Consider the following matrix in reduced row echelon form:
Row Echelon Form
What can you say about the solution to the associated linear system?
Answers
The reduced row echelon form of a matrix allows us to determine whether the associated linear system is consistent or inconsistent, unique or has infinitely many solutions.
In reduced row echelon form, a matrix has the following properties:
Each leading entry (the leftmost nonzero entry) of a row is equal to 1.
Each leading entry is the only nonzero entry in its column.
All entries below a leading entry are zeros.
The leading entry in each row is to the right of the leading entry in the row above it.
Based on these properties, we can make the following conclusions about the solution to the associated linear system:
Consistency: If there are no rows of the form [0 0 ... 0 | b] (where b is a nonzero constant), meaning there are no contradictory equations, the linear system is consistent. In other words, there is at least one solution.
Uniqueness: If there are no free variables (columns without leading entries), meaning each column corresponds to a pivot column, the linear system has a unique solution. This means there is only one set of values for the variables that satisfies all the equations.
Infinite solutions: If there are one or more free variables, the linear system has infinitely many solutions. This occurs when there are more variables than equations or when there are dependent equations.
The reduced row echelon form provides an organized representation of the linear system that simplifies the process of determining its solution. By analyzing the structure of the matrix, we can determine the consistency, uniqueness, and the nature of the solution set.
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Related Questions
Find the complete factored form of the
polynomial :
-8m²n-7m² nª
Enter the correct answer.
Answers
The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).
To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:
-8m²n - 7m²n = (-m²n) (8 + 7a)
Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.
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You determine the percent abundance of
each length of nail and record it in the data
table below.
Sample
Type
Short nail
Medium nail
Long nail
Number Abundance
of Nails
(%)
67
18
10
70.5
19.0
10.5
Nail Length
(cm)
2.5
5.0
7.5
What is the weighted average length, in cm,
of a nail from the carpenter's box?
Weighted Ave Length
Enter
Answers
The weighted average length of a nail from the carpenter's box whose distribution is give in image is: 3.5cm.
What is weighted average ?
Weighted average is a type of average that takes into account the relative importance or weight of each data point. In a weighted average, each data point is multiplied by a corresponding weight, which reflects its relative importance, and the products are then summed and divided by the sum of the weights.
To find the weighted average length of a nail, we need to multiply each nail length by its percent abundance, then add up all the products and divide by the total percent abundance.
Let's start by calculating the product of each nail length and its percent abundance:
Short nail: (2.5 cm) x (70.5%) = 1.7625 cm
Medium nail: (5.0 cm) x (19%) = 0.95 cm
Long nail: (7.5 cm) x (10.5%) = 0.7875 cm
Now, we add up all the products:
1.7625 cm + 0.95 cm + 0.7875 cm = 3.5 cm
Finally, we divide by the total percent abundance:
70.5% + 19.0% + 10.5% = 100%
Therefore, the weighted average length of a nail from the carpenter's box is: 3.5 cm ÷ 100% = 3.5cm
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Question 1-2
What is the value of a³ + b (6 + c), when a = 2, b = 3, and c = 4?
Answers
Answer:
\(\huge\boxed{\sf 38}\)
Step-by-step explanation:
Given expression:= a³ + b (6 + c)
Put a = 2, b = 3 and c = 4
= (2)³ + 3 (6 + 4)
= 8 + 3(10)
= 8 + 30
= 38\(\rule[225]{225}{2}\)
Answer:
Step-by-step explanation:
the requied answer is 38.
according to the question the value of a=2,b=3,c=4.
here,
to find the value of a³ + b (6 + c)we have to do it in steps:
step 1: solve the bracket (6+4) =10.
step 2: solve the value of a³ =8.
now put these values ,
=8+3(10)
=38.
find the x and y of the graph of 3x +2y=15. State each answer as an integer or an improper fraction in simplest form.
Answers
Answer:
Step-by-step explanation: To find the x let y=0
We substitute into the equation 3x+2y=15
3x+2 *0=15
3x=15
x=15/3=5
To find the y let x=0
we substitute into the equation x =0
3*0+2y=15
2y=15
y=15/2
Mark’s birthday is 32 weeks away. How many days until his birthday?
Answers
So multiply 32 by 7
32*7 =224 days
solve for x: 5x+3+8x-4=90
Answers
Answer:
\(x = 7\)
Step-by-step explanation:
We can solve the equation \(5x+3+8x-4=90\) by isolating the variable x on one side. To do this, we must simplify the equation.
\(5x+3+8x-4=90\)
Combine like terms:
\(13x - 1 = 90\)
Add 1 to both sides:
\(13x = 91\)
Divide both sides by 13:
\(x = 7\)
Hope this helped!
Answer:
x = 7
Step-by-step exxplanation:
5x + 3 + 8x - 4 = 90
5x + 8x = 90 - 3 + 4
13x = 91
x = 91/13
x = 7
probe:
5*7 + 3 + 8*7 - 4 = 90
35 + 3 + 56 - 4 = 90
Andrew reads 90 pages a day. He has 3 books that are each 60 pages. How many days will andrew need to read all 3 books?
Answers
By applying direct proportion, it would take Andrew 2 days to read all three (3) books.
What is a proportion?A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
Mathematically, a direct proportion can be represented by the following equation:
y = kx
Where:
y and x are the variables.k represents the constant of proportionality.First of all, we would determine the total number of pages in the three (3) books as follows:
Three (3) books = 3 × 60 pages
Three (3) books = 180 pages.
By applying direct proportion, we have:
90 pages = 1 day
180 pages = X days
Cross-multiplying, we have:
90X = 180
X = 180/90
X = 2 days.
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Dillon thinks of a number, multiplies it by 3 pand subtracts 5 from his answer. The result is 7. a. Using backtracking, what number did he think of? b. Write an equation to represent this problem
.
Answers
(7+5)3=36?
What is the slope of the line whose equation is 12=4x-6y?
Answers
Answer:
slope is 2/3
Step-by-step explanation:
12=4x-6y
We add 6y both sides
12+6y=4x
than subtract 12 from both sides
6y=4x-12
than divide both sides by 6
y=2/3x-2
and the slope is 2/3
Where will X be after a rotation 90° clockwise about (-5,-1)?
Click on the grid to place the point.
Answers
The image point of the coordinate X after the rotation is (-1, 5).
Calculating the image point of the coordinate XWhen a point is rotated 90° clockwise around the origin, the new point will be formed by switching the x and y-coordinates and then negating the new x-coordinate.
So for point X (-5, -1), the new x-coordinate will be -1, and the new y-coordinate will be -(-5) = 5, giving the new point (-1, 5).
Therefore, after a rotation of 90° clockwise, point X (-5, -1) will be at the new location (-1, 5).
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Mabel, Adeline and Charlie share 34500ft2 of land Mabel ownes 26%of the land area and Adeline Owens 47% of the land area . What is the land area that charlie owns ?
Answers
Answer:
Charlie owns 9,315 ft2 of the land area
Step-by-step explanation:
There are 34,500 ft2 of land shared between Mabel, Adeline, and Charlie.
Mabel owns 26% of the land area, that is:
26*34,500 ft2 / 100 = 8,970 ft2
Adeline owns 47% of the land area, or:
47*34,500 ft2 / 100 = 16,215 ft2
The land owned by Mabel and Adeline is: 8,970 ft2 + 16,215 ft2 = 25,185 ft2
Since the total area land is 34,500 ft2, Charlie owns:
34,500 ft2 - 25,185 ft2 = 9,315 ft2
Charlie owns 9,315 ft2 of the land area
b) Find the least number that must be subtracted from 2120 so that the result is a perfect square.
Answers
Answer: 4
I’m sorry, I could not find any other methods except for finding the closest perfect square which was 2116. (46^2)
Superior Segway Tours gives sightseeing tours around Chicago, Illinois. It charges a one-time fee of $40, plus $35 per hour. What is the slope of this situation?
80
65
40
35
Answers
Answer:
d. 35
Step-by-step explanation:
y = 35x + 40
The slope is 35 as 'm' is the slope of the equation
LMK IF IT WAS RIGHT!!
Answer:
D (35)
Step-by-step explanation:
HELP PLEASE I’ll give you 5 stars
Answers
Answer & Step-by-step explanation:
On the left:
There are 4 triangles that indicate -x, so this is -4
There are 3 circles that indicate -1, so these are -3.
Insert as an expression:
\(-4x-3\)
On the right:
There are 2 triangles that indicate -x, so this is -2x.
There are 2 circles that indicate -1, so these are -2.
Insert as an expression:
\(-2x-2\)
Combine both expressions into an equation:
\(-4x-3=-2x-2\)
Solve for x. Add 3 to both sides:
\(-4x-3+3=-2x-2+3\\\\-4x=-2x+1\)
Add 2x to both sides:
\(-4x+2x=-2x+2x+1\\\\-2x=1\)
Isolate the variable. Divide both sides by -2:
\(\frac{-2x}{-2} =\frac{1}{-2}\\\\ x=-\frac{1}{2}\)
:Done
Jasmine makes an origami picture frame to display her favorite family photo. The size of the frame is 3.5 In by 8 in. What is the area of the frame?
Answers
Answer:
28 sq in
Step-by-step explanation:
Area =LxW
3.5x8=28
if x-y = 8 and xy=5 , find x^2 + y^2
Answers
Answer:
x² + y² = 74
Step-by-step explanation:
given
(x - y) = 8 ( square both sides )
(x - y)² = 8² ← expand left side using FOIL
x² - 2xy + y² = 64 ← substitute xy = 5
x² - 2(5) + y² = 64
x² - 10 + y² = 64 ( add 10 to both sides )
x² + y² = 74
The distribution of monthly charges for cellphone plans in the United States is approximately normal with a mean of $62 and a standard deviation of $18. What percentage of plans have charges that are less than $83.60?
Answers
About 88.49% of cellphone plans have charges that are less than $83.60.
How to determine the percentage of plans have charges that are less than $83.60?To determine the percentage of plans that have charges less than $83.60, we need to find the z-score (z) using the given mean and standard deviation, and then look up the corresponding area under the normal distribution curve.
z = (x – μ) / σ
where x = 83.60, mean, μ = 62 and standard deviation, σ = 18
Thus, the z-score of $83.60 is:
z = (83.60 - 62) / 18 = 1.2
Using a standard normal distribution table, we can find that the area to the left of z = 1.20 is 0.8849 or 88.49% (check image attached).
Therefore, about 88.49% of cellphone plans have charges that are less than $83.60.
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What is the value of n in the proportion below?
n/28 = 4/7
•1
•12
•14
•16
Answers
Answer:
n = 16
Step-by-step explanation:
Given the proportion, n/28 = 4/7:
Cross multiply the two fractions:
7n = 28 × 4
7n = 112
Divide both sides by 7 to solve for n:
7n/7 = 112/7
n = 16
Therefore, the value of n = 16.
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Explanation: 7 goes into 28 four times which would set the denominators as equal. But to finish converting the fraction, you would have to multiply 4 by four just like you did the denominator which gives you 16.
Ebony kept her bank account open for only 3 weeks, and the graph shows the entire 3 weeks. During that time, her greatest balance was $400.
(a) Give the domain and range of the function.
(b)Give an estimate to the nearest hundreds for . Explain how you determined your estimate and tell what means in context of the situation.
(c)Ebony’s bank balance first reached $0 on Day 12. How would you show that information in function notation?
(d)Ebony’s bank balance remained at $0 from Day 12 through Day 15. As you count segments from the left, which segment on the graph1, 2, 3, 4, 5, or 6 represents that information? Explain how you know.
Answers
The domain of the function B(d) is from d = 0 to the number of days the account was open will be 0 ≤ d ≤ 21.
How to illustrate the information?The range is the set of values the bank balance might have. We know the minimum is 0 and the maximum is 400 0 ≤ B ≤ 400.
The balance on day 12 is B(12). We're told it is zero, so B(12) = 0 The 4th segment of the graph is at B(d) = 0.
In this context, it is reasonable to assume the vertical scale starts at 0 at the horizontal axis. We are told that (12, 0) is a point on the graph.
It is consistent with this assumption that slightly more than halfway through the graphed domain, the graph meets the horizontal axis. The graph stays at the horizontal axis for segment 4.
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What are the 4 main functions of the family?
Answers
Answer: sexual regulations, reproduction, economic cooperation and socialization/education.
Step-by-step explanation:
I’m not sure if that’s right
The set of all numbers greater than −8
Answers
Answer:
\(\{ x|x > -8\}\)
Step-by-step explanation:
Can Somone Help me with my homework
Answers
Answer:
part A) yes, the bases and heights are the same
Part B) yes, the bases and heights are the same
Part C) not enough info
Step-by-step explanation:
Part C)
area of the circle = π(1/2h)²
area of ellipse = π(1/2h)(1/2 major axis)
A school is holding a raffle to raise money to buy new books for the library. The school plans on awarding 18, $200 prizes, 120 $25 prizes and 270 $5 prizes. Is $10 enough to charge per ticket if they only sell 1000 tickets?
Answers
Answer:
Yes
Step-by-step explanation:
18 × 200 = 3600
120 × 25 = 3000
270 × 5 = 1350
in total 7950
tickets = 10 × 1000 = 10000
7950 < 10000
PLEASE HELP ME DONT ANSWER IF YB
(Surface Area of Cylinders MC)
A makeup artist purchased some lipsticks and wants to wrap them individually with gift wrap. Each lipstick has a radius of 0.4 inch and a height of 2.2 inches. How many total square inches of gift wrap will the makeup artist need to wrap 5 lipsticks? Leave the answer in terms of π.
10.4π square inches
4.8π square inches
2.08π square inches
1.76π square inches
Answers
Answer:
A would be correct
Step-by-step explanation:
the answer is A.
The coordinates of point R are (-3,2) and the coordinates of point T are (4,1). What is the length of RT?
Answers
In the following image we represent the position of the points R and T in the cartesian plane:
To find the distance between the points we draw a right triangle between them:
Where the resulting triangle has legs of measure 1 and 7, and "d" is the distance between the points.
If we call the legs
a=1
and b=7
Using the Pythagorean theorem, the formula to find "d" is as follows:
\(d=\sqrt[]{a^2+b^2}\)Next, we substitute the values for the legs a and b:
\(d=\sqrt[]{1^2+7^2}\)and we solve this operations:
\(\begin{gathered} d=\sqrt[]{1+49} \\ d=\sqrt[]{50} \end{gathered}\)The distance is square root of 50.
If you need it, we can simplify the square root of the answer as follows:
\(d=\sqrt[]{50}=\sqrt[]{25\times2}=5\sqrt[]{2}\)So the answer is:
\(\sqrt[]{50}=5\sqrt[]{2}\)
When the x-values are the same, then the slope is
Answers
Answer:
the x value when u add them or subtract them
Step-by-step explanation:
Answer: it is undefined
Step-by-step explanation: there is no way you will find an answer because of the axis
2 1/6
years =
How many months
Answers
Answer:
26 months
Step-by-step explanation:
There are 12 months in a year 1/6 of 12 is 2. So 24 +2 = 26.
I'd say that 2 1/6 years is 26 months.
Answer:
26 months
Step-by-step explanation:
12 months = 1 year
24 months = 2 years
1/6 = 2/12
So, it is 26 months
Have a wonderful day! :)
The image of B translated using (x + 2, y + 3) would have what coordinates?
Answers
Answer:
(5, 4)
Step-by-step explanation:
(x + 2, y + 3)
Substitute x and y for that of B's position.(3 + 2, 1 + 3)
(5, 4)
Answer:
B' (5, 4 )
Step-by-step explanation:
the translation rule (x, y ) → (x + 2, y + 3 )
means add 2 to the original x- coordinate and add 3 to the original y- coordinate , then
B (3, 1 ) → B' (3 + 2, 1 + 3 ) → B' (5, 4 )
If you are driving 30 miles per hour, how far will you go in 5 hours? To solve this problem, all you need to do is multiply your rate by 5. Remember to multiply both the numerator and denominator by the same number.
30 miles/1 hour × 5/5 = 150 miles/5 hours.
You will drive 150 miles in 5 hours. Don’t forget to label your answer with the correct units!
Clarence is skateboarding down the street. He estimates that a skateboard wheel goes around 20 times in 1 minute. About how many times will his wheels rotate in 5 minutes?
Answers
Answer:
100
Step-by-step explanation:
20 times = 1 minute
x times. = 5 minutes
1 x 5 =5
20 x 5 = X
20 x 5 = 100
Answer:
1 minute = 20 wheel spins x 5 = 1oo wheelspins
What is the least common multiple of the numbers 5, 25, and 15?
ОА.
25
B.
50
OC.
75
D.
100
E.
125
Answers
Answer:
C. 75
Step-by-step explanation:
Factorize the numbers first
5=5×1
25=5×5
15=5×3
LCM of 5,25,15 will be 5×5×3=25×3=75