solve the system by using elementary row operations on the equations. follow the systematic elimination procedure. x1 3x2
Answers
On solving, the given system reduces to x1 = 12, & x2 = —7 which is the required solution.
What is matrix?Linear algebra is a subfield of mathematics that mostly uses matrices. When you start solving linear equation systems, linear algebra first starts to seem good. You may concentrate on the figures and greatly simplify the procedure by condensing all the information into a single large chart and leaving out the rest.
Which 4 types of matrices are there?Almost as their name implies, square, symmetric, triangular, and diagonal matrices. All-zero identity matrices except along the major diagonal, where the values are
T he augmented matrix of the given system is B =
\([AB] = \left[\begin{array}{ccc}2&4&-4\\5&7&11\\\end{array}\right] \\on solving we get \\ [AB] = \left[\begin{array}{ccc}1&0&12\\0&1&-7\\\end{array}\right] \\\)
Hence the given system reduces to x1 = 12 x2 = -7
Hence the given system reduces to
x1 = 12, & x2 = —7
which is the required solution.
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Related Questions
6.334*104=6.334*10<sup>4</sup>=
Answers
Answer:
what's that
Step-by-step explanation:
5. Find x.
Trapezoids Worksheet
Answers
Answer:
(1/2)(x + 4 + 100) = 3x
x + 104 = 6x
5x = 104, so x = 20.8
what is the volume of a cylinder with a diameter of 8 name m and a height of 5.5
Answers
To begin, you must plug all the values you have into a formula, and also putting them in the right form.
The formula for the volume of a cylinder is: πr²h
FINDING RADIUS: With this in mind, now we know that, our diameter must be converted to a radius. To do this, you divide your diameter by two. This gives you, 4 as your radius.
FINDING HEIGHT: In the question you sent, you can tell they've given you, your height, so all you need to do is plug it into the equation.
PLUGGING IT IN:
Your pi, stays the same when using a calculator, just press your pi symbol depending on the calculator you are using. Your radius is 4, therefore it wants you to square it, which is 4x4, which equals 16. Next, you want to multiply it by the height, so just multiply it with your height, 5.5
YOUR ANSWER:
276.46m
Which of the following tables represents a linear function? x −4 −1 0 1 2 y −4 2 −4 0 2 x 1 1 1 1 1 y −3 −2 −1 0 1 x −6 −1 0 2 3 y −7 negative sixteen thirds −5 negative thirteen thirds −4 x −2 −1 0 2 4 y −4 negative two thirds −1 two thirds 1 Question 5(Multiple Choice Worth 5 points) (Experimental Probability MC) A bag is filled with an equal number of red, yellow, green, blue, and purple socks. The theoretical probability of a child drawing 2 yellow socks from the bag with replacement is one fifth. If the experiment is repeated 175 times, what is a reasonable prediction of the number of times he will select 2 yellow socks? one fifth 10 25 35 Question 6(Multiple Choice Worth 5 points) (Identifying Functions LC) The graph represents a relation where x represents the independent variable and y represents the dependent variable. a graph with points plotted at negative 5 comma 1, at negative 2 comma 0, at negative 1 comma negative 1, at 0 comma 2, at 1 comma 3, and at 5 comma 1 Is the relation a function? Explain. No, because for each input there is not exactly one output. No, because for each output there is not exactly one input. Yes, because for each input there is exactly one output. Yes, because for each output there is exactly one input. Question 7(Multiple Choice Worth 5 points) (Line of Fit MC) A movie theater wanted to determine the average rate that their diet soda is purchased. An employee gathered data on the amount of diet soda remaining in the machine, y, for several hours after the machine is filled, x. The following scatter plot and line of fit was created to display the data. scatter plot titled soda machine with the x axis labeled time in hours and the y axis labeled amount of diet soda in fluid ounces, with points at 1 comma 30, 1 comma 40, 2 comma 34, 3 comma 24, 3 comma 30, 4 comma 18, 5 comma 15, 5 comma 24, 6 comma 4, 6 comma 20, 7 comma 10, and 8 comma 0, with a line passing through the coordinates 3 comma 26.7 and 7 comma 7.66 Find the y-intercept of the line of fit an
Answers
The y-intercept of the line of fit is approximately 43.94 fluid ounces.
What is Probability ?
Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.
The answer is 35. If the theoretical probability of drawing two yellow socks is one fifth, then the experimental probability of drawing two yellow socks in one trial with replacement is also one fifth. Therefore, out of 175 trials, the number of times he will select two yellow socks can be predicted by multiplying the number of trials by the experimental probability: 175 * (1/5) = 35.
No, because for each input there is not exactly one output. The relation is not a function because for the input x = -5, there are two possible outputs: y = 1 and y = -1. Therefore, the relation violates the vertical line test, which requires that every vertical line intersects the graph at most once for the relation to be a function.
The y-intercept of the line of fit is approximately 43.94 fluid ounces. To find the y-intercept, we can look at the point where the line of fit intersects the y-axis (i.e., when x = 0). From the equation of the line of fit, we can see that the y-coordinate when x = 0 is approximately 43.94, which represents the initial amount of diet soda in the machine before it starts to be purchased.
Therefore, The y-intercept of the line of fit is approximately 43.94 fluid ounces.
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help me fast rapidly is of khan academy:
Answers
Answer:
0 hundreds
0 tens
7 ones
.
4 tenths
0 hundredths
8 thousandths
Standard form=7.408
Step-by-step explanation:
Lets first solve (7x1)+(4x1/10)+(8x1/1000)
7+0.4+0.008
Simplify:
7.408
PLEASE MARK AS BRAINLIESTFind the zeros of the function
k(x) = -5x² - 125
The zeros of k are x= □ and x= □
Answers
Answer:
x = ±5i
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASAlg II
√-1 is imaginary number iStep-by-step explanation:
Step 1: Define function
k(x) = -5x² - 125
Step 2: Find roots
Set function equal to 0: 0 = -5x² - 125Factor out -5: 0 = -5(x² + 25)Divide both sides by -5: 0 = x² + 25Subtract 25 on both sides: -25 = x²Rewrite: x² = -25Square root both sides: x = ±√-25Rewrite: x = √-1 · ±√25Evaluate: x = ±5i10 Ten Atlas batteries were tested to find their average life. The times, in hours, that the batteries lasted were as follows: 10.8, 10.6, 11.4, 8.9, 10.1, 10.6, 9.9, 12.6, 10.5, 11.9. a Find, to the nearest tenth of an hour, the average life of the ten batteries. b Which of the following advertisements is more accurate? i Atlas batteries are guaranteed to last 10 hours. ii Atlas batteries have an average life of over 10 hours.
Answers
a) To find the average life of the ten batteries, we need to calculate the mean, which is the sum of all the values divided by the number of values.Sum of all values = 10.8 + 10.6 + 11.4 + 8.9 + 10.1 + 10.6 + 9.9 + 12.6 + 10.5 + 11.9 = 106.2
Number of values = 10
Average life = Sum of all values / Number of values = 106.3 / 10 ≈ 10.63
Therefore, the average life of the ten batteries, rounded to the nearest tenth of an hour, is approximately 10.6 hours.
b) Comparing the two advertisements:
i) The first advertisement claims that Atlas batteries are guaranteed to last 10 hours. This means that all Atlas batteries are expected to last at least 10 hours. However, based on the data provided, we can see that the average life of the batteries is approximately 10.6 hours, which is higher than the guaranteed 10-hour minimum
ii) The second advertisement claims that Atlas batteries have an average life of over 10 hours. This statement aligns with the data we have, as the average life of the batteries is indeed over 10 hours.
Based on the information provided, the second advertisement claiming that Atlas batteries have an average life of over 10 hours is more accurate, as the average life calculated from the given data is 10.6 hours.
In summary, the average life of the ten batteries is approximately 10.6 hours, and the second advertisement stating an average life of over 10 hours is more accurate based on the data provided.
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Lindsay is sewing a square quilt with 118 square feet of fabric without any overlap. Which measurement is closest to the side length of this quilt in feet? Side Length: __________
Answers
Answer:
11ftStep-by-step explanation:
Using the formula finding the area of a square.
Area of a square =L²
L is the length of the quilt
Given area of the square quilt = 118ft²
Substituting into the formula;
118 = L²
square root both sides
√L² = √118
L = √118
L = 10.86ft
L ≈ 11ft
The measurement that is closest to the side length of this quilt in feet is 11ft
The distances, in light years, of four stars from a space probe are shown. Put the stars in order from the closest one (least distance) to the farthest one (greatest distance). 0.886 0.883 1.25 0.89
A.
0.883, 0.886, 0.89, 1.25
B.
0.883, 0.886, 1.25, 0.89
C.
1.25, 0.89, 0.886, 0.883
D.
0.886, 0.883, 0.89, 1.25
Answers
The stars in order from the closest one to the farthest one are:
0.883, 0.886, 0.89, 1.25
so, the answer is A.
What is a sequence?
A sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).
To put the given distances in order from the closest one to the farthest one, we need to arrange them in ascending order.
That means we need to start with the smallest value and move toward the largest value.
Looking at the given distances, we see that the smallest value is 0.883, followed by 0.886, then 0.89, and finally 1.25, which is the largest value.
Putting the given distances in ascending order, we get:
0.883, 0.886, 0.89, 1.25
Therefore, the stars in order from the closest one to the farthest one are:
0.883, 0.886, 0.89, 1.25
so, the answer is A.
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Help need answer will give brainliest
Answers
which of the following does not influence the consumer when he or she is deciding whether or not to buy a product?
A. Opinion factors
B. Multiple factors
C. external factors
D. The stock market
Answers
Answer:external factor
Step-by-step explanation:
Factor the difference of cubes. Select prime if the polynomial cannot be factored
Answers
Answer:
(m-(1/3))(m^2+(1/3)m+(1/9)
Step-by-step explanation:
Just use the difference of cubes
Combine as indicated by the signs.
4/y^2-9 + 5/y+3
Answers
The combined expression for the given expression will be ( 5y -11 ) / ( y² - 9 ).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is ( 4 / y² - 9 ) + ( 5 / y + 3 ).
The expression will be solved as below,
E = ( 4 / y² - 9 ) + ( 5 / y + 3 ).
E = 4 / ( y +3 ) ( y - 3 ) + 5 / ( y + 3 )
E = 1 / ( y + 3 ) [ ( 4 / ( y- 3 ) + 5 ]
E = 1 / ( y +3 ) [ ( 4 + 5y - 15 ) / ( y - 3 ) ]
E = ( 5y - 11 ) / ( y² - 9 )
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please help this is due bye 6:00
5+ – 6f–9+8f–8f
Answers
The simplified expression for the expression (5 – 6f–9+8f–8f) is (-4 - 6f).
How to apply operation on Expression?The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition and Subtraction (from left to right).
Given:
5 – 6f–9+8f–8f
Solving the Expression
= 5 – 6f–9+8f–8f
= 5 - 9 -6f + 8f - 8f
= -4 + f(-6 +8 -8)
= -4 + f(-6)
= -4 - 6f
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collect like terms
-3b cubed subtract 2b cubed
Answers
Answer: -5b cubed
Step-by-step explanation:
first, collect like terms (-3-2)b^2
then, calculate the difference which makes
-5b^2
Triangle PQR is a right triangle.
Triangle P Q R. Angle P is 90 degrees, angle Q is x degrees, angle R is 2 x degrees.
Which equation could be used to find the measure of Angle Q?
Answers
Answer:
90 + 2 = 92
180 - 92 = 88
Angle Q = 88
Step-by-step explanation:
All a triangles, angles should equal to 180.
Answer:
180 = 3 x + 90
Step-by-step explanation:
Hope it helps.Give me a brainliest please.
A vertical tower is 20 m high from the horizontal ground. The angle of depression of aball from the top of the tower is 42°. Calculate the distance, in m, of the ball from thebase of the tower
Answers
ANSWER
22.2 m
EXPLANATION
Let us make a sketch of the problem.
From the diagram:
T = top of the tower
B = Ball
O = Base of the tower
Now, we have to find x, which is the distance from the ball to the base of the tower.
Since the angle of depression is 42°, it means that angle
To find x, we can apply Pythagoras Rule:
\(\begin{gathered} \tan (<\text{OTB) = }\frac{x}{20} \\ \Rightarrow\text{ x = 20 }\cdot\text{ tan(48)} \\ x\text{ = 20 }\cdot\text{ 1.11} \\ x\text{ = 22.2 m} \end{gathered}\)The distance of the ball from the base of the tower is 22.2 m
If the prime factorization of 600 is 2 x 2 × 2 × 3 × 5 × 5, what would you need to multiply it by to get the prime factorization of 3000?
Answers
To get the Prime factorization of 3000 we need to multiply by 5.
What is Prime Factorization:When the number is factored using prime numbers, or primes, the process is known as prime factorization. The easiest method to determine the prime factors of a given number is to keep dividing the given number by the prime factors until we will get 1.
For example, the Prime factorization of 45 is given below
=> 45/5 = 9, 9/3 = 3, 3/3 = 1
=> 45 = 5 × 3 × 3
Here we have
The prime factorization of 600 is 2 x 2 × 2 × 3 × 5 × 5
Let us assume that on multiplying with p,
we will get the factorization of 3000
=> 2 x 2 × 2 × 3 × 5 × 5 × p = 3000
=> p = \(\frac{3000}{2\times 2 \times 2 \times 3 \times 5 \times 5}\)
Her 2 x 2 × 2 × 3 × 5 × 5 = 600
=> p = \(\frac{3000}{600}\)
=> p = 5
Therefore,
To get the Prime factorization of 3000 we need to multiply by 5.
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-2 x + 4 =2 x - 4 solve .
Answers
Answer:
\(\sf{x = 2}\)
Step-by-step explanation:
Question type: solving equations with variables on both sides.
\(\textsf{This is a question with variables on both sides, to solve this we need to get the variable x }\)
\(\textsf{alone. (getting the x on one side)}\)
--------------------------------------------------------------
\(\sf{-2x~+~4~=~2x~-~4\)
Subtract 4 from both sides.
\(\sf{-2x~=~2x~-8\)
Subtract 2x from both sides.
\(\sf{-4x~=~-8}\)
Divide both sides by -4.
\(\bf{x~=~2\)
Therefore, x would be 2.
\(-jurii\)
Answer:
x=2
Step-by-step explanation:
Please help fast! 100 POINTS
Answers
Answer:
65
Step-by-step explanation:
Answer: the answer is 41
Step-by-step explanation: 4+2+3+3+6+2+5+3+6+7=41
simplify the expression. Write the answer using scientific notation. (4x10^8) ^-2
Answers
Given:
\((4\times10^8)^{-2}\)Aim:
We need to write the given expression in scientific notation.
Explanation:
\(Use\text{ \lparen a}\times b)^n=a^n\times b^n.\)\((4\times10^8)^{-2}=4^{-2}\times(10^8)^{-2}\)\(Use\text{ \lparen a}^n)^m=a^{n\times m}.\)\((4\times10^8)^{-2}=4^{-2}\times10^{-16}\)\(Use\text{ a}^{-n}=\frac{1}{a^n}\)\((4\times10^8)^{-2}=\frac{1}{4^2}\times10^{-16}\)\((4\times10^8)^{-2}=\frac{1}{16}\times10^{-16}\)\((4\times10^8)^{-2}=0.0625\times10^{-16}\)\(Use\text{ -16=2-18.}\)\((4\times10^8)^{-2}=0.0625\times10^{2-18}\)\((4\times10^8)^{-2}=0.0625\times100\times10^{-18}\)\((4\times10^8)^{-2}=6.25\times10^{-18}\)Final answer:
\((4\times10^8)^{-2}=6.25\times10^{-18}\)6x-5=6x+5 pls help me fast
Answers
Answer:
No solution
Step-by-step explanation:
6x - 5 = 6x + 5
6x = 6x + 10
0 = 10
0 cannot be equal to 10 at anytime, so this equation has no solution
Answer: No solution.
Step-by-step explanation:
Given:
6x - 5 = 6x + 5
Add 5 to both sides of the equation:
6x = 6x + 10
Subtract 6x from both sides of the equation
0 ≠ 10
Since 0 does not equal 10, there is no solution to this equation.
PLEASE HELP
I HAVE TO FINISH IN 5 MINS
Answers
Step-by-step explanation:
the answer is
Remove 8 anchors
Elias and Mark together have $756.80. Elias has $489.50. Write and solve an addition equation to determine how much money Mark (m) has.
Below, select the answer choice that includes both the correct ADDITION equation and the correct solution.
m - $489.50 = $756.80 ; m = $1246.30
m - $489.50 = $756.80 ; m = $1246.30
$756.80 + m = $489.50; m = $267.30
$756.80 + m = $489.50; m = $267.30
m + $489.50 = $756.80; m = $1246.30
m + $489.50 = $756.80; m = $1246.30
$489.50 + m = $756.80; m = $267.30
Answers
Answer:
489.5 + m = 756.80 (the amount elias has, added to marks is equal to the total
(756.8- 489.5 = 267.30 which is the amount mark has.)
m= 267.3
the last option is the correct option
Step-by-step explanation:
Answer: the answer is the last equation ($489.50 + m = $756.80; m = $267.30)
Step-by-step explanation:
I say this because all you have to do is subtract 756.80-489.50 to find out how much money Mark has. Thats how you get 267.30. Hope it helps
please help I appreciate it also have a good day!
Answers
Let \(\beta\) be a real number. Consider the matrix \( \rm A = \begin{bmatrix} \beta &0&1 \\ 2 &1& - 2 \\ 3&1& - 2\end{bmatrix}\) . If \( \rm A^7 - ( \beta - 1) {A}^{6} - \beta {A}^5\) is a singular matrix, then the value of \(9\beta \) is
Answers
Compute the characteristic polynomial of \(A\).
\(p(\lambda) = \det(A - \lambda I) \\\\ ~~~~~~~~ = \begin{vmatrix} \beta - \lambda & 0 & 1 \\ 2 & 1 - \lambda & -2 \\ 3 & 1 & -2-\lambda \end{vmatrix} \\\\ ~~~~~~~~ = (\beta-\lambda)\begin{vmatrix}1-\lambda&-2\\1&-2-\lambda\end{vmatrix} + \begin{vmatrix}2&1-\lambda \\ 3 & 1 \end{vmatrix} \\\\ ~~~~~~~~ = -\lambda^3 + (\beta-1) \lambda^2 + (\beta + 3) \lambda - 1\)
By the Cayley-Hamilton theorem,
\(p(A) = -A^3 + (\beta - 1) A^2 + (\beta + 3) A - I = 0\)
Note that
\(A^7 - (\beta - 1) A^6 - \beta A^5 \\\\ ~~~~~~~~ = -(-A^3 + (\beta - 1) A^2 + \beta A) A^4 \\\\ ~~~~~~~~ = -(\underbrace{-A^3 + (\beta - 1) A^2 + (\beta + 3) A - I}_{p(A)=0} - 3A + I) A^4 \\\\ ~~~~~~~~ = (3A - I) A^4\)
Recall that \(\det(AB) = \det(A) \det(B)\). Note that \(A\) is not singular, and hence \(A^n\) is not singular for any natural \(n\).
\(\det(A) = \begin{vmatrix} \beta & 0 & 1 \\ 2 & 1 & -2 \\ 3 & 1 & -2 \end{vmatrix} \\\\ ~~~~~~~~ = \beta \begin{vmatrix}1&-2\\1&-2\end{vmatrix} + \begin{vmatrix}2&1\\3&1\end{vmatrix} \\\\ ~~~~~~~~ = -1 \neq 0\)
Then \(3A-I\) must be singular. So
\(\det(3A-I) = \begin{vmatrix} 3\beta - 1 & 0 & 3 \\ 6 & 2 & -6 \\ 9 & 3 & -7 \end{vmatrix} \\\\ ~~~~~~~~ = (3\beta-1) \begin{vmatrix}2&-6\\3&-7\end{vmatrix} + 3 \begin{vmatrix}6&2\\9&3\end{vmatrix} \\\\ ~~~~~~~~ = 4 (3\beta-1)\)
\(4(3\beta-1) = 0 \implies \beta = \dfrac13 \implies 9\beta = \boxed{3}\)
what's the difference between j(7) and j(x) = 7 PLEASE HELP
Answers
The difference between j(7) and j(x) = 7 is that x = 7 in j(7) and x may not be 7 in j(x) = 7
How to determinet the differencej(7) and j(x) = 7 have different meanings in mathematics.
j(7) is a function notation, it is used to represent the output of a function j when the input is 7.
So j(7) is a single value, it is the output of the function j when the input is 7.
j(x) = 7, on the other hand, is an equation. It represents the function j, in which the input (x) has a fixed output (7) for x
It can be used to make predictions about the output of j for any value of x. For example, if we input x = 2, the output of j(x) = 7 would be 7, so j(2) = 7.
So in summary, j(7) is an output value of a function, while j(x) = 7 is the function that defines a relationship between input and output values.
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AA.1 Solutions to inequalities P9N
Which of the following are solutions to the inequality below? Select all that apply.
3 ≤ 47
x = 24
Submit
x = 51
X = 6
X = 99
Answers
Answer: 3 ≤ 47
Step-by-step explanation:
The inequality given is 3 ≤ 47.
To determine the solutions to this inequality, we need to find the values of x that satisfy the inequality.
Looking at the options provided:
x = 24: This is not a solution because 24 is less than 47.
x = 51: This is a solution because 51 is greater than or equal to 47.
x = 6: This is not a solution because 6 is less than 47.
x = 99: This is a solution because 99 is greater than or equal to 47.
Therefore, the solutions to the inequality 3 ≤ 47 are x = 51 and x = 99.
There were 44 dogs and cats at the pet store if 75% were cats how many cats were at the pets store?
Answers
Answer:
33.
Step-by-step explanation:
75% x
100 44
x = (44 * 75 ) / 100 = 33.
Find the sum of the polynomials (ax²+2x-5) and (-2ax² + a) and evaluate that sum when a = 7 and x = -5. The sum of polynomials is the value is
Answers
Answer:
29+3374=32483 that is the solution for the question