The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.
Answers
Answer:
x = -5; y = 4, z = 1
Step-by-step explanation:
Given the row echelon form as:
[tex]\left[\begin{array}{cccc}1&0&\ \ 4|&-1\\0&1&-1|&3\\0&0&\ \ 1|&1\end{array}\right][/tex]
This matrix can be represented as:
[tex]\left[\begin{array}{ccc}1&0&4\\0&1&-1\\0&0&1\end{array}\right]\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}-1\\3\\1\end{array}\right] \\\\Performing\ matrix\ multiplication\ gives:\\\\\left[\begin{array}{c}x+4z\\y-z\\z\end{array}\right] =\left[\begin{array}{c}-1\\3\\1\end{array}\right][/tex]
Therefore:
z = 1
y - z = 3;
y = 3 + z = 3 + 1 = 4.
Hence, y = 4
x + 4z = - 1;
x = -1 - 4z = -1 - 4(1) = -5
x = -5
Related Questions
What is the least number of cuts you would need to make to cut a 3 by 3 by 3 inch block of cheese into 1 by 1 by 1 inch blocks of cubes?
Answers
Answer:
6 Cut Minimum
Step-by-step explanation:
According to the Question,
You have a 3x3x3 cube.
First make two cuts parallel to base of the cube each at a distance of 1 unit . This leaves you with three cuboids of dimensions 3x3x1. Now make two parallel cuts parallel to the height of the cube. This leaves you with nine cuboids of dimensions 3x1x1. Now make the final two cuts each 1 unit apart parallel to width and you are left with 27 cubes of 1x1x1.So , the final answer is 6 cuts.
I need help
Solve for X when:2X=8
Answers
Answer:
x=4
Step-by-step explanation:
x=8/2 =4
this question is quite easy
Please help I’ll give brainliest
Answers
Answer:
D. 12m^3n^5
Step-by-step explanation:
Answer:
12m³n⁵
Step-by-step explanation:
3 · 4 = 12
m² · m = m³
n³ · n² = n⁵
Therefore, 3m²n³ · 4mn² = 12m³m⁵
It takes 26 recyclable plastic soda bottles to make one polyester suit. How many bottles will be needed to make one dozen suits??
Need your help.
Answers
Answer:
It would take 312 bottles to make one dozen suits.
Step-by-step explanation:
One dozen suits = 12 suits.
As each suit costs 26 plastic soda bottles to make, we simply multiply 26 bottles by 12 suits to get 312 bottles.
Which of the following is the product of the rational expression shown below?[tex]((x)/(x+3))*((x)/(x+2))[/tex]
A. x^2/ x^2+5x+6
B. x^2/ x^2+6
C. 2x/ x^2+5x+6
D. x^2/x^2+5
Answers
Answer:
A
Step-by-step explanation:
A
8. The Oklahoma Museum of Natural History claims that on average, a square foot of grass contains 3.1 x 10^3 blades of grass. The soccer field has an area of 1.148 x 10^5 square feet. How many blades of grass are on the entire soccer field?
Answers
Answer:
3.5588 x 10⁸
Step-by-step explanation:
(3.1 x 10³) (1.148 x 10⁵) = (3.1 x 1.148) (10³ x 10⁵)
= 3.5588 x 10⁸
9514 1404 393
Answer:
3.6×10^8
Step-by-step explanation:
Your calculator or spreadsheet can multiply these numbers for you and give you the answer in scientific notation.
(3.1×10^3)×(1.148×10^5) = (3.1×1.148)×10^(3+5) = 3.5588×10^8
The supplied numbers have 2 and 4 significant digits, so rounding of the answer to 2 significant digits is appropriate.
about 3.6×10^8 blades of grass are on the entire soccer field
4x−6y=36
Put the following equation of a line into slope-intercept form, simplifying all fractions.
Answers
Answer:
y = -6 + 2x/3 = 2x/3 -6
where
2/3 is the slope and -6 is the intercept
Step-by-step explanation:
4x-6y = 36
Simplify
2x - 3y = 18
put y on the LHS
-3y = 18 - 2x
divide by -3
y = -6 + 2x/3 = 2x/3 -6
where
2/3 is the slope and -6 is the intercept
Solve for X in the triangle. Round your answer to the nearest tenth
Answers
Answer:
x ≈ 10.4
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos42° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{14}[/tex] ( multiply both sides by 14 )
14 × cos42° = x , then
x ≈ 10.4 ( to the nearest tenth )
Which statement is false?
A.
The inequality sign always opens up to the larger number.
B.
The greater number in an inequality is always above the other number on the vertical number line.
C.
The smaller number in an inequality is always located to the left of the other number on the horizontal number line.
D.
The inequality sign always opens up to the smaller number.
Answers
Answer:
D.) The inequality sign always opens up to the smaller number
Hope This Helps :)
660 g of 3 kg
Express as percentage
please tell how the answer is 22%..
:(
Answers
Answer:
Percent * base = Amount
660 g = 660 g
3kg = 3000g
percent(3000) = 660
percent = 660/3000
percent = .22
.22 = 22%
Step-by-step explanation:
A factory employs 200 men and 50 women. 80 of the men are each paid $100, the rest are paid $80 and the women are paid $50, what is the total wage bill.
Answers
hey I have a doubt isn't for this question the ans supposed to be 36 but the option is not there so could you plzz help me
Answers
Answer:
Its actually 31
Step-by-step explanation:
Try drawing it and counting the matches
analyze the histogram comparing the frequencies shown for the annual temperatures of kentucky and illinois
Answers
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the required histograms are not provided; however, the general explanation is as follows.
(a) If any of the histograms has more bars at the left hand side, then it means that the distribution is skewed left.
(b) If any of the histograms has more bars at the right hand side, then it means that the distribution is skewed right.
(c) If any of the histograms has appears to have increasing number of bars at the middle, then it means the such histogram is symmetrical.
Use the above illustration to answer your question.
Answer:
C: Both distributions are skewed right.
Step-by-step explanation:
25.673 round off to the nearest hundredth
Answers
Answer:
25.67
Step-by-step explanation:
Look at the thousandth place. If it is 5,6,7,8 or 9 then add 1 to hundredth place. If it is less than 5, then write the hundredth place as it is
25.67
Write the equation of the line
a) Slope = -2
Y intercept=5
b) Slope = 0.5
Passes through (0,1)
Answers
B) y=0.5x+1
What fraction of an hour is 45 minutes?
Give your answer in its simplest form.
Answers
Answer:
3/4
Step-by-step explanation:
1 hour is 60 minutes
45 minutes
---------------------
60 minutes
Divide top and bottom by 15
3
----
4
A solid right pyramid has a regular hexagonal base with an area of 5.2 cm2 and a height of h cm.
A solid right pyramid has a regular hexagonal base with an area of 5.2 centimeters squared and a height of h centimeters.
Which expression represents the volume of the pyramid?
One-fifth(5.2)h cm3
StartFraction 1 Over 5 h EndFraction(5.2)h cm3
One-third(5.2)h cm3
StartFraction 1 Over 3 h EndFraction(5.2)h cm3
Answers
Answer:
its c
Step-by-step explanation:
cause this dude think u gonna open a word link^^^^
Answer:
c) One-third(5.2)h cm3
Step-by-step explanation:
edge 2023
In a direct variation, y = 12 when x = 3. Write a direct variation equation
that shows the relationship between x and y.
O y = 12x
O y = 4x
O y = 3x
O y = 2x
helpppp
Answers
Answer:
fourth one
Step-by-step explanation:
Rikki decided to collect data to determine if a runner's time and speed are correlated. She determined the data to have a correlation coefficient of −0.5. What does this r value indicate?
Answers
the R value in the calculator
also known as the amount of correlation the data points fit
Saw a board 5 ft 1 in. Long into six equal pieces. If the loss per cut is 1/5 in., how long will each piece be?
Answers
Answer:
The length of each piece is 0.833 ft.
Step-by-step explanation:
Length of board, L = 5 ft 1 inch
loss per cut = 1/5 inch
The board should be cut by 5 times to get the 6 pieces.
The loss in 5 cuts = 5 x 1/5 = 1 inch
So, the length of each piece is
[tex]L' =\frac{5 ft 1 in - 1in }{6}\\\\L' =\frac{5}{6}\\\\L' = 0.833 ft[/tex]
The length of each piece is 9 13/15 inches.
What is the length of each piece?The first step is to determine the length of the board in inches. In order to do this, feet should be converted to inches.
1 feet = 12 inches
(12 x 5) + 1 = 61 inches
Total losses of the 6 cuts = 1/5 x 6 = 6/5 = 1 1/5 inches
Total length left = 61 inches - 1 1/5 inches = 59 1/5 inches
Length of each board = 59 1/5 ÷ 6
296 / 5 x 1/6 = 296 /30 = 9 26/30 = 9 13/15 inches
To learn more about multiplication of fractions, please check: https://brainly.com/question/1114498
explanation about Cardinal number Carolyn relation cardinals
Answers
Answer:
Cardinal Numbers
The cardinality of a group represents the number of objects available in that group.
The number of elements or members in a set is the cardinal number of that set. ...
For example, set A = {1, 3, 6, 9, 10, 12, 18}, the cardinal number of set A is 7.
Step-by-step explanation:
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Fiona and Pip win some money and share it in the ratio 3:1. Fiona gets £30. How much did they win in total?
Answers
Answer:
40
Step-by-step explanation:
Fiona: Pip
3 1
If fiona gets 30
30/3 = 10
Multiply each side by 10
Fiona: Pip
3*10 1*10
30 10
The total is 30 +10 = 40
$125 to the markup rate of 80% what is the final price?
Answers
Answer:
$225
Step-by-step explanation:
mark rate = 80%
original price = $125
mark amount = 80% of $125
=80/100 *125
=10000/100
=$100
final price = $125 + $100
=$225
What is the scale factor of Triangle XYZ to Triangle UVW? A.10 B.5 C.1/5 D. 1/10
This da last question for
A
P
E
X
Please help!!
Answers
Answer:
1/10
Step-by-step explanation:
Take the side length of figure B and divide by the same side of figure A
This is the number we need to multiply Figure A by to get to Figure B
6/60 = 1/10
We need to multiply figure XYZ by 1/10 to get to UVW
1/10
Add the following numbers. -6 + 5 =
Answers
= -1.
Regards............
Step-by-step explanation:
-6 + 5 = -1!!!!!!!!!!!!!!!!!!!!!!!
What is the measure of USQ
pls help
Answers
Answer:
USQ = 227°
Step-by-step explanation:
∠ QPR = ∠ UPT = 47° ( vertical angles )
∠ QPR is equal to the measure of the arc that subtends it , so
arc QR = 47°, then
arc USQ = arc USR + arc QR = 180° + 47° = 227°
Answer:
227º
Step-by-step explanation:
USQ = 180+47 = 227º
Please help I’ll give brainllist
Answers
There is a bag filled with 3 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 blue?
Answers
Answer:
5/7 is the answer to your question
Rearrange the formula to make x the subject.
y = 4x + 3
Answers
Answer:
[tex]x=\frac{y-3}{4}[/tex]
Step-by-step explanation:
[tex]y=4x+3[/tex]
[tex]y-3=4x[/tex]
[tex]\frac{y-3}{4}=x[/tex]
[tex]x=\frac{y-3}{4}[/tex]
Answer:
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
[tex]y = 4x + 3 \\ y - 3 = 4x \\ \frac {y - 3}{4} = x [/tex]
⎆ The formula will be [tex]\hookrightarrow\boxed{\underline\frac {y - 3}{4}=x}[/tex]
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a car loan is $2,500 with an interest rate of 8.5% for three years. what is the interest on the car loan?
a)$63,750
b)$212.50
c)$637.50
d)$6,375.00
Answers
Answer:
c) $637.50
Step-by-step explanation:
Formula: I= PRT
2500×8.5%×3 = 637.5