 173
99 129
108 111
So, the coordinate points are (29, 215) and (62, 225)
The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).
Here, slope = (225-215)/62-29)
= 10/33
= 0.30
Therefore, the slope of the regression line predicting y from x is 0.30.
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Keisha and Ryan walk around a track. Keisha walks each lap in 5 minutes. Ryan walks each lap in 7 minutes. The two of them begin at the starting line at the same time. They walk until the meet again at the starting line. Answer the following questions.
Answers
Answer:
See below
Step-by-step explanation:
Keisha walks faster than Ryan so she will lap Ryan as a way of catching up to him.
LCM of 7 and 5 is 35 which is the time taken to meet up again at the starting line
Thus she will have walked 7 laps and he will have walked 5
A client's inventory is recorded at $600,000 and is comprised of 1,000 items. The auditors examined a sample of items with a recorded balance of $100,000 and determined an audited value of $90,000. What is the estimated audited value for inventory
Answers
Based on the calculation done below, the estimated audited value for inventory is $540,000.
How is the estimated audited value for inventory calculated?This can be calculated using the following formula:
E = (T / S) * A ……………………… (1)
E = Estimated audited value for inventory = ?
T = Total value of inventory recorded by client = $600,000
S = Value of inventory sampled by the auditor as recorded by the client = $100,000
A = Audited value of the inventory sampled = $90,000
Substituting the values into equation (1), we have:
E = ($600,000 / $100,000) * $90,000
E = 6 * $90,000
E = $540,000
Therefore, the estimated audited value for inventory is $540,000.
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whats the sum of 1 3/5 + 8 1/2
Answers
Answer: i hope this helps
i need the brainliest
Step-by-step explanation:
Answer: 43 1/10
Step-by-step explanation:
A rectangular television is 45 inches by 30 inches. What is the length of its diagonal?
Answers
Answer:
54.1 inches (round to 1 dp)
Step-by-step explanation:
the formula to calculate the diagonal or a rectangle is
\(\sqrt{(w^{2} +l^{2})}\)
30^2+45^2 is 2925
and \(\sqrt{2925}\)
and the answer to that is 54.1 inches (to 1 dp)
5. To qualify for the state cross-country championships, Nora needs to run 4 miles in 30 minutes or less. Which is the slowest average rate, in minutes per mile, Nora could run to qualify for the state cross-country championships?
a) 7.2 b) 7.4 c) 7.5 d) 7.8
Answers
Nora could run 7.5 minutes per mile to qualify for the state cross-country championships. The correct answer is option c.
To qualify for the state cross-country championships, Nora needs to run 4 miles in 30 minutes or less. So, her average rate should be:
average rate = total time / total distance
If she runs at the slowest rate possible to still qualify, then her average rate would be:
average rate = 30 / 4 = 7.5 minutes per mile
Therefore, the correct option is c) 7.5.
If she runs slower than this average rate, then her total time would exceed 30 minutes and she would not qualify.
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which set of angles has the same terminal arm as 70 degrees?
Answers
Answer: B = B ∈ {70° + n*360° I n ∈ Z } where Z is the set of the integer numbers.
Step-by-step explanation:
If we have an angle A, the other angles that have the same terminal arm than A can be written as:
B = A + n*360°
Here B is a "coterminal" angle to A. (they have the same terminal side)
where n can be any integer number (if n = 0 we have A = B, which is trivial, this means that any angle can be coterminal with itself.)
So we can write the set as:
B = B ∈ {70° + n*360° I n ∈ Z }
The set of angles that has the same terminal arm as 70 degrees is B = B ∈ {70° + n*360°, n ∈ Z}.
We have to determine, which set of angles has the same terminal arm as 70 degrees.
According to the question,
Let, The angle A and other angle B that have the same terminal arm as A can be written as,
B = A + n × 360°
Where the value of angle A is 70 degrees.
B is the coterminal angle, and they have the same terminal,
And n is the number of integers.
Substitute the value of A in the equation,
B = 70 + n × 360°
Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.
Since the value of n is equal to 0 then A = B,
Therefore, The angles coterminal with itself is called trivial.
Hence, The set of angles that has the same terminal arm as 70 degrees is B = B ∈ {70° + n*360°, n ∈ Z}.
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Help with slope pleaseee
^^
Answers
You have to do to get the answer
Carly bought some nike air force ones for $90. If the sales tax was 8.5%. How much did he pay in total?
Answers
have a good day =)
Please solve this problem and show work.
Answers
Option c) 4.8 is solution to this equation.
Define cube root.The factor we multiply by itself three times to obtain a number is its cube root. 3 cube root of, end cubic root is the symbol for the cube root. The definition of a cube is the process of multiplying a number by itself three times, and a cube root is the opposite of a cube. Alternately, we could state that a number's cube root gives us a number that, when cubed, gives us the same number and is referred to as a perfect cube. Both the prime factorization approach and the long division method can be used to get a number's cube root.
Given Data
x³ + 9 = 117
x³ = 117 - 9
x³ = 108
x =∛108
Cube root:
x = 4.76
Option c) 4.8 is solution to this equation.
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60% of the teachers completed the last survey sent out from the school. If 30 teachers completed the survey, how many total teachers are at the school?
Answers
Answer:
50
Step-by-step explanation:
Let the number of teachers is t.
60% of t is 30
0.6t = 30
t = 30/0.6
t = 50
Abdurrahman wants to go to the movies ($11.00) and get popcorn ($4.50) and a coke ($2.95). He asks for at most $20.00. His dad gives him $18.00.
T/F Abdurrahman got what he asked for.
Select one:
True
False
Answers
Answer:
True
Step-by-step explanation:
1) Add up the cost of all items.
11+4.50+2.95=18.45
2) Compare with 18.
18.45>18
Therefore, Abdurrahman got what he asked for.
Find the area of each
Answers
Answer:
44.73 (C)
Step-by-step explanation:
Because 6.3 and 7.1 multiplyed together is 44.73 this answer is correct
Answer:
it is C.
Step-by-step explanation:
You multiply 7.1 times 6.3 to get your answer.
how does one do this equasion 6234653928+294292342-424624642x16515615615165161x1156+6466456
Answers
The given Expression simplifies to -8.1069556e+27
What is BODMAS rule?BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. A mathematical expression's order of execution is explained using the BODMAS.
Given an equation to solve,
6234653928 + 294292342 - 424624642 x 16515615615165161 x 1156 + 6466456
Let us consider this Expression as A + B - C * D * E + F, with the corresponding terms being equal
By, the BODMAS rule,
First step: Multiply C, D, E. Let this be G
Now, the equation will look like this: A + B - G + F
Second step: We can add and subtract according to the signs now
On solving, the expression simplifies to -8.1069556e+27
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Prove that the medians to the legs of an isosceles triangle are congruent.
Answers
Step-by-step explanation:
Let ABC be an isosceles triangle with sides AC and BC of equal length.
We need to prove that the medians AD and BE are of equal length.
Consider the triangles ADC and BEC.
They have two congruent sides that include congruent angles.
Indeed, AC = BC by the condition, because the triangle ABC is isosceles.
Since the lateral sides AC and BC are of equal length, their halves EC
and DC are of equal length too: EC = DC.
Finally, the angle ECD is the common angle.
Thus, the triangles ADC and BEC are congruent, in accordance to the
postulate P1 (SAS) (see the lesson Congruence tests for triangles of the
topic Triangles in the section Geometry in this site).
Hence, the medians AD and BE are of equal length as the corresponding sides
of these triangles.
The proof is completed.
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Answers
1/2 or 0.5
Step-by-step explanation:
The equation is y=rx
And you know what y and x is.
Substitute the first numbers in;
4.5 = r (9)
Divide by r 9 each side, so r = 4.5/9 = 1/2
Hope this helps!