Construct an augmented matrix for this linear system: x − y − 4z = 5 2x 2z = 0 4x y z = 3.
The augmented matrix is,
[tex]\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)[/tex]
We have given system of linear equation is,
[tex]x - y - 4z = 5,2x + 2z = 0 ,4x +y +z = 3.[/tex]
What is the meaning of augmented matrix?In an augmented matrix, each row represents one equation in the system and each column represents coefficients (with signs) of variables or the constant terms.
So, the first row is
[tex]1\ -1\ -4\ 5[/tex]
the second row is
[tex]2\ 0\ 2\ 0[/tex]
and the third row is
[tex]4\ 1\ 1\ 3[/tex]
Therefore the augmented matrix for this linear system is,
[tex]\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)[/tex]
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The augmented matrix for the given linear equations will be constructed as follows
[tex]\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right][/tex]
What will be the augmented matrix of the given linear equations?The augmented matrix is generally a matrix form of the given linear equations and the coefficient of the variables are arranged in the form of a matrix.
The given equation has three variables so the matrix form will be of [tex]3\times3[/tex]
The given linear equations are
[tex]x-y-4z=5\\2x+0y+2z=0\\4x+y+z=3[/tex]
From the above equations, we will make an augmented matrix.
[tex]\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right][/tex]
The first equation will be followed by the first row of the matrix and the rest will be followed the same.
Thus the augmented matrix for the given linear equations will be constructed as follows
[tex]\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right][/tex]
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A regulation bowling ball has a diameter of 8. 5 inches. What is the volume of the bowling ball?and why.
A 302. 49 in
B 75. 62 in
C 2,571. 14 in
D 321. 39 in
Answer: D: 321. 39 in³
Step-by-step explanation:
Bowling balls are spheres:
the volume of a sphere is calculated as:
V = 4/3 πr³
V = 4/3 π 4.25³
V = 4/3 x 241.044
V ≅321.39 in³
The answer is D
A right rectangular prism has a length of 412 cm, width of 4 cm, and height of 212cm. What is the volume of the prism? Enter the answer in the box. cm³
Answer: Volume = 349376 cm^3
Step-by-step explanation:
The volume of a rectangular prism is the length*width*height.
We can plug in the values given:
Volume = 412 cm * 4 cm * 212 cm
Volume = 349376 cm^3
Answer:
the awnser is 3 over 9
Step-by-step explanation: bc i like suck\
iykyk
An angle whose measure is –102° is in standard position. In which quadrant does the terminal side of the angle fall? Quadrant I Quadrant II Quadrant III Quadrant IV.
Angle is formed by the two rays. The angle with measurement –102° will lie in the third quadrant.
What is an angle?An angle is formed by the two rays, the two rays are known as the two sides of the angle.
As it is given that the measure of the angle is –102°, therefore, the angle will be measured from the positive x-axis in the clockwise direction, therefore, the angle will lie in the third quadrant as shown in the image below.
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Select the decimal that is equivalent 29/30
Answer:
0.96666666666667
Step-by-step explanation:
YOU WILL GET BRAINLY!!
Please help me and please explain.
Answer:
Measure of side a: 6
Measure of side b: 8
Measure of side c: 10
Side a/c: 6/10 = 3/5
Side b/c: 8/10 = 4/5
Side a/b: 6/8 = 2/3
Step-by-step explanation:
[tex]\beta=59\ degrees[/tex]
Step-by-step explanation:
[tex]< ABC+ < BAC=90\ degrees\\ The\ acute\ angles\ of\ a\ right\ triangle\ are\ complementary.[/tex]
[tex]\beta+31\ degrees=90\ degrees\\ Substitute\ < ABC=\beta, < BAC=31\ degrees\ into\\ < ABC+ < BAC=90\ degrees[/tex]
[tex]\beta=59\ degrees\\ Calculate\ \beta+31\ degrees=90\ degrees[/tex]
I hope this helps you:)leslie worked for 180 minutes. How many hours did she work
Answer:
3 hours
Step-by-step explanation:
divide the time value by 60
Answer:
Leslie worked for 3 hours
Step-by-step explanation:
There are 60 minutes in an hour, so simply divide 180 by 60, and you will get your answer, which is 3
Hope that helps
You are creating strings picking letters from the English alphabet at random. What is the probability that your randomly created string of length 11 will contain exactly 7 A's
There are 4 positions in the string that each have 25 choices (any letter in the English alphabet except A) and the other positions are filled with A, so there are 25⁴ possible strings containing exactly 7 A's.
Overall, there are 26¹¹ possible strings of length 11.
Then the probability of randomly generating a string containing exactly 7 A's is
25⁴ / 26¹¹ ≈ 0.000000000106427
Which of the following inequalities matches the graph? (2 points)
Answer:
b
Step-by-step explanation:
if the line is solid the it is <> or equal to which it is in this case
the line also goes through the x axis so it is to do with x
and the shaded region is covering values of -7 and less so it is
[tex]x \leq -7[/tex]
good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.
put x=4
[tex]\\ \rm\longmapsto y=40(0.6)^4[/tex]
[tex]\\ \rm\longmapsto y=40(2.4)
[tex]\\ \rm\longmapsto y=40(0.13)
[tex]\\ \rm\longmapsto y=5.2ft[/tex]
Why did the freshman eat his homework? Because his teacher said it was a piece of cake.
Answer:
lol
Step-by-step explanation:
aaaaaaaaa stop brainly
Answer:
the guy that invented umbrellas didnt know what to call it so he said "ummm... brella"
Step-by-step explanation:
My math grade went from a 78 to a 86. What is the percent increase
Answer:
10.25641...% or 10.3%
Step-by-step explanation:
(86/78)/78 = 8/78
8/78 * 100 = 400/39 = 10.25641...%
On Saturday, Lukas drove 4x – 5 miles. On Sunday, he drove 3x – 10 miles. What is the total amount of miles lukas drove
Answer:
first is -20 second is -30 and if you add those it is -50
What’s 2/3 + 3/5?
2/3 +3/5 = _/15 + _15
Answer:
= 1 4/15 or 19/15
Step-by-step explanation:
2/3 + 3/5 = 10/15 + 9/15
improper = 19/15
proper = 1 4/15
How do I solve?
Angle is 60°
Bottom is X
Top is 12
(cm)
Answer:
x = 6
Step-by-step explanation:
using the cosine ratio in the right triangle and the exact value
cos60° = [tex]\frac{1}{2}[/tex] , then
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{12}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 12 ( divide both sides by 2 )
x = 6
PLEASE HELP ME WITH this question I need help a number one through four could you also explain how you got the answer thank you the person with the best answer will get BRAINLY !!!!!!!20 POINTS
Answer:
1. (c-d)(c+d)
2. (2c-3d(2c+3d)
3. (4ab-5cd)(4ab+5cd)
4. cannot be factorised into difference of two squares
Classify each pair of labeled angles as complementary, supplementary, or neither.
Drag and drop the choices into the boxes to correctly complete the table. Each pair of angles may belong to more than one category.
Answer:
The angles 53 and 127 are supplementary.
The angles 56 and 34 are complementary.
The angles 67 and 67 are neither.
Step-by-step explanation:
Supplementary angles are two angles that add up to 180 degrees.
Complementary angles are two angles that add up to 90 degrees.
Add the angles found in each choice to get 180, 90, and 134.
what is 3x^3 + 20x^2 + 28x +15
Answer:
(3x^2 + 5x +3) (x + 5)
multiply polynomials ( 1.3xy^2) (-2.2x^2y)
pls solve this :)
Zahria deposited her $500 savings in a high yield fund. See the end of year balances in the table below.
will give brainliest
Step-by-step explanation:
please I don't understand the question
-2/3 a + 5/6a-1/6 Answer this
Answer:
a=1
Step-by-step explanation:
2/3a + 5/6a - 1/6 = 0
-2/3a + 5/6a = 1/6
5/6a - 2/3a = 1/6
Lowest common multiple of 3 and 6 =6
(5/6-4/6)a =1/6
1/6a = 1/6
a=1/6 / 1/6
a=1
One rectangle is divided into 4 parts. How much is one part?
The measure of one part of a rectangle divided into 4 parts is 1/4
How to solve fractionA rectangle is a whole = 1If 1 whole is divided into 4 equal parts
= 1/4
So, if the perimeter of the rectangle is 60cm
1 part of 4 = 1/4 × 60cm
= 60/4
= 15 cm
Therefore, the measure of one part of a rectangle divided into 4 parts is 1/4
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if the width of a rectangle with perimeter P is 6 units , what is the length.
Answer:
L= P/2 - 6
Step-by-step explanation:
As you know that the Perimeter of a Rectangle = 2(L+W)
since Perimeter = P and Width = 6
Then P = 2(L+6)
Expanding
P=2L+12 --> 2L=P-12
Then L=(P-12)/2=P/2-6
The perimeter is twice the sum of width and length. Then the length of the rectangle is P/2 – 6 units.
What is a rectangle?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a rectangle, opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at the mid-point.
If the width of a rectangle with perimeter P is 6 units.
Perimeter = P
Width = 6 units
Then the length of the rectangle will be
Perimeter = 2 (Width + Length)
P = 2 (6 + L)
L = P/2 – 6
The length of the rectangle is P/2 – 6 units.
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1. A car is traveling down a road at a constant speed of 50 miles per hour. a. Complete the table with the amounts of time it takes the car to travel certain distances, or the distances traveled for certain amounts of time. Help please and thank you :)
By finding the linear equation that relates distance and time, we can see that the complete table is:
time (hours) distance (miles)
2 100
1.5 75
t (50)*t
1 50
6 300
d/(50) d
How to complete the table?
After a small online search, I've found that the table is:
time (hours) distance (miles)
2
1.5
t
50
300
d
Now, remember the relation:
distance = speed*time.
In this case, we know that the speed is 50 mi/h, so if we define d as the distance and t as the time, we can write:
d = (50mi/h)*t
To complete the table, we just replace the value that appears in the table, and then we solve the equation for the other variable.
First we have t = 2 hours:
d = (50 mi/h)*2h = 100 mi
Then we have t = 1.5 hours
d = (50 mi/h)*1.5 h = 75 mi
Then we assume that we evaluate in t, so there we just write the equation:
d = (50 mi/h)*t
Now we go to the other side of the table, now we evaluate d, so we can write:
t = d/(50 mi/h)
(that is what goes in the table when we need to evaluate in d).
Then the fourth place in the table has d = 50 mi, replacing that:
t = (50mi)/(50 mi/h) = 1h
And finally, we evaluate in d = 300mi
t = (300 mi)/(50 mi/h) = 6h
Then the complete table is just:
time (hours) distance (miles)
2 100
1.5 75
t (50)*t
1 50
6 300
d/(50) d
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In circle EE, m\angle FEG=70^\circ∠FEG=70
∘
and the length of \overset{\LARGE\frown}{FG} = \frac{7}{9}\pi
FG
⌢
=
9
7
π. Find the length of \overline{EF}
EF
.
The length of EF from the given diagram is 2.98
How to calculate the length of an arcThe formula for calculating the length of an arc is expressed as;
L = rtheta
where
r is the radius
theta is the subtended angle
Given the following
r = 7/9π
theta = 70 degrees
L = 70/360 * 2 * 7/9π * π
L = 2.98
Hence the length of EF is 2.98
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A simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is x Overbar, while the standard deviation is s. What is the 99% confidence interval for the population mean? Use the table below to help you answer the question. Confidence Level 90% 95% 99% z*-score 1. 645 1. 96 2. 58.
Using the z-distribution, as we have the standard deviation for the population, it is found that the 99% confidence interval for the population mean is given by:
[tex]\overline{x} \pm 2.58\frac{s}{\sqrt{n}}[/tex]
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.s is the standard deviation for the population.99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so [tex]z = 2.58[/tex].
The other parameters are symbolic, hence the interval is given by:
[tex]\overline{x} \pm 2.58\frac{s}{\sqrt{n}}[/tex]
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PLS HELP I'M DESPERATE!!!!!!!!!!!
Translate this phrase into an algebraic expression. 43 less than twice a number Use the variable n to represent the unknown number.
what is the slope of each line Line A y=1/2 x -4 Line B y=2x-3 The slope of line a = 1/2 The slope of line b=2 The slope of line a =-4 The slope of line b =-3 the slope of a =-1/2 the slope of b =-2 The slope of line a =-3 the slope of line b =-4
Answer: 1/2 and 2
Step-by-step explanation:
The slope of a line, where the equation is in y=mx+b form, is m.
If you were told that the exchange rate between the U.S. dollar and the Canadian dollar was 1.2, that would mean that Canadians would have to spend ____ to buy a $12 watch in New York City. a. 10 U.S. dollars b. 18 Canadian dollars c. 14.4 U.S. dollars d. 12 U.S. dollars
Answer:
C.14.4
Step-by-step explanation:
Can someone please help Im failing , I also need the work . It’s trig
Answer:
what's the question pls?.......