Find all values of x so that rank(A)=2.A=⎡⎢⎣−210701x910−31⎤⎥⎦
Answers
The values of x that satisfy rank(A)=2 are x = -9/10 and all values except x = -9/10. To find all values of x so that rank(A) = 2, we first need to perform row reduction on matrix A:
A = ⎡⎢⎣−210701x910−31⎤⎥⎦
Begin by swapping the first and second rows:
A = ⎡⎢⎣7101x−210−31⎤⎥⎦
Now, divide the first row by 7:
A = ⎡⎢⎣101x/7−3/107/103/10−31⎤⎥⎦
Next, add 2 times the first row to the second row:
A = ⎡⎢⎣101x/7−3/1003/10 + 2x/7−1⎤⎥⎦
In order for rank(A) to be 2, the second row cannot be a multiple of the first row. Thus, the coefficients of x in the second row must not be a multiple of the first-row coefficients.
3/10 + 2x/7 ≠ k(x/7), where k is any scalar multiple.
Multiplying both sides by 70 to eliminate fractions, we get:
21 + 20x ≠ 10kx
Rearrange the equation:
20x - 10kx ≠ -21
Factor out x:
x(20 - 10k) ≠ -21
For the rank to be 2, x cannot be equal to -21/(20 - 10k) for any integer k.
So, the values of x that make rank(A) = 2 are all real numbers except -21/(20 - 10k), where k is any integer.
To find all values of x so that rank(A)=2, we need to perform row operations on matrix A to bring it to reduced row echelon form and count the number of non-zero rows. If the number of non-zero rows is 2, then the rank of A is 2.
Starting with matrix A:
⎡-2 1 0⎤
⎢ 0 -7 1⎥
⎣ 0 9 10x⎦
Performing row operations:
R2 -> R2 + 3/2 R1
R3 -> R3 + 9/2 R1
⎡-2 1 0 ⎤
⎢ 0 -7 1 ⎥
⎣ 0 0 10x+9 ⎦
Now we have three possible cases:
1. If 10x+9 = 0, then the third row is all zeros and the rank of A is 2. Solving for x, we get:
10x+9 = 0
10x = -9
x = -9/10
2. If 10x+9 ≠ 0 and x ≠ -9/10, then the third row is non-zero and the rank of A is 3.
3. If 10x+9 ≠ 0 and x = -9/10, then the third row becomes all zeros and the rank of A is 2.
Therefore, the values of x that satisfy rank(A)=2 are x = -9/10 and all values except x = -9/10.
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Related Questions
In the figure below, m||n. Match the angle pairs with the
correct label for the pairs.
Answers
On solving the provided question, by properties of parallel lines we got to know that - 1 - A 2 - C 3 - B 4 - D
what is alternate exterior angles?When two or more lines cross the intersection line, alternate exterior angles result. These angles are created on a number of sides outside the transverse lines. Any two parallel lines that cross one another create two angles with the horizontal line. In the area between the parallel lines, interior angles are formed, while alternate exterior angles are formed in the area outside the parallel lines.
Matches are -
1 - A
2 - C
3 - B
4 - D
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Replace the polar equation rcosθ+rsinθ=1
with an equivalent Cartesian equation. Then identify the graph.
Answers
Since r = √(x² + y²) in Cartesian coordinates, we can substitute it into the equation: x + y = √(x² + y²).
How can we convert a polar equation to a Cartesian equation?To convert the polar equation rcosθ + rsinθ = 1 into a Cartesian equation, we can use the trigonometric identities cosθ = x/r and sinθ = y/r.
Substituting these identities, we get x + y = r. Since r = √(x² + y²) in Cartesian coordinates, we can substitute it into the equation: x + y = √(x² + y²).
To identify the graph, we can rearrange the equation to form x² + y² = (x + y)², which simplifies to x² + y² = x² + 2xy + y². Canceling out the x² and y² terms, we obtain 2xy = 0.
This equation represents two perpendicular lines, one along the x-axis and the other along the y-axis, intersecting at the origin.
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Big D decided to lose a few pounds and began
training for a triathlon. At first, he began
walking and eating a cheeseburger but soon
realized that wouldn't work too well. Months
went by and he built up his endurance so that
over the course of one particular week, he ran
seven times as much as he swam and biked
three times as far as he ran. At the end of the
week he realized he went a total of 232 miles!
How many miles did Big D train for each for the
week?
Answers
Answer:
NO
Step-by-step explanation:
What is the inverse of this function? f(x)=1/3x-2
Answers
The inverse of the function f(x) = 1/3x-2 is f^-1(x) = (1 + 2x)/3x.
Inverse of a functionA function f is has an inverse if it is both one-to-one and onto.
Given the function f(x) = 1/3x-2
we replace f(x) with y and make x the subject of the formula to derive the inverse function f^-1(x) as follows ;
y = 1/3x - 2
by cross multiplication
3x - 2 = 1/y
add 2 to both sides of the equation
3x = 1/y + 2
3x = (1 + 2y)/y
divide both sides of the equation by 3
x = (1 + 2y)/y ÷ 3
x = (1 + 2y)/3y
So, f^-1(x) = (1 + 2x)/3x
Therefore, the inverse of the function f is derived by interchanging the value of x for y and vice versa, that is f^-1(x) = (1 + 2x)/3x.
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Here is an equation that is true for all values of x: 6(x + 3) = 6x + 18. Londyn saw this equation and says she can tell 18( x + 3) + 32 = 3(6x + 18) + 32 is also true for any value of x. How can she tell? Explain your reasoning.
Answers
Londyn can tell that 18(x + 3) = 3(6x + 18) by factorization
What is Factorization?factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is a factorization of the integer 15, and (x – 2)(x + 2) is a factorization of the polynomial x2 – 4.
6(x + 3) = 6x + 18 which is true as a result of multiplying each term in the bracket by 6 otherwise say expansion.
But in 18(x + 3) + 32 = 3(6x + 18) +32, can be done by expansion and then factoring out 3. She can tell that both are equal by expanding the two expression at the left and right which will give the same result.
In conclusion expanding both terms of the equation will yield the same result.
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If sin θ=4/5 and 90°<θ<180°, what is cos θ?
Answers
Answer:
Cos ∅ = 3/5
BUT COSINE IS NEGATIVE IN THE SECOND QUADRANT.
Thus cos∅= -3/5
Two drivers, A and B, are archrivals competing in an automobile race. Driver A had been leading driver B for a while by a steady 3 miles, but at exactly 2 miles from the finish, driver A ran out of gas and decelerated thereafter at a rate proportional to the square of his remaining speed. One mile later, driver A's speed was exactly halved. If driver B's speed remained constant, who won the race? An outline for how to answer this question is given below: 1. Let s(t) denote the distance in miles traveled by driver A for t≥0, where t=0 is the point at which driver A ran out of gas. (Side note: As it turns out, we will not need to know the units for t to answer our given problem!). Let vA (t) be driver A's velocity, so that ds/dt=vA(t), and let vB be the constant velocity of driver B. Using k for the constant of proportionality, set up and solve an initial value problem to find an expression for vA(t) that depends only on vB,k, and t. 2. Using your result from problem 1, set up and solve an initial value problem to find an expression for s(t) that (again) only depends on vB,k, and t. 3. Let t=t1 be the moment when driver A's speed was halved-i.e., the moment when A has traveled for one mile after running out of gas. Use this to show that k=ln2. Write an expression for s(t) that depends only on vB and t. 4. Let tB be the moment when driver B crosses the finish line. Write tB as an expression depending only on vB, then evaluate s(tB). Did driver A cross the finish line before or after driver B?
Answers
By evaluating the expression for s(tB), we can determine whether driver A crossed the finish line before or after driver B. If s(tB) is positive, it means driver A crossed the finish line before driver B. If s(tB) is negative, it means driver A crossed the finish line after driver B.
To solve the initial value problem, we start with the equation vA'(t) = -k(vA(t))^2, where vA'(t) represents the derivative of vA with respect to t.
This equation describes the deceleration of driver A, proportional to the square of his remaining speed. Rearranging and solving the differential equation, we get vA(t) = 1 / (kt + C), where C is a constant determined by the initial conditions.
To find the expression for s(t), we integrate vA(t) with respect to t: s(t) = ∫(1 / (kt + C)) dt. Integrating this expression gives us s(t) = (1/k) ln(kt + C) + D, where D is another constant determined by the initial conditions.
At t = t1 (when driver A's speed is halved, i.e., one mile after running out of gas), we have vA(t1) = vA(0) / 2. Plugging this into the expression for vA(t) from step 1, we find 1 / (k * t1 + C) = (1 / (k * 0 + C)) / 2. Simplifying, we get k = ln(2) / t1.
Using the expression for s(t) from step 2, we can find tB by settings S(tB) = 3 (since driver A was leading by 3 miles). Simplifying this equation, we find tB = (e^(3k) - C) / k. Plugging in the value of k we found in step 3, we have tB = (e^(3ln2 / t1) - C) / (ln2 / t1).
To evaluate s(tB), we substitute t = tB into the expression for s(t) from step 2, resulting in s(tB) = (1/k) ln(ktB + C) + D. Since tB depends only on vB and t1, and C and D are constants determined by the initial conditions, s(tB) depends only on vB.
If s(tB) is positive, it means driver A crossed the finish line before driver B. If s(tB) is negative, it means driver A crossed the finish line after driver B.
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Please help out, I need it right this instant!!
Answers
Skye's estimated cost per year with the financial aid, is x - 6400
The estimated costFrom the question, we have the following
Scholarship and grant = $4300
Work-study = $2100
So, the total is
Total = 4300 + 2100
Total = 6400
This is then subtracted from the total estimated expenses for the year
Representing this with x, we have
Estimated cost = x - 6400
How much will Skye contribute each yearIn (a), we have
Estimated cost = x - 6400
Then we have
Famiily = 7000
This means that
Skye's contribution = x - 6400 - 7000
Evaluate
Skye's contribution = x - 13400
Checking if Skye will save enoughWe have
Monthly savings = $300
So, the total savings per year is
Annual = $3600
In (b), we have
Skye's contribution = x - 13400
So, the remaining is
Remaining = x - 13400 - 3600
Evaluate
Remaining = x - 17000
The above may or may not cover the total expenses, depending on the value of x
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Which rate of change is the fastest 0 to 3 or 6 to 9?
Answers
Answer:
actually they both have equal rates of change
Step-by-step explanation:
so what you would do here would be count from 0 and go to 3 however many fingers it took to go from 0 to 3 which in this case would be 3 that's the rate of changes and do the same thing for 6 to 9 and you also get 3.
hope this helps
In the figure, AE and BD intersect at C.
Prove that a + b = d + e.
Answers
Answer:
Please see the attached picture for full solution.
−3(a−8)+4a=−8(a+3)+3
Answers
Reason
Distribute multiply parentheses first
-3(a-8) +4a= -8(a+3)+3
-3a +24 +4a = -8a -24 +3
Now combine like terms to isolate “a”
-3a +4a +8a = -24 +3 -24
9a = -45
Now divide both sides by 9 to solve for “a”
a= -5
identify the characteristics of a spontaneous reaction. δg° < 0 δe°cell > 0 k > 1 all of the above none of the above
Answers
Spontaneous reactions are those that occur with no input of energy, and are characterized by a negative standard Gibbs free energy, a positive standard cell potential, and an equilibrium constant greater than one.
A spontaneous reaction is one that occurs without any external input of energy, and it always proceeds in a single direction. Characteristics of a spontaneous reaction include the following:
1. The standard Gibbs free energy of the reaction (δG°) is negative, indicating that the reaction is energetically favorable and will occur on its own.
2. The standard cell potential (δE°cell) is greater than zero, indicating that the reaction is capable of producing a useful electrical current.
3. The reaction's equilibrium constant (K) is greater than one, indicating that the reaction's products are favored over its reactants at equilibrium.
In summary, spontaneous reactions are those that occur with no input of energy, and are characterized by a negative standard Gibbs free energy, a positive standard cell potential, and an equilibrium constant greater than one.
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find the measure of each lettered angle. a=, b=, c=, d=, e=
Answers
Answer:
a= 20
b= 70
c= 20
d=70
e=110
Step-by-step explanation:
a + the 70 degree angle have to equal 90 degrees (the right angle marking) and the same with b + a. So to ind a, you do 90-70 and to find b, because you now have the value of a, you do 90-20.
a+b+c+70 is equal to a 180 degree angle, so since you know the value of a and b, now you can figure out c by doing 180-(70+20+70).
d and the 70 degree angle are vertical angles so they are equal to each other.
lastly for e, d+e is equal to 180 degrees so since you know the value of d, you just do 180-70 to find e.
Answer:
a = 20°
b = 70°
c = 20°
d = 70°
e = 110°
Step-by-step explanation:
Angle A is complementary with 70°, so they add together to = 90° (as indicated by the 90° mark).
90° - 70° = 20°
Angle A = 20°
Angle B is complementary with angle A, 20°, so they also add together to = 90°.
90° - 20 = 70°
Angle B = 70°
Although not indicated by a 90° mark, Angle C and Angle B are complementary since they share a straight line with the complementary angles A and 70°. This means Angles C + B = 90°
90° - 70° = 20°
Angle C = 20°
Angle D is vertical to 70°, so Angle D = 70°
Angle E is supplementary to 70°, so they should combine to = 180°
180° - 70° = 110°
Angle E = 110°
Enter 8 100 as a money amount and as a decimal in terms of dollars
Answers
Answer:
8.1-00
Step-by-step explanation:
Enter 8 100 as a money amount and as a decimal in terms of dollars
how much mewtal is needed to cast a cubical metal box with 12 inch long exterior edges if the thickness of its walls should be exactly 3 inches?
Answers
Total metal needed to cast a cubical metal box with exterior edge length 12 inches and thickness 3 inches is equal to 999cubic inches.
Length of the exterior edge of the cubical metal box = 12 inches
Thickness of the wall of cubical metal box = 3 inches
Length of the interior edge of the cubical metal box
= 12 inches - 3 inches
= 9 inches
Volume of the exterior cubical metal box = 12³
= 1728 cubic inches
Volume of the interior cubical metal box = 9³
= 729cubic inches
Total metal required to cast a cubical metal box
= (Volume of the exterior - Volume of the interior )cubical metal box
= (1728 - 729 )cubic inches
= 999 cubic inches
Therefore, the total metal required to cast a cubical metal box is equal to 999 cubic inches.
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of the $261,000 received from contributors, $240,000 came from four contributors, each giving $60,000; the other $21,000 came from small individual contributions.
Answers
In the total amount of $261,000 received from contributors, a majority of $240,000 came from four contributors, with each contributing $60,000. The remaining $21,000 was obtained from smaller individual contributions.
This statement describes the breakdown of contributions received from different sources. Out of the total amount of $261,000, the majority, which is $240,000, came from four specific contributors. Each of these contributors donated $60,000, resulting in a combined contribution of $240,000. The remaining $21,000 represents the sum of smaller individual contributions from various sources.
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A 90% confidence interval for the mean of a population is computed to be 135 to 160. Which one of the following claims would the interval tend to refute?A. The population mean is more than 110.B. The population mean is less than 150.C. The population mean is between 140 and 150.D. The population mean is more than 140.E. The population mean is less than than 125.
Answers
Therefore, the only claim that the interval would tend to refute is option E: The population mean is less than 125.
Based on the 90% confidence interval of 135 to 160, we can conclude that the population mean is likely to be within this interval with a 90% degree of confidence.
A. The claim that the population mean is more than 110 is not refuted by the confidence interval since the lower limit of the interval is above 110.
B. The claim that the population mean is less than 150 is not refuted by the confidence interval since the upper limit of the interval is above 150.
C. The claim that the population mean is between 140 and 150 is not refuted by the confidence interval since both values are within the interval.
D. The claim that the population mean is more than 140 is not refuted by the confidence interval since the lower limit of the interval is above 140.
E. The claim that the population mean is less than 125 is refuted by the confidence interval since the lower limit of the interval is above 125.
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I need explanation i already know answer
Jack k buys four apples.
He pays with a £2 coin.
He gets £1.20 change.
How much does one apple cost? Ans=20p
Answers
Step-by-step explanation:
so he goes with a 200p, spends 80p, so he comes back with 120p
4 x 20 = 80p and he's paying for it so he gives the money away
120 -80 =20
what are solutions for |x+4|=3x-5
Answers
Answer:
Step-by-step explanation:
what structure is indicated by: 10a, 15t, 3g, 7c?
Answers
The structure indicated by: 10a, 15t, 3g, 7c? is a structure related to the composition of a DNA or RNA sequence.
The given information "10a, 15t, 3g, 7c" suggests a pattern or structure related to the composition of a DNA or RNA sequence.
In molecular biology, DNA and RNA are made up of nucleotides, which consist of a nitrogenous base (adenine, thymine/uracil, guanine, or cytosine) and a sugar-phosphate backbone.
Based on the provided data, it appears that the numbers preceding each letter indicate the count or frequency of that particular nucleotide in the sequence.
Therefore, the structure indicated by "10a, 15t, 3g, 7c" implies the composition of a DNA or RNA sequence with the following nucleotide counts:
10 adenine (A) nucleotides (abbreviated as 10a)
15 thymine (T) nucleotides (abbreviated as 15t)
3 guanine (G) nucleotides (abbreviated as 3g)
7 cytosine (C) nucleotides (abbreviated as 7c)
Together, these nucleotides make up a portion of the DNA or RNA sequence, indicating the presence and quantity of each base in that particular section.
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PLease help due today! I will give brainliest!!
Select the correct answer.
Simplify the expression.
\(\(\sqrt[5]{224x^{11}yx^{8} }\)\)
![PLease help due today! I will give brainliest!! Select the correct answer.Simplify the expression.[tex][tex]\sqrt[5]{224x^{11}yx^{8}](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/2QPEOMbfMPswDcBHTcfTCbdoPOXVM1gU.png)
Answers
Hopes this helps
find the quadratic equation
Answers
The temperature in a town is 34.1°F during the day and −8.6°F at night. Find the difference in the temperatures.
Answers
Answer:
42.7 °F
Step-by-step explanation:
To find difference, just subtract it. 34.1 - (-8.6) = 42.7°F
A bus is traveling from Miami, Florida to Charlotte, North Carolina. The distance it travels in miles, d, is
related to the rate in miles per hour, r, by the equation d 60t.
What is the average rate of speed for the bus?
1
How far will it travel in 2.5 hours?
T
miles How long will it take to go 330 miles? Round to the nearest tenth.
Answers
Answer:
the other day I dey bro you doing today I hope
If I can read 54 pages in 3 days, how many can I read in 1 day?
Answers
Answer:
18
Step-by-step explanation:
Step 1)
54 ÷ 3 = 18
Answer:
54/3
Step-by-step explanation:
we can use crisscross multipleWhat is the equation of this line?
•y=-1/2x
•y=1/2x
•y=-2x
•y=2x
Answers
Answer:
Y= 2X
Step-by-step explanation:
The Y intercept is 0, therefore it would not have a "b" if it were in the form y=mx+b.
The line is going right, so it's positive. From 0, the line goes over 2, up 2, so the slope is 2.
Find the surface area of the prism.
5m
4 m
m²
6 m
5m
7 m
Answers
Answer:
160m².
Step-by-step explanation:
In this case, the prism has two identical rectangular faces with dimensions of 5m by 4m, and four identical rectangular faces with dimensions of 5m by 6m.
Therefore, the surface area of the prism can be calculated as follows:
Surface Area = 2(5m x 4m) + 4(5m x 6m)
Surface Area = 40m² + 120m²
Surface Area = 160m²
So the surface area of the prism is 160m².
Please help me! :( 30 points
What are the x-values when y = 0 for this function?
x =
x =
Answers
Answer:
The x-values when y = 0 for this function are -2 and 3.
Answer:
Step-by-step explanation:
\(y=0\) when the graph cuts the x-axis.
So when \(y=0,\) \(x=-2\) and \(x=-9\).
Given that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2, the probability that X is between 46 and 54 is
A.0.9544
B. 04104
C. 0.0896
D. 0.5896
Answers
The correct answer is option A, 0.9544. The probability that the normally distributed random variable X, with a mean of 50 and a standard deviation of 2, falls between 46 and 54 is approximately 0.9544.
To find the probability, we can use the standard normal distribution table or calculate it using z-scores. In this case, we need to find the z-scores for both 46 and 54.
The z-score formula is given by:
z = (X - μ) / σ
where X is the value of interest, μ is the mean, and σ is the standard deviation.
For 46:
z1 = (46 - 50) / 2 = -2
For 54:
z2 = (54 - 50) / 2 = 2
We can now look up these z-scores in the standard normal distribution table or use a calculator to find the corresponding probabilities. The area under the curve between -2 and 2 represents the probability that X falls between 46 and 54.
Using the standard normal distribution table, we find that the area under the curve between -2 and 2 is approximately 0.9544. Therefore, the correct answer is option A, 0.9544.
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Express 1/10 cm as a fraction of 3 metres
Answers
Answer:
1/3000
Step-by-step explanation:
3 meters to centimeters:
3 × 100 = 300
= 1/10 ÷ 300
= 1/10/300
= 1/(10×300)
= 1/3000