The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.
1 0 -1 -3
0 1 5
00 1
a.
X=-3
y--9
z-1
b. x-2
y=-9
N
I
T
C. X=-2
y--9
2-1
d. x-3
y=-9
2-1
Answers
The question is incomplete. Below you will find the missing content.
The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.
The correct option will be Option C: x=5t-3
y=4t-5
z=t
where t is the real number.
A matrix is in row echelon form when the first non-zero number from the left i.e. leading coefficient is always to right of the first non-zero number in the row above and rows consisting of all zeros are at bottom of the matrix.
The row echelon form of the matrix is given in the question.
from row-echelon form of the matrix, we can write the equation as,
x-5z=-3
y-4z=-5
Let's assume z=t, where t is the real number
now we can find x and y by putting z=t in the equation
x-5t=-3
⇒x=-3+5t
y-4t=-5
y=-5+4t
Now we get the solution of x,y,z in terms of t
x=5t-3
y=4t-5
z=t
where t is the real number.
So the correct option will be Option C: x=5t-3
y=4t-5
z=t
where t is the real number.
Learn more about row-echelon form
here: https://brainly.com/question/24036095
#SPJ10
Related Questions
What expression below is equivalent to -71n -
29?
A) -29 - 71n
B) 71n + (-29)
C) 29 + 71n
D) -29 - (-71n)
Answers
Answer:
A
Step-by-step explanation:
both numbers are negative, you can rearrange them in any order provided you keep the sign
Reason:
An expression in the form -a-b is the same as -a + (-b)
Recall we can add two numbers in any order we want. For instance, 2+3 = 3+2 since both sides are equal to 5. This is the commutative property of addition.
Therefore, the -a + (-b) is the same as -b + (-a) which in turn becomes -b - a
In short: -a - b = -b - a
This rule lets us say that -71n - 29 = -29 - 71n
Triangle ABC is shown on the graph. What are the coordinates of the image of point B after the triangle is rotated 270° about the origin?
(4, 2)
(2, 4)
(–4, –2)
(–2, –4)
Answers
The coordinates of the image of point B after the triangle is rotated 270° about the origin is (4, 2)
How to determine the image of point B?The complete question is added as an attachment
From the attached image, we have the following coordinate
B = (-2, 4)
When the triangle is rotated by 270 degrees, the rule of rotation is:
(x, y) ⇒ (y, -x)
For point B, we have:
B' = (4, 2)
Hence, the coordinates of the image of point B after the triangle is rotated 270° about the origin is (4, 2)
Read more about rotation at:
https://brainly.com/question/7437053
#SPJ1
A tree height when planted was 5ft. 8inches. It has grown 14ft. 10 inches how much did it grown
Answers
Answer:
Subtraction will happen in this case.
14ft-5ft= 9ft
10 inches-8 inches= 2 inches
So, it grew 9ft. and 2 inches.
5 m
2m
6 m
2 m
Mrs Phillips is going to cover the floor with floor boards.
One pack of floor boards will cover 2.5 m².
How many packs of floor boards does she need?
You must show your working.
Diagram NOT
accurately drawn
Answers
Mrs. Phillips needs to buy 8 packs of floor boards
In contrast to a square, a rectangle is a planar figure having four equal neighboring sides, four straight sides, and four right angles. An enclosed 2-D form called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposing sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.
As per the figure attached Mrs. Phillips floor plan can divided into two rectangles
The area of rectangle is as follow:
Area = length(l) x Width(w)
Area of part 1 will be:
A = 6 x 2 = 12 m²
Area of part 2 will be :
a = 3 x 2 = 6 m²
Total area of floor = A + a
Total area of floor = 12 + 6
Total area of floor = 18 m²
Given one pack of floor boards will cover 2.5 m².
So total pack of floor block needed will be as follow:
Total pack of floor block = Total area of floor/Area covered by one pack of floor boards
Total pack of floor block = 18/2.5
Total pack of floor block = 7.2 packs ≈ 8 packs
Hence Mrs. Phillips needs to buy 8 packs of floor boards
Learn more about rectangle here:
https://brainly.com/question/17297081
#SPJ10
PLS HELP!!! 50 POINTS!!!
Part C:
In the section describing the survey methods, the report states, “Each sample of national adults includes a minimum quota of 60% cell phone respondents and 40% landline respondents.” Do you think this is a good minimum quota for this survey? Should it be lower or higher?
Part D:
The report begins by showing three bulleted highlights from the survey. At the end of the article, you can click a link to view the complete question responses and trends. Click the link and interpret the results of question 5. Use your interpretation of the statistics to write one more bullet point that could be added as a fourth bullet at the beginning of the report.
Answers
This is not a good minimum quota for this survey. For us to have a good minimum quota, there must be equality. i,e 50% for cell phone respondents and 50% for landline respondents.
What is the survey method in Statistics?Survey methodology is the study of the sampling of discrete units or groups from a population and the procedures used to gather survey data, including the design of questionnaires and approaches for increasing survey response rates and precision.
A good minimum quota for this survey should be 50% for cell phone respondents and 50% for landline respondents.
It implies that the quota for cell phone respondents should be 10% lower and 10% higher for landline respondents.
For us to answer Part D, kindly provide or repost the complete question since we cannot see any link added.
Learn more about the sample survey method here:
https://brainly.in/question/15404191
#SPJ1
A blueprint of a house shows a dining room with
an area of 7 square inches. If the blueprint's
scale is 1 inch: 6 feet, what would be the actual
area of the dining room?
A = 7 in.²
Actual Area = [?] ft²
Answers
Answer: The Actual area of the dining room is 252 square feet.
Explanation:
How to Find the Actual Area Using Scale?
Given that the area of the house on a blueprint = is 7 square inches.
The scale of the blueprint = is 1 inch: 6 feet.
Therefore, we would have the following proportion:
The area on the blueprint/actual area = square of the scale
7/actual area = 1²/6²
7/actual area = 1/36
Actual area = (7)(36)
Actual area = 252 square feet.
In a grop of 25 student 6 study art & biology 10 study biology but not art 3 study neither subject given that a randomly selected study art what is the probability the student study art & biology
Answers
½ 0r 50% is the probability that the student studies Art and biology.
What is Probability?Probability is a branch of mathematics that deals with the occurrence of a random event . i.e. Probability means possibility.
According to the question,
Total number of students in the group;
n = 25 students
No. of students that study both art and biology;
n(P u Q) = 6
No. of students that study biology but not art;
n(Q u P') = 10
No. of students that study none of the 3 subjects;
n(P' u Q') = 3
So,
No. of students that study only arts is;
n(P n Q') = 25 - 6 - 10 - 3 = 6
Since, n(P u Q) = 6
Therefore by using formula;
n(P) = n(P u Q) + n(P n Q')
n(P) = 6 + 6
n(P) = 12
Hence,
Probability of the students who studies Art and biology is;
P(P n Q) = [tex]\frac{6}{12}[/tex]
P(P n Q) = ½ i.e. 50%
The probability the student study art & biology ½ i.e. 50%.
Learn more about probability here:https://brainly.com/question/11234923
#SPJ1
Which inequality is equivalent to 3+4/x>_x+2/x
Answers
Answer:
the right answer is the first one
2x+2 over x >0
Someone please help!!
Answers
Answer:
I believe the answer would be option D
Step-by-step explanation:
the distance formula is
[tex] \sqrt{(x - x1)^{2} + (y - y1)^{2} } [/tex]
So, substituting the values of the coordinates, you will get the answer of D
wich calculation can be used to find the value of p in the equation p^3=8
Answers
Answer:
The answer is 2
p³ = 8
p = ³√8
p = 2.
10.
(06.01 MC)
Classify the expression: 5x3 + 2x − 3 (1 point)
Quadratic expression
Linear expression
Cubic expression
Exponential expression
Answers
The correct answer is option C which is the given expression is cubic.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given expression
5x³ + 2x − 3
The cubic expression is one in which the highest power of the variable is three or we can say that the degree of the expression is three so the expression will have three solutions.
Therefore the correct answer is option C which is the given expression is cubic.
To know more about Expression follow
https://brainly.com/question/723406
#SPJ1
does y - x = 2 show direct variation
Answers
Answer:
no
Step-by-step explanation:
if I use any numbers too .the numbers can not be constant numbers so this equation is not a direct variation
7 - 5 = 2
6- 4 = 2
not contstant
A number written in scientific notation has a ________ that indicates the digits used in the number and is always written with 1 digit to the left of the decimal place.
Answers
A number written in scientific notation has a Negative Exponent that indicates the digits used in the number and is always written with 1 digit to the left of the decimal place.
The coefficient is always a number larger than or equal to one and less than ten in scientific notation. There is an integer exponent. When using scientific notation to write integers bigger than ten
The exponent is positive and equals the number of spaces to the left of the original decimal point. When expressed in scientific notation, a negative exponent. The exponent's value is equal to how many places to the right the decimal has been pushed.As a result, when a number is smaller than 1, it will have a negative exponent in scientific notation.
Learn more about scientific notation here :
https://brainly.com/question/18073768
#SPJ4
NEED HELP ASAP 1 HOUR LEFT
Answers
Using the vertex of a quadratic function, it is found that:
a) The revenue is maximized with 336 units.
b) The maximum revenue is of $56,448.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.The demand function is given by:
p(x) = 336 - 0.5x.
Hence, the revenue function is:
R(x) = xp(x)
R(x) = -0.5x² + 336x.
Which has coefficients a = -0.5, b = 336.
Hence, the value of x that maximizes the revenue, and the maximum revenue, are given, respectively, as follows:
[tex]x_v = -\frac{336}{2(-0.5)} = 336[/tex][tex]y_v = -\frac{336^2 - 4(-0.5)(0)}{4(-0.5)} = 56448[/tex]More can be learned about the vertex of a quadratic function at https://brainly.com/question/24737967
#SPJ1
Find the inequality represented by the graph
Answers
Which is the graph of the system x + 3y > –3 and y < One-halfx + 1?
Answers
Step-by-step explanation:
hope it helps you understand
what can this be classified as?
Answers
Answer: None of the above
Step-by-step explanation:
Complementary Angles add up to 90
Supplementary Angles add up to 180
Parallel Angles are Supp., Comp., or Congruent
Micah is keeping track of how much he spends this month on gas. In the first week, he bought x gallons of gas at $2.39 per gallon. In the second week, he bought 3 fewer gallons of gas than the first week at $2.49 per gallon. So far this month, he has spent a total $46.21 on gas.
In the first week, Micah bought
x gallons of gas.
In the second week, Micah bought
x gallons of gas.
Answers
Answer: In the first week, Micah bought 11 gallons of gas,
and in the second week, he bought 8 gallons of gas
Step-by-step explanation:
In the first week, Micah bought x gallons of fuel at $2.39/gallon
In the second week, he bought (x - 3) gallons at $2.49/gallon
Formulating an equation and solving for x gallons of fuel:
x × 2.39 + (x - 3) × 2.49 = 46.21
2.39x + x × 2.49 − 3 × 2.49 = 46.21
2.39x + 2.49x − 7.47 = 46.21
4.88x − 7.47 = 46.21
4.88x = 53.68
[tex]\frac{4.88x}{4.88} = \frac{53.68}{4.88}[/tex]
x = 11
Therefore,
In the first week, Micah bought 11 gallons of gas
In the second week, he bought (11 - 3) = 8 gallons of gas
which one is the correct graph
Graph f(x) = -1/2x
Click on the graph until the graph of f(x) = -1/2x appears
Answers
Answer:
The third graph
Step-by-step explanation:
The third graph depicts the function f(x) = -1/2x because for every 1 unit decrease along the y-axis, you travel 2 units on the x-axis.
Also, the two points on the third graph can satisfy the equation.
Point 1: (-2,1)
f(-2) = (-1/2)(-2)
f(-2) = 1
Point 2: (0,0)
f(0) = (-1/2)(0)
f(0) = 0
Show work, can someone help me out having trouble with this problem
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: f = \cfrac{9}{a}+7[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \:a = \cfrac{9}{f - 7} [/tex]
[tex]\qquad \tt \rightarrow \:a(f - 7) = 9[/tex]
[tex]\qquad \tt \rightarrow \:(f - 7) = \cfrac{9}{a}[/tex]
[tex]\qquad \tt \rightarrow \:f = \cfrac{9}{a} + 7[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
4 kg 2 dag when converted in g gives you?
Answers
Answer:
4020 grams
Step-by-step explanation:
4kg=4000g
2 dag= 20g
Total: 4000g + 20g = 4020g
Answer:
4020 grams
Step-by-step explanation:
1 kg = 1000 g
1 dag = 10 g
4 x1000= 4000
2 x 10 = 20
4000 + 20
Find the midpoint of the segment with the following endpoints. (10, 6) and (4, 9)
Answers
Answer:
(10+4/2, 6+9/2)
(7, 7.5)
The Midpoint is (7, 7.5)
Step-by-step explanation:
I just added the x values and divided them by 2 and then the same for the y values.
Answer:
(7,7.5)
Step-by-step explanation:
midpoint formula:
(X1,X2) divided by two and (Y1,Y2) also divided by two.
so you get
10+4/2 and 6+9/2
Add it all up you get
14/2 and 15/2
divide it:
(7,7.5)
The width of a certain rectangle is 2 m greater than half its length. Four times its length is 26 m greater than its perimeter. What are the dimensions of the rectangle?
Answers
Answer:
Length = 30
Width = 17
Step-by-step explanation:
Let L = length of rectangle and W = Width
The first sentence gives the equation
W = L/2 + 2 ==>
2W = L +4 ==>
L = 2W - 4 .... (1)
The perimeter of the rectangle is 2(L+W) = 2L +2W
Second sentence gives us the equation
4L = 2L + 2W + 26 ===>
2L = 2W + 26 ...... (2)
(2) - (1) ==> L = 30 (2W cancels out)
From (1), W = 30/2 + 2 = 15 + 2 = 17
Check:
Using these values and substituting in equation 2 gives us
2 * 30 = 2* 17 + 26
60 = 34 + 26
which matches
What is the missing reason in the proof?
Given: ∠ABC is a right angle, ∠DBC is a straight angle
Prove: ∠ABC ≅ ∠ABD
Answers
Answer: Since they have the some points in common we can just plot them and seeing ang. DBC would just be a straight line and angle ABC would be 90 degrees and half of that angle so they would be equal
Which expression is equivalent to 3^0x3^-3?
Answers
Step-by-step explanation:
[tex] = {3}^{0} \times {3}^{ - 3} [/tex]
[tex] = 1 \times \frac{1}{ {3}^{3} } [/tex]
[tex] = \frac{1}{3 \times 3 \times 3} [/tex]
[tex] = \frac{1}{27} [/tex]
The unit rate of change of yyy with respect to xxx is the amount yyy changes for a change of one unit in xxx.
Is the unit rate of change of yyy with respect to xxx less in the equation y=6.5xy=6.5xy, equals, 6, point, 5, x or in the graph below?
Answers
The unit rate of change of y with respect to x is less in the graph
How to compare the rate of change?The attached graph represents the missing information in the question
The graph passes through the following points
(0,0) and (5,1)
The rate of change of the graph is then calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
This gives
[tex]m = \frac{1-0}{5-0}[/tex]
Evaluate
m = 0.2
The equation is given as:
y = 6.5x
The slope of the above equation is 6.5
By comparison, 6.5 is greater than 0.2
Hence, the unit rate of change of y with respect to x is less in the graph
Read more about unit rate of change at:
https://brainly.com/question/17037198
#SPJ1
Answer:
The equation
Step-by-step explanation:
i did it on khan academy
pls help answer ASAP
Answers
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
what is the square root of 10,000
Answers
Answer:
100
Step-by-step explanation:
The square root of 10000 can be written as (10000)1/2. Thus,
(10000)^/2 = (100 × 100)^1/2
(10000)^1/2 = [(100)2]^1/2
(10000)^1/2 = (100)^2/2
(10000)^1/2 = (100)^1
So,
√10000 = 100
The length of a conference room is one and a half times its width. There is a carpet in the
centre of the room. The length of the carpet is twice its width. This leaves a 3m wide
border around the edges of the carpet. Find the area of the carpet.
Answers
The Area of carpet for the given dimension is 72m².
What is Area of rectangle?Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides.
Let the width of the room w = x m
and the length, L = 1.5x
Length of carpet + 6 = length of room
2(x-6)+6=1.5x
2x-12+6=1.5x
0.5x=6
x = 6 / 0.5
x = 12
length of room x = 12 m
width of room = 18 m
18-6 by 12-6 = 12 by 6 dimensions of carpet
Area of carpet = 12 X 6=72 m²
Thus, the Area of carpet for the given dimension is 72m².
Learn more about Area of rectangle from:
https://brainly.com/question/20693059
#SPJ1
What is the value of x in the equation 8x – 2y = 48, when y = 4?
Answers
Answer: x = 7
Step-by-step explanation:
First, we will plug 4 in for y. Then, to solve we will isolate the variable "x" in the equation.
Given:
8x – 2y = 48
Plug in the y value of 4:
8x – 2(4) = 48
Multiply -2 times 4:
8x – 8 = 48
Add 8 to both sides of the equation:
8x = 56
Divide both sides of the equation by 8:
x = 7
Answer:
x=7
Step-by-step explanation:
8x – 2y = 48
Let y=4
8x -2(4) = 48
8x - 8 = 48
Add 8 to each side
8x-8+8= 48+8
8x = 56
Divide by 8
8x/8 = 56/8
x = 7
