Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with z arbitrary
Answers
Write each equation in standard form:
3x + y + 3z = 11
x + 2y + z = 7
-x + y + z = 0
In matrix form, this is
[tex]\begin{bmatrix}3&1&3\\1&2&1\\-1&1&1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}11\\7\\0\end{bmatrix}[/tex]
and in augmented matrix form,
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\1&2&1&7\\-1&1&1&0\end{bmatrix}\right][/tex]
Now for the row operations:
• Add row 1 to -3 (row 2), and add row 1 to 3 (row 3):
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&-5&0&-10\\0&4&6&11\end{bmatrix}\right][/tex]
• Multiply row 2 by -1/5:
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&4&6&11\end{bmatrix}\right][/tex]
• Add -4 (row 2) to row 3:
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&0&6&3\end{bmatrix}\right][/tex]
• Multiply row 3 by 1/6:
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]
• Add -1 (row 2) and -3 (row 3) to row 1:
[tex]\left[\begin{array}{ccc|c}3&0&0&\frac{15}2\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]
• Mutiply row 1 by 1/3:
[tex]\left[\begin{array}{ccc|c}1&0&0&\frac52\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]
Then the solution to the system is (x, y, z) = (5/2, 2, 1/2).
Related Questions
use elimination to solve the system for 4x + 7 y equals -14 + 8 x + 5 y equals 8 for x
Answers
9514 1404 393
Answer:
(x, y) = (3.5, -4)
Step-by-step explanation:
Elimination is easiest if one of the coefficients of a variable is a multiple of the other coefficient of the variable. Here, we have x-coefficients of 4 and 8, so it will be easiest to eliminate x.
Subtract the second equation from 2 times the first.
2(4x +7y) -(8x +5y) = 2(-14) -(8)
9y = -36 . . . . . simplify
y = -4 . . . . . . . divide by 9
4x +7(-4) = -14 . . . . substitute for y in the first equation
4x = 14 . . . . . . . add 28
x = 3.5 . . . . divide by 4
The solution is (x, y) = (3.5, -4).
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x=t−t−1, y=1+t2, t=1
Answers
Answer:
Step-by-step explanation:
First, I would find the point on the curve. By substituting t=1, I get (x, y). Next, I will try to eliminate the t and make a xy equation. In this case, the t's will cancel out in 'x=t-t-1" which wouldnt make this a curve. To find the equation of the tangent line, find the deretitave of the xy equation, and subsitute x in to find the slope at that point. Next, use point slope form to find the equation at the point.
What is the value of 3?
Answers
9514 1404 393
Answer:
3 ⇒ 12
Step-by-step explanation:
Apparently "a = b" in this case is used to mean f(a) = b. It appears as though the function is ...
f(x) = x(x+1)
Then f(3) = 3(3+1) = 3·4 = 12
_____
Additional comment
IMO this is a poor use of the equal sign, which should be reserved for situations where the left side expression has the same value as the right side expression.
Write an equivalent expression to 1/2 (2n+6).
Answers
Answer:
n+3
Step-by-step explanation:
1/2 × 2(n+3)=n +3
I hope this helps
Find x please explanation need it
Answers
(Cos 19)(21) = 19.9
Find the measure of the missing angles. WILL GIVE BRAINLIEST
Answers
This is because any line is equal to 180 degrees, we see that d is situated on a line that continues into another angle, the other angle is 90 degrees, so we minus 90 from 180, to get 90.
E = 99
E is situated on a line with the other angle F, F = 81 (see below) so we minus 81 from 180
F = 81
F is situated on a line, we minus it from the other angle situated on the same line, so we minus 99 from 180to get 81
Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.
Determine the area of the given parallelogram with length 11 and altitude five
Answers
9514 1404 393
Answer:
55 square units
Step-by-step explanation:
The area of a parallelogram is the product of base length and height:
A = bh
A = (11)(5) = 55 . . . area of the given parallelogram in square units
My flvs teacher said that she was asked to hold off on grading my assignment. She will give me a call back when when gets more information. Anyone have the same problem?
Answers
Answer:
yeah, teachers kinda suck
Your calculator is showing a result of 248.592.
What is this to the nearest whole number?
Answers
What is the slope of the line that contains these points? xxx 454545 494949 535353 575757 yyy 101010 555 000 -5−5minus, 5 slope:
Answers
Answer:
-5/4
Step-by-step explanation:
Given :
x : 45, 49, 53, 57
y : 10, 5, 0, - 5
The slope of the line :
Slope = Rise / Run
y2 = - 5, y1 = 10
x2 = 57, x1 = 45
Rise = y2 - y1 = - 5 - 10 = - 15
Run = x2 - x1 = 57 - 45 = 12
The slope = Rise / Run = - 15 / 12 = - 5/4
Answer:
-1
Step-by-step explanation:
i brought the answer correct
A map that was created
using a scale of 1 inch : 3 miles
shows a lake with an area of
18 square inches. What is the
actual area of the lake?
Answers
9514 1404 393
Answer:
162 mi²
Step-by-step explanation:
The area on the map is ...
18(1 in)²
Then the area on the ground will be ...
18(3 mi)² = 18·9 mi² = 162 mi²
Rationalize the denominator and simplify
Answers
Answer:
x² - √3x / x² - 3
Step-by-step explanation:
To Do :-
To rationalize the denominator .Solution :-
We need to rationalize ,
x/ x + √3Multiply numerator and denominator by x-√3 :-
x( x - √3 ) / ( x +√3)( x -√3) x² - √3x / (x)² - (√3)² x² - √3x / x² - 3If an orange seller bought 5 dozen oranges at the rate of tk.60 per four and sold them at the rate of tk50 per four,how much did he lose
Answers
Answer:
tk 30
Step-by-step explanation:
5 dozen = 5 * 12 = 60 oranges
12/4 = 3
total cost = 60 * 3 = tk.180
total sell = 50 * 3 = tk 150
total lose = 180 - 150 = tk 30
a yogurt shop offers 7 different flavors of frozen yogurt and 11 different toppings. How many choices are possible for a single serving of frozen yogurt with one topping
Answers
answer: 77
Step-by-step explanation:
7×11=77
sorry if I'm wrong
Answer:
fijatebie nl aperguntaa
Step-by-step explanation:
Salma invested $8000 in a fund for 6 years and was paid simple interest. The total interest that she received on the investment was $1400. As a percentage, what was the annual interest rate of her investment?
Answers
9514 1404 393
Answer:
about 2.917%
Step-by-step explanation:
The simple interest formula can be used. Fill in the known values and solve for the unknown.
I = Prt . . . . principal P invested at rate r for t years
1400 = 8000(r)(6)
r = 1400/48000 = 7/240 = 0.0291666...
Salma's interest rate was about 2.917% per year.
Please help out really need it !!
Answers
Answer:
use the area formula
Step-by-step explanation:
Answer:
rounded to the nearest tenth i think its 40
Add O used 6 cups of whole wheat flour and eggs we flower and ax cups of white flour in the recipe what is the equation that can be used to find the value of Y the total amount of flour that adult used in the recipe and what are the constraints and the values of X and Y
Answers
Answer:
6x+y
Step-by-step explanation:
Find the measure of the missing angles.
WILL GIVE BRAINLIEST
Answers
Answer:
<d = 90
<e = 46
<f = 134
Step-by-step explanation:
<d = 90 since it forms a straight line with a 90 degree angle
<e = 46 since they are vertical angles and vertical angles are equal
<f = 134 since it is a linear pair with 46 ( they add to 180) f+46 = 180
f = 180-46 f =
[tex]{\footnotesize{\bold{\textbf{\textsf{{\fcolorbox{brown}{gold}{~Brainliest~answer}}}}}}}[/tex]
See this attachment
Find the length of BC
A. 6.81
B. 7.64
C. 13.37
D. 29.44
Answers
Answer:
13.37 = BC
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = opp / hyp
cos 27 = BC / 15
15 cos 27 = BC
13.36509 = BC
Rounding to the nearest hundredth
13.37 = BC
I need help with the question below
Answers
Answer:
a: 1/12
b: 1/6
c: 1/2
d: 1/2
e: 1/12
f: 1/3
Step-by-step explanation:
Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.)
f(x) = 7/1+x a=2
Answers
If f(x) = 7/(1 + x), then
f (2) = 7/3
f '(x) = -7/(x + 1)² ==> f ' (2) = -7/9
f ''(x) = 14/(x + 1)³ ==> f '' (2) = 14/27
f '''(x) = -42/(x + 1)⁴ ==> f ''' (2) = -14/27
Then the Taylor series of f(x) about a = 2 is
7/3 + 1/1! (-7/9) (x - 2) + 1/2! (14/27) (x - 2)² + 1/3! (-14/27) (x - 2)³
= 7/3 - 7/9 (x - 2) + 7/27 (x - 2)² - 7/81 (x - 2)³
A quality control inspector has drawn a sample of 18 light bulbs from a recent production lot. If the number of defective bulbs is 1 or more, the lot fails inspection. Suppose 30% of the bulbs in the lot are defective.
Required:
What is the probability that the lot will pass inspection?
Answers
Answer:
0.0016 = 0.16% probability that the lot will pass inspection.
Step-by-step explanation:
For each bulb, there are only two possible outcomes. Either it is defective, or it is not. The probability of a bulb being defective is independent of any other bulb, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Sample of 18 light bulbs
This means that [tex]n = 18[/tex]
30% of the bulbs in the lot are defective.
This means that [tex]p = 0.3[/tex]
What is the probability that the lot will pass inspection?
It will pass inspection if there are no defective bulbs, that is, we have to find P(X = 0). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{18,0}.(0.3)^{0}.(0.7)^{18} = 0.0016[/tex]
0.0016 = 0.16% probability that the lot will pass inspection.
The figures to the right are similar. Compare the first figure to the second. Give the ratio of the perimeters and the ratio of the areas
(integer or a simplified fraction)
Thank you!
Answers
9514 1404 393
Answer:
perimeter: 3 : 4area: 9 : 16Step-by-step explanation:
The perimeter ratio smaller : larger is the same as the side length ratio.
18 : 24 = 3 : 4 . . . smaller : larger perimeter ratio
The area ratio is the square of this.
3^2 : 4^2 = 9 : 16 . . . smaller : larger area ratio
How does the function notation compare with the standard notation?
Answers
Use the drop-down menus to select answer.
Use the fraction bars and the expression provided to answer the questions.
Answers
Answer:
loser you called me a bad word so now I'm taking points
Step-by-step explanation:
Suppose you deposit $500 in a savings account where the interest earned is compounded
continuously at a rate of 10%. How many years will it take the balance in the account to reach
$8000 (round your answer to the nearest year)?
Answers
Plz help me find side x on the triangle
Answers
Answer:
x=71
Step-by-step explanation:
Since this is an isosceles triangle as indicated by the lines on the sides, the sides lengths are equal.
When the sides are equal, the base angles are equal
x=71
given f(x)=2x-4 and g(x)=x213, determine gf[x]]
Answers
Step-by-step explanation:
you have to substitute the function g(x) where there's x in the function f(x)
gf(x)=2(x213)-4
if that's x two thirteen then you can multiply the 2 outside the brackets by it
giving you a final answer of
gf(x)=426x-4
hope it helps and sorry if am wrong
write your answer in simplest radical form
Answers
Answer:
3 =f
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 60 = f/ sqrt(3)
sqrt(3) tan 60 = f
sqrt(3) * sqrt(3) = f
3 =f
How many of 320 million Americans would you predict wear contact lens
Answers
Answer:
I think 40 - 60 Million Americans would wear contact lenses.
