1. Find all exact solutions on [0, 2π). (Enter your answers as a comma-separated list. )2 cos2(t) + cos(t) = 1t =2. Find all exact solutions on [0, 2π). (Enter your answers as a comma-separated list. )2tan2(t) = −3 sec(t)t =3. Solve for 0 ≤ θ < π. (Enter your answers as a comma-separated list. )sin(θ) = sin(2θ)θ =4. Find all exact solutions on the interval [0, 2π). (Enter your answers as a comma-separated list. )cos(2t) = −sin(t)t =5. Find all exact solutions on the interval [0, 2π). Look for opportunities to use trigonometric identities. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE. )cos(2x) − cos(x) = 0x =
Answers
a) The exact solutions on [0, 2π) are t = π/3, π, and 5π/3. b) The exact solution on the interval [0, π) is t = 2π/3. c) The solutions are θ = π/3 and θ = 5π/3. d) The exact solutions on the interval [0, 2π) are: t = arcsin[(-1 + \(\sqrt{41}\))/4] and t = 2π - arcsin[(-1 + \(\sqrt{41}\))/4] using trigonometric identities.
a) We can rewrite the equation as:
2\(cos^{2}t\) + cos(t) - 1 = 0
Using the quadratic formula, we get:
cos(t) = [-1 ± \(\sqrt{1-4(2)(-1)}\) ] / (4)
cos(t) = [-1 ± \(\sqrt{9}\)]/4
cos(t) = [-1 ± 3]/4
Thus, we have two solutions:
cos(t) = 1/2, which gives us t = π/3 and t = 5π/3
cos(t) = -1, which gives us t = π
Therefore, the exact solutions on [0, 2π) are t = π/3, π, and 5π/3.
b) We can use the identity \(tan^{2}t\) + 1 = \(sec^{2}t\) to rewrite the equation as:
\(tan^{2}t\) = - \((3/2)^{2}\)
Taking the square root of both sides and remembering that tan(t) is negative in the third quadrant, we get:
tan(t) = -3/2
Using the identity tan(t) = sin(t)/cos(t), we can rewrite this as:
sin(t)/cos(t) = -3/2
Multiplying both sides by cos(t) and rearranging, we get:
sin(t) = -3cos(t)/2
Squaring both sides and using the identity \(sin^{2}t\) + \(cos^{2}t\) = 1, we get:
9\(cos^{2}t\)/4 + \(cos^{2}t\) = 1
Expanding and simplifying, we get:
13 \(cos^{2}t\) /4 = 1
\(cos^{2}t\) = 4/13
Taking the square root of both sides and remembering that cos(t) is negative in the third quadrant, we get:
cos(t) = -2\(\sqrt{13}\) /13
Using the identity \(sin^{2}t\) + \(cos^{2}t\) = 1, we can solve for sin(t) as:
sin(t) = -3/2 cos(t) = 3\(\sqrt{13}\) /13
Therefore, the exact solution on the interval [0, π) is t = 2π/3.
c) We can use the identity sin(2θ) = 2sin(θ)cos(θ) to rewrite the equation as:
sin(θ) = 2sin(θ)cos(θ)
Dividing both sides by sin(θ) (assuming sin(θ) is non-zero), we get:
1 = 2cos(θ)
cos(θ) = 1/2
Therefore, the solutions are θ = π/3 and θ = 5π/3.
d) We can use the identity cos(2t) = 1 - 2 \(sin^{2}t\) and rearrange the equation as:
2 \(sin^{2}t\) + sin(t) - 5 = 0
Solving this quadratic equation using the quadratic formula, we get:
sin(t) = [-1 ± \(\sqrt{41}\)]/4
Since the sine function has a range of [-1, 1], only the positive solution is possible, so we have:
sin(t) = (-1 + \(\sqrt{41}\))/4
Using the identity \(cos^{2}t\) = 1 - \(sin^{2}t\) , we can solve for cos(t) as:
cos(t) =\(\sqrt{1-sin^{2}t}\) = \(\sqrt{17-\sqrt{41} }/4\)
Therefore, the exact solutions on the interval [0, 2π) are:
t = arcsin[(-1 + \(\sqrt{41}\))/4] and t = 2π - arcsin[(-1 + \(\sqrt{41}\))/4]
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Related Questions
HURRY PLEASE!!!
It is given that y varies inversely as x varies. If x = 15 and y = 2, what is the value of y when x = 5?
A) 12
B) 6
C) 4
D) 3
Answers
Answer:
b
Step-by-step explanation:
comment if it was correct
Bo drove 448 miles in 7 hours. If he continued at the same rate, how long would it take to travel 1152 miles?
Answers
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
If 448 miles = 7 hours
1 miles = 7/448 hours
The time taken to travel 1152 miles is 18 hours.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
448 miles = 7 hours
Divide both sides by 448.
1 miles = 7/448 hours
Multiply 1152 on both sides.
1152 miles = 1152 x 7/448 hours
1152 miles = 18 hours
Thus,
If 448 miles = 7 hours
1 miles = 7/448 hours
The time taken to travel 1152 miles is 18 hours.
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Answer:18hours
Step-by-step explanation:
Giant pandas can spend up to 16 hours a day eating bamboo. How many minutes per day is this? Hint: 1 day = 1440 minutes
Answers
Answer:
960 minutes
Step-by-step explanation:
If there are 24 hours a day with 60 minutes then there are 1440 hours a day.
There 16 hours multiplied by 60 minutes will give you your answer! \(16*60=960\)
it is 690 minutes per 16 hours
1. There are 372 students in a middle school. Each school bus holds 32 students. lf every student in the school rides a bus, how many buses will be filled completely?
Answers
11 buses will be completely full and one bus will be partially full
please answer
4. Suppose that for 3MA Forecast, my Mean Absolute Deviation (MAD) is \( 3.0 \) and my Average Error (AE) is \( -2.0 \). Does my forecast fail the bias test? a. Yes b. No
Answers
The answer is: a. Yes, the forecast fails the bias test.
To determine whether the forecast fails the bias test, we need to compare the Average Error (AE) with zero.
If the AE is significantly different from zero, it indicates the presence of bias in the forecast. If the AE is close to zero, it suggests that the forecast is unbiased.
In this case, the Average Error (AE) is -2.0, which means that, on average, the forecast is 2.0 units lower than the actual values. Since the AE is not zero, we can conclude that there is a bias in the forecast.
Therefore, the answer is:
a. Yes, the forecast fails the bias test.
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plz help me asap i will mark you brainly :)
Answers
Answer:
413
Step-by-step explanation:
236 ÷ 4 = 59
59 x 7 hrs = 413
Answer:
413 miles
Step-by-step explanation:
236 miles: 4 hours
59 miles: 1 hour
59 miles per hour
In a 7 hour day the dump truck can travel 59 * 7 = 413 miles.
3x - 4.5 = -19.5
solve for x
Answers
Answer:
Step-by-step explanation:
3x=-15
x=-5
Answer:
-5
Step-by-step explanation:
1- Which of the following has had the greatest success treating major depression? Select one
A) MAO inhibitors
B) Lithium
C) tricyclic
D) SSRIs
2- Believing that you are being singled out for attention is a (an) Select one
A) delusion of persecution
B) delusion of reference
C) delusion of orientation
D) delusion of grandeur
Answers
1. The option D) SSRIs, The greatest success in treating major depression has been observed with the use of selective serotonin reuptake inhibitors (SSRIs).
These drugs are a type of antidepressant that work by increasing the levels of serotonin in the brain. SSRIs are considered to be the most effective medication for the treatment of depression, particularly in the long-term.
2. the option B) delusion of reference ,A belief that an individual is being singled out for attention is known as delusion of reference. Delusions are a common symptom of schizophrenia and other psychotic disorders.
A delusion of reference is characterized by the belief that everyday events or objects have a special meaning that is directed specifically towards the individual. For example, an individual with this delusion may believe that the radio is broadcasting a message meant for them or that strangers on the street are staring at them because they are part of a conspiracy.
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whats the answer pls
Answers
Answer:
y=0.75x-1
Step-by-step explanation:
What is 75% of 85$?
Pls help
Answers
Answer:63.75 :)
Step-by-step explanation:
Answer:
$63.75
Step-by-step explanation:
85 x 75/100
85/1 x 3/4
255/4 - > $63.75
- You should already know how to do this yourself as this is very easy and basic question.
Find the slope
Answers:
Question 1 options:
-3
3
-2
Answers
Answer:
b
Step-by-step explanation:
Suppose a doctor assigns treatment T, solely on the basis of three factors: age of the patient, blood pressure, and blood sugar level. Can you estimate the following regression equation Y, = α + pT1+ β,Age, + β2 (Blood pressure), + β3 (Blood sugar), + ei to get the causal effect of treatment on the outcome Y? Why or why not?
Answers
The regression equation cannot be estimated because additional confounding factors are needed.
To estimate the causal effect of treatment T on the outcome Y using the given regression equation, you would need to account for potential confounding factors. The equation you provided is:
Y = α + pT + β1(Age) + β2(Blood pressure) + β3(Blood sugar) + ei
In this equation, α represents the intercept, p represents the causal effect of treatment T, β1, β2, and β3 are coefficients for age, blood pressure, and blood sugar respectively, and ei is the error term.
In this specific scenario, the doctor is assigning treatment T solely based on age, blood pressure, and blood sugar level, which are already included in the model. If these are the only factors affecting both treatment assignment and the outcome Y, you can estimate the causal effect of treatment T on outcome Y using this regression equation. The coefficient p in this equation would represent the causal effect of treatment T on the outcome Y.
However, if there are other unmeasured or omitted variables that influence both treatment assignment and the outcome Y, the estimate of the causal effect may be biased. To draw accurate conclusions about the causal effect, you would need to account for any additional confounding factors.
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USE MATLAB
The transfer function of a system is given as G(s) = 3s+5:s²+6s+9 Find the zero input response y(t) if y(0) = 3 and y'(0) = −7
Answers
The zero input response y(t) can be written as: \(y(t) = -2/3e^{-3t} + 2/9te^{-3t} + 5/9 + 8/9e^{-3t}\)
Also , the zero input response y(t) is given as:\(y(t) = (8/9 - 2/3)e^{-3t} + 2/9te^{-3t} + 5/9\)
In the given question, we are given the transfer function of the system. The zero input response y(t) can be calculated using the following steps:
Step 1: Find the roots of the denominator of the transfer function. In the denominator, we have:s²+6s+9 = 0Using the quadratic formula, we get: s1 = s2 = -3Therefore, the denominator of the transfer function can be written as:
s²+6s+9 = (s+3)²
Step 2: Find the partial fraction of the transfer function. To find the partial fraction, we need to factorize the numerator of the transfer function.
G(s) = (3s+5):(s+3)²= A:(s+3) + B:(s+3)² + C Where A, B, and C are constants.
Multiplying both sides by (s+3)², we get:3s+5 = A(s+3)(s+3) + B(s+3)² + C On substituting s=-3 in the above equation, we get: C = 5/9On equating the coefficients of the terms with s and the constant term, we get:
A + 2B + 9C = 3A + 3B = 0On substituting C=5/9 in the above equation, we get: A = -2/3 and B = 2/9Therefore, the partial fraction of the transfer function can be written as: G(s) = -2/3:(s+3) + 2/9:(s+3)² + 5/9
Step 3: Find the inverse Laplace transform of the partial fraction of the transfer function. The inverse Laplace transform of the partial fraction of the transfer function can be calculated as: \(y(t) = -2/3e^{-3t} + 2/9te^{-3t} + 5/9\)
On substituting y(0) = 3 and y'(0) = −7, we get:3 = -2/3 + 5/9y'(0) = -2 + 10/9 = -8/9
Therefore, the zero input response y(t) can be written as: \(y(t) = -2/3e^{-3t} + 2/9te^{-3t} + 5/9 + 8/9e^{-3t}\)
Therefore, the zero input response y(t) is given as:\(y(t) = (8/9 - 2/3)e^{-3t} + 2/9te^{-3t} + 5/9\)
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Please help on 19 this needs to be finished tonight and I’m desperate I need help really bad my mom doesn’t understand this and my dad knows how to do it but can’t explain it and I don’t have any older siblings so I’m on my own when it comes to math please help me please
Answers
Step-by-step explanation:
\((4 {x }^{2} + 3 {y}^{2} ) {}^{0} \\ rule \: of \: zero = {x}^{0} = 1 \\ answer = 1\)
A byte is how many bits?
a. 8
b. 80
c. 800
d. Depends on the computer
Answers
Answer:
A byte is 8 bits.
how many ways are there to select a set of 8 donuts from 3 varieties in which at most 2 chocolate donuts are selected?
Answers
There are 3 possible scenarios for selecting a set of 8 donuts: no chocolate donuts are selected, 1 chocolate donut is selected, or 2 chocolate donuts are selected. For the first scenario, we choose 8 donuts from the 2 non-chocolate varieties, which can be done in (2+1)^8 ways (using the stars and bars method). For the second scenario, we choose 1 chocolate donut and 7 non-chocolate donuts, which can be done in 2^1 * (2+1)^7 ways. For the third scenario, we choose 2 chocolate donuts and 6 non-chocolate donuts, which can be done in 2^2 * (2+1)^6 ways. Therefore, the total number of ways to select a set of 8 donuts from 3 varieties in which at most 2 chocolate donuts are selected is (2+1)^8 + 2^1 * (2+1)^7 + 2^2 * (2+1)^6 = 3876.
To solve this problem, we need to consider the possible scenarios for selecting a set of 8 donuts. Since we want to select at most 2 chocolate donuts, we can have 0, 1, or 2 chocolate donuts in the set. We can then use the stars and bars method to count the number of ways to select 8 donuts from the remaining varieties.
The total number of ways to select a set of 8 donuts from 3 varieties in which at most 2 chocolate donuts are selected is 3876. This was calculated by considering the possible scenarios for selecting a set of 8 donuts and using the stars and bars method to count the number of ways to select donuts from the remaining varieties.
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The lines below are
perpendicular. If the slope of the green line is 2/3 what is
the slope of the red line?
Answers
Answer:
3/2 is the slope of red line
Step-by-step explanation:
The slope of a line that is perpendicular to another line is the reciprocal.
The reciprocal is when the numerator and denominator switch places. For example, the reciprocal of 2/3 us 3/2
We know that the slope of green line is 2/3.
So all we got to do is to find the reciprocal of 2/3, which is 3/2 as listed above.
So the slope of the red line is 3/2.
This is correct because i just learned this like 2 weeks ago and got good scores
the sum of two numbers is 23 and their difference is 5.
Let the two numbers be x and y.
Write two equations and solve them to find the two numbers
Answers
Answer:
y = 9
x = 14
Step-by-step explanation:
1st equation ⇒ x + y = 23
2nd equation ⇒ x - y = 5
1st equation - 2nd equation;
(x + y) - (x - y) = 23 - 5
x + y - x + y = 18
2y = 18
y = 18/2
y = 9
Substitute above solution in the 1st equation to find x;
x + y = 23
x + 9 = 23
x = 23 - 9
x = 14
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Placements of swimmers in a swim meet Choose the correct level of measurement. O A. Ratio OB. Ordinal O C. Interval OD. Nominal
Answers
Option B: One of the four levels of measurement (nominal, ordinal, interval, ratio) is best suited for determining the ordinal level.
Swimmer positions in a swim competition are a good illustration of an ordinal level of measurement. The existence of a natural order or ranking between the values being measured is what distinguishes ordinal data from other types of data.
The swimmers are appraised for this situation as indicated by how they are put on the platform; the primary spot finisher is positioned higher than the second-place finisher, etc.
The hole in time or distance between the positions, in any case, isn't consistent all the time. For example, there can be a greater time differential between the first and runner-up finishers than between the second and third-place finishers.
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If the diameter of a circle is 8. 4 in. , find the area and the circumference of the circle. Use 3. 14 for pi. Round your answers to the nearest hundredth
Answers
The circumference of the circle is 26.38 inches and the area of the circle is 55.39 square inches, both rounded to the nearest hundredth.
The diameter of a circle is the distance across the circle passing through its center. In this problem, the diameter of the circle is given as 8.4 inches. We can use the formula for the circumference and the area of a circle in terms of its diameter to find the solutions.
First, we can find the radius of the circle by dividing the diameter by 2. So, the radius is 8.4/2 = 4.2 inches.
To find the circumference of the circle, we can use the formula:
C = πd
where d is the diameter. Substituting the value of d = 8.4 inches and π = 3.14, we get:
C = 3.14 x 8.4 = 26.376
Therefore, the circumference of the circle is 26.38 inches (rounded to the nearest hundredth).
To find the area of the circle, we can use the formula:
A = πr²
where r is the radius. Substituting the value of r = 4.2 inches and π = 3.14, we get:
A = 3.14 x (4.2)² = 55.3896
Therefore, the area of the circle is 55.39 square inches (rounded to the nearest hundredth).
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Graph a parabola whose vertex is at (3,5)(3,5)left parenthesis, 3, comma, 5, right parenthesis with yyy-intercept at y=1y=1y, equals, 1.
Answers
Using the given information we found that the equation of the parabola is:
y = (-4/9)*(x - 3)^2 + 5
And its graph is below.
How to get the equation of the parabola?
For a parabola with vertex (h, k), the equation is:
y = a*(x - h)^2 + k
Here the vertex is (3, 5), so the equation is:
y = a*(x - 3)^2 + 5
And the y-intercept is y = 1, this means that:
1 = a*(0 - 3)^2 + 5
1 = a*9 + 5
1 - 5 = a*9
-4/9 = a
So the parabola is:
y = (-4/9)*(x - 3)^2 + 5
And its graph is below.
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Sally's balance on her credit card is $75.00 on the first day of august. she makes a payment of $18.00 on august 17 and
a new purchase of $41.00 on august 29. the annual interest rate is 21.25%. what is sally's average daily balance and
finance charge for the month of august?
Answers
The average daily balance for the month was $84.21, and the finance charge for the month was $30.13.
AveragesGiven that Sally's balance on her credit card is $75.00 on the first day of August, and she makes a payment of $18.00 on August 17 and a new purchase of $41.00 on August 29, and the annual interest rate is 21.25%, to determine what is Sally's average daily balance and finance charge for the month of August, the following calculation must be made:
75 x ((21.15/12 x 16) / 100) + 75 = A = 86.8957 x ((21.15/12 x 13) / 100) + 57 = B = 70.0698 x ((21.15/12 x 3) / 100) + 98 = C = 103.18(86.89 x 16 + 70.06 x 13 + 103.18 x 3) / 31 = X84.21 = X86.89 + 70.06 + 103.18 - 75 - 57 - 98 = Y30.13 = YTherefore, the average daily balance for the month was $84.21, and the finance charge for the month was $30.13.
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Ranger was given this expression to simplify.
4(2x – 5)
What advice to simplify the expression would you give Ranger? Check all that apply.
Answers
8 This will be your result, check 3 kisses to see if it was okay, I hope and it will serve you well.
Answer:
what the real answer?
Step-by-step explanation:
Assuming x and y are two odd numbers and x/y is an integer. Which of the following statements are true?
1: x + y is odd.
2: xy is odd.
3: x/y is odd.
4: x-y is odd.
A: 1 and 2 only.
B: 1 and 3 only.
C: 2 and 3 only.
D: 2, 3, and 4 only.
E: 2 and 4 only.
Answers
9514 1404 393
Answer:
C: 2 and 3 only.
Step-by-step explanation:
We know the sum or difference of two odd numbers is even, eliminating choices (1) and (4).
The product of two odd numbers is odd, so (2) is one of the true statements.
__
Let x/y = k, where x and y are both odd. Then x = ky. If k is even, then x is even, a contradiction. So, k must be odd. The integer ratio of two odd numbers is odd, so (3) is one of the true statements.
Only statements (2) and (3) are true.
What is the y-intercept of the linear function graphed here?
Answers
Answer:
The y intercept is -2
Step-by-step explanation:
The line passes through the Y-axis at one point, that point is -2. This therefore, is the Y-intercept.
15 first-year algebra students are learning how to solve two-step equations. the teacher notices that the students are not using precise mathematical language. which two instructional strategies should the teacher employ to encourage students to use precise mathematical language when completing this task? choose 2 answers
Answers
Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.
However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.
So the list goes as
1. Exponents
2. Roots
3. Multiplication
4. Division
5. additional
6. Subtraction
However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.
Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.
Furthermore, the preferred behavior norm for division and multiplication is different.
Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.
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What is the equation used to find the slope of two points?
Answers
Answer:
To find the slope of a line using 2 points on that line, you use the equation m = y₂ - y₁/x₂ - x₁, where (x₁, y₁) and (x₂, y₂) represent 2 random points on the line.
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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Pablo's is a popular Mexican restaurant, known especially for its homemade salsa. During dinner last night at Pablo's, 7 tables of people ordered chips and salsa for every 2 tables that did not.
Answers
Answer: =84
Step-by-step explanation:
2х + Зу = 9
-3х + Зу = -6
Answers
Answer:
Point Form:
(3 , 1 )
Equation Form:
x = 3 , y = 1
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.