An augmented matrix is invertible if the linear system has a unique solution.
What is an augmented matrix?
The augmented matrix is known as a rectangular matrix.
The properties of an augmented matrix includes:
The number of columns is equal to the number of variables in the linear equations. The number of rows is the same as the number of linear equations.The rows of the augmented matrix can be also be interchanged.Note that the inverse of a matrix must be unique
And If A is invertible, then its inverse is unique.
If the linear system is unique, then the augmented matrix is invertible.
Thus, an augmented matrix is invertible if the linear system has a unique solution.
Learn more about augmented matrices here:
https://brainly.com/question/12994814
#SPJ12
Find the values of the variables indicated below
M=
K=
Answer:
m=120
k=60
Step-by-step explanation:
a trapezoid has 360 degrees. subtract 120 degrees to get 240 degrees. we know that m=2k. 240=2k+2k which is 4k. 240 is 4k. k=60. m=2k, so mulitply 60 by 2 to get m=120
A ship is stationary at sea.
A tugboat is 36 km away at a bearing of 130°, and a yacht is 27 km from the tugboat at a bearing of 260°.
Draw a scale diagram showing the positions of the three vessels.
Use a scale of 1 : 450,000.
Measure the distance from the ship to the yacht to the nearest km.
Bearing is a topic that deals with the distance and location of a given object with respect to a reference point. Thus in the given question, the ship is 57.23 km to the yacht.
Bearing is a topic that considers the distance and position of a given object with respect to a reference point. Thus the angles are usually measured with reference to the north pole.
Thus to solve the given question, let the required distance be represented by x.
Applying the cosine rule, we have;
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos C
The angle C between the line from ship to tugboat and from tugboat to yacht can be determined as;
C = [tex]10^{o}[/tex] + [tex]40^{o}[/tex]
C = [tex]50^{o}[/tex]
Thus,
[tex]c^{2}[/tex] = [tex]36^{2}[/tex] + [tex]27^{2}[/tex] + 2(36 x 27) Cos [tex]50^{o}[/tex]
= 1296 + 729 + 1944(0.6429)
= 2025 + 1249.8
[tex]c^{2}[/tex] = 3274.8
c = [tex]\sqrt{3274.8}[/tex]
= 57.2259
c = 57.23
Therefore, the distance from the ship to the yacht is 57.23 km.
For more clarifications on Bearing, visit: https://brainly.com/question/22013596
#SPJ1
Kindly contact a 1-on-1 tutor if more explanations are needed.
Which of the following is a factor of x^3-7x-6?
A. X+3
B. X+4
C. X-2
D. X+1
pls help answer ASAP
Answer:
a: 1
b: -1
c: -3
Step-by-step explanation:
You can rearrange the terms and make the equation become:
x - y - 3
There, you can see that the values are the following:
a: 1
b: -1
c: -3
5b+a-2c when a=2,b=1&c=3
5b+a-2c when a=2,b=1&c=3
5(1) + 2 - 2(3)
5 + 2 - 6
7-6
Answer: 1
Which graph shows the solution to the system of linear inequalities? Edge.
x + 3y > 6
y ≥ 2x + 4
A system of inequalities can be solved graphically.
See attachment for the required graph
The inequalities are given as
[tex]x + 3y > 6\\y \geq 2x + 4[/tex]
The options are not given.
So, I have attached the graph that illustrates the solution to the system of inequalities.
What is the inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
From the graph, we have the solutions as
[tex]x > -0.857[/tex]
[tex]y\geq 2.276[/tex]
To learn more about graphs of inequalities at:
brainly.com/question/15748955
#SPJ1
Which choice is the most efficient first step to solve this set of
equations?
y=3x-5
2x+6y=20
Answer:
b) Substitute (3x - 5) for y in the second equation.
Step-by-step explanation:
If using the substitution method, then the second choice is the most efficient first step.
What is the substitution method?
The substitution method can be used to solve a system of equations. It is when you isolate any of the variables from one of the equations and then substitute that value into the other equation.
Here, the first equation already has an isolated variable, y. We can then substitute its value into the second equation. Like so:
⇒ 2x + 6y = 20
⇒ 2x + 6(3x - 5) = 20
Learn more about the substitution method here:
brainly.com/question/27728118
brainly.com/question/26094713
Find the equation of the line of best fit and the correlation coefficient for the data shown.
(1, 88), (2, 75), (3, 71), (4, 69), (5,66), (6, 68), (7, 50)
Regression equation:
Using a calculator, we have that:
The regression equation is given by: y = -4.75x + 88.57143.The correlation coefficient is given by: -0.906.How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
In this problem, we have that:
The values of x are: 1, 2, 3, 4, 5, 6, 7.The values of y are: 88, 75, 71, 69, 66, 68, 50.Hence the regression equation is:
y = -4.75x + 88.57143.
Also using a calculator, the correlation coefficient is of -0.906.
More can be learned about a line of best-fit at https://brainly.com/question/22992800
#SPJ1
Find the product of (x − 5)2.
Group of answer choices
x2 + 10x + 25
x2 − 10x + 25
x2 − 25
x2 + 25
Answer:
x² - 10x + 25
Step-by-step explanation:
The formula for squaring any binomial (an expression with two terms) is:
(a ± b)² = a² ± 2ab + b²
Let a = x and b = 5.
∴ Substituting:
(x - 5)² = x² - 2(x)(5) + (-5)²
= x² - 10x + 25
Jared bought eighteen doughnuts to share with his coworkers. If each doughnut cost c cents, which expression represents his total cost?
About how many people moved away from the great plains states during the depression? 100,000 250,000 2.5 million 10 million
Answer:
the answer is 2.5 million
Step-by-step explanation:
About 2.5 million people moved away from the Great Plains states during the Great Depression.
What is the great depression?The 1930s saw a catastrophic economic collapse known as the Great Depression. It was the twentieth century's longest, most widespread, and deepest depression, affecting countries all over the world. The Great Depression began on October 29, 1929, with a stock market catastrophe in the United States known as "Black Tuesday."
This movement was called the Dust Bowl migration and was caused by a combination of factors including drought, soil erosion, and economic hardship.
Many people left the region in search of better opportunities and living conditions.
Therefore, 250,0000 people moved.
To learn more about the great depression;
https://brainly.com/question/29762000
#SPJ7
An automobile company is running a new television commercial in five cities with approximately the same population. the following table shows the number of times
the commercial is run on tv in each city and the number of car sales in hundreds). find the linear regression line for the data given in the table. round any intermediate
calculations to no less than six decimal places, and round the coefficients to two decimal places.
number of tv commercials, x
car sales, y (in hundreds)
13 6 12 14 17
3 28 97
The linear regression equation is y = 0.50x - 0.36
How to determine the linear regression equation?The proper format of the table of values is:
Number of tv commercials, x: 13 6 12 14 17
Car sales, y (in hundreds): 3 2 8 9 7
Next, we determine the linear regression equation using a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 62Sum of Y = 29Mean X = 12.4Mean Y = 5.8Sum of squares (SSX) = 65.2Sum of products (SP) = 32.4The regression equation is the calculated as:
y = bx + a
Where
b = SP/SSX = 32.4/65.2 = 0.49693
a = MY - bMX = 5.8 - (0.5*12.4) = -0.36196
Substitute these values in y = bx + a
y = 0.49693x - 0.36196
Approximate
y = 0.50x - 0.36
Hence, the linear regression equation is y = 0.50x - 0.36
Read more about linear regression equation at:
https://brainly.com/question/25987747
#SPJ1
help … fr …. D: D: D: D:
Step-by-step explanation:
Let x be mixture x liters and y be mixture y liters.
We need a total of 4 liters so
[tex]x + y = 4[/tex]
Mixture x is 20% saline solution
Mixture Y is a 10% saline solution
4 liters of a 15% saline solution is 60% saline solution.
[tex].20x + .10y = 0.6[/tex]
So a is the system of equations,
Using Elimination, eliminate the variable x.
[tex] - 5(.20x + .10y) = 0.6[/tex]
[tex]( - x - .50y) = - 3[/tex]
Add to the first system.
[tex]0.50y = 1[/tex]
[tex]y = 2[/tex]
Plug this into the of system of equations, to find x
[tex]x + 2 = 4[/tex]
[tex]x = 2[/tex]
So our solution is (2,2) We would need 2 liters of Mixture X and 2 liters of Mixture Y
What are the coordinates for point b?
a. (7, 0)
b. (0, 7)
c. (0, 8)
d. (1, 7)
The coordinates for point B are (a) (7,0)
Complete QuestionPoint B is located 7 units right of the origin. What are the coordinates for point b?
How to determine the coordinates?The origin is located as:
(0,0)
From the question, we understand that:
B ⇒ 7 unit right of origin
This means that:
B = (0 + 7, 0)
Evaluate the sum
B = (7,0)
Hence, the coordinates for point B are (a) (7,0)
Read more about coordinates at:
https://brainly.com/question/17206319
#SPJ1
Answer:a
Step-by-step explanation:
Kayla has just subscribed to a music streaming service. For a one-time fee of $12.99, she can download songs for $0.65 each, for an entire month. Kayla's budget will allow her to spend no more than a total of $27 on the streaming service this month. What is the maximum number of songs she can download while still remaining within her budget?
a) x <= 22
b) <= 41
c) x <= 21
d) X <= 42
The maximum number of songs she can download while still remaining within her budget is x <= 21
How to determine the maximum number of songs?The given parameters are:
One-time fee = $12.99
Rate = $0.65 per song
Budget = $27
The inequality is then represented as:
One-time fee + Rate * x <= Budget
So, we have:
12.99 + 0.65x <= 27
Subtract 12.99 from both sides
0.65x <= 14.01
Divide both sides by 0.65
x <= 21.55
Round down
x <= 21
Hence, the maximum number of songs she can download while still remaining within her budget is x <= 21
Read more about inequality at:
https://brainly.com/question/25275758
#SPJ1
Mr. T has 784 marbles. he has 263 marbles more than Indie. how many marbles do they have altogether?
Answer:
Step-by-step explanation:
784-263=521
784+521=1305
answer=1305
Find the value [[23]] (step functions) helpp pls im so confused if you could also explain it :3
I assume [[x]] stands for "the largest integer smaller than or equal to x".
If x is already an integer, then x itself satisfies the definition. 23 is an integer that is equal to 23. So [[23]] = 23.
LCM of 18 , 25 , 35, 40 ,80 81 , and 72
Answer:
the LCM of 18 25 40 80 81 and 72 is 226800
i hope this helps you
Step-by-step explanation:
by which method
prime factorization , division or defination method
Brian wants to fence in his triangular plot of farm land that measures 1.1 by 1.5 by 2.2 miles. Determine the angles at which the fences of the three sides will meet. 1.1 mi A 1.5 mi 2.2 mi B Rounding each angle to m/A 125 X = COMPLETE m/Ba DONE degrees
The angles at which the fences will meet is 27 , 38 ,114 degree.
What is a Triangle ?A triangle is a polygon with three sides , three angles and three vertices.
It is given that the triangle has sides
1.1 miles * 1.5 miles * 2.2 miles
The law of cosines can be used to calculate the angle
a² = b² + c² -2bc cosA
1.1² = 1.5² + 2.2² -2 *1.5 *2.2 cosA
A = 27.01 degree
Similarly
b² = c² +a² -2ac cosB
1.5² = 2.2² +1.1² -2 * 2.2*1.1 cos B
B = 38.27 degree
By angle sum property
Angle C = 180-38.27-27.01
C = 114.72 degree
Therefore , the angles at which the fences will meet is 27 , 38 ,114 degree.
To know more about Triangle
https://brainly.com/question/2773823
#SPJ1
PLEASE HELP
using the data that was collected,
determine the experimental probability of each outcome of
the die over the course of three games and write as a fraction, decimal, and percentage.
When the dice is rolled 14 times then from the given data the probability of 1,2,3,4,5,6 is 3/14,1/14,4/14,1/14,3/14,2,14.
Given Roll of dice and outcomes from 1 to 14 is 1,3,5,4,5,3,3,1,3,5,6,1,6,2.
From the given collected data we can find out number of times each number came when the dice is rolled.
Number of times 1 came=3
Number of times 2 came=1
Number of times 3 came=4
Number of times 4 came=1
Number of times 5 came=3
Number of times 6 came=2
The probabilities are in fraction form:
P(1)=3/14
P(2)=1/14
P(3)=4/14
P(4)=1/14
P(5)=3/14
P(6)=2/14
The probabilities in decimal form:
P(1)=0.21
P(2)=0.07
P(3)=0.28
P(4)=0.07
P(5)=0.21
P(6)=0.14
The probabilities in percentage:
P(1)=21%
P(2)=7%
P(3)=28%
P(4)=7%
P(5)=21%
P(6)=14%
Hence the probabilities are 3/14,1/14,4/14,1/14,3/14,2,14.
Learn more about probabilities here https://brainly.com/question/24756209
#SPJ10
The cash price of a mobile phone is $540. Andrea bought the mobile phone by paying $42 monthly instalments over 15 months. Find the flat rate interest of the instalments, give your answer correct to 3 significant figures.
The rate of interest of the instalment is 13%
What is Instalments ?The part payment of a loan is called Instalment
It is given that
The Cash price is $540
Instalment of $42
Time = 15 month = 15/12 = 1.25 years
Total Amount paid = 42 * 15 =$630
Interest Paid is $90
90 = 540 * 1.25 *Rate
Rate = 13%
The rate of interest of the instalment is 13%
To know more about Instalment
https://brainly.com/question/13267432
#SPJ1
the number of cows in the field minus 12...
Answer:
maybe minus 12 there was no number of cows
Answer:
x - 12
Step-by-step explanation:
x represents the number of cows since we do not know the number
then "minus 12"
bada bing bada boom
can someone help me?
Answer:
-6
30
22
8x² + 18x + 4
8x² - 2x - 6
Step-by-step explanation:
f(x) = 8x² + 2x - 6
f(0) = 8(0²) + 2(0) - 6 = -6
f(2) = 8(2²) + 2(2) - 6 = 32 + 4 - 6 = 30
f(-2) = 8 × (-2)² + 2(-2) - 6 = 32 - 4 - 6 = 22
f(x + 1) = 8(x + 1)² + 2(x + 1) - 6 = 8(x² + 2x + 1) + 2x + 2 - 6 = 8x² + 18x + 4
f(-x) = 8(-x)² + 2(-x) - 6 = 8x² - 2x - 6
Drag the boxes to order the decimals from least to greatest from left to right.
316.011
306.324
306.359
Answer:
306.324
306.359
316.011
Step-by-step explanation:
Hope it helped!
15. 3x-5=3
16. 3(x-2) = 4(x + 3)
17. +3=
18. 2==
19. 4-2-3
X+2
20.-2-3-3
21. 쭉 = 큭
22. 2x-5-1=3-x
3. 2x + ==3(x-1)
4. 10x-1=x+4
5. k=8k-2
6. -x + 2 = 3x-27
4
7. 1-6x = -x +
B.
9. 2-(x + 1) = 2 + 5x
D. 2(1-x) = 10 - (x + 2)
. 9x - (4x - 5) = 3x - 11
x-9=3(x + 1)
-xx-2)-4=x+6▸
+ 2x
6(5-4x) = -4(5x + 11)
Answer:
tgnjfgznjE XVNJ
Step-by-step explanation:
rtjtejWEJAREfnndzjt
Answer:
15. 2.66
16. - 18
17. Impossible
18. Impossible
19. - 1
20. - 8
21.
which graph correctly represents 3x+y > 7
Answer:
What graph? add a photo?
Find the value of x.
Answer:
x=21°
Step-by-step explanation:
40°+5x+14°+x=180°
5x+x=180°-40°-14°
6x=126°
x=21°
Answer:
x = 21
Step-by-step explanation:
The sum of the angles of a triangle is 180 degrees
x + 40 + 5x+14 = 180
Combine like terms
6x+54 =180
Subtract 54 from each side
6x+54-54 = 180-54
6x =126
Divide each side by 6
6x/6 =126/6
x = 21
For every 1 litre of water used to make a
medicine, 311ml of sucrose and 29ml of
saline solution are used. Express the amount
of water, sucrose and saline solution needed
as a ratio in its simplest form.
Step-by-step explanation:
hope you can understand
5|2x+6|=26...can someone answer this please
Answer:
x = -2/5 or x = -28/5
Step-by-step explanation:
Let's solve your equation step-by-step.
5(|2x+6|)=26
Step 1: Divide both sides by 5.
5(|2x+6|)/5 = 26/5
|2x+6|=26/5
Step 2: Solve Absolute Value.
|2x+6|=26/5
We know either2x+6= 26/5 r2x+6=−26/5
2x + 6 = 26/5(Possibility 1)
2x+6−6= 26/5 - 6 (Subtract 6 from both sides)
2x = -4/5
2x/2 = -4/5/2 (Divide both sides by 2)
x = -2/5
2x + 6=-26/5 (Possibility 2)
2x+6= -26/5 (Simplify both sides of the equation)
2x + 6 - 6 = -26/5 - 6 (Subtract 6 from both sides)
2x = -56/5
2x/2 = -56/5/2(Divide both sides by 2)
x = -28/5
Answer:
x = -2/5 or x = -28/5
The market value of a home is $180,000. The assessment rate is 55%. What is the assessed value of the home?
Answer:
$99 000
Step-by-step explanation:
[tex](180000)(\frac{55}{100} )=99000[/tex]
Hope this helps
