Some symbols and numbers are missing. I assume the system is supposed to read
2x - y + 2z + w = -3
x + 2y - 3z + w = 12
3x - y - z + 2w = 3
-2x + 3y + 2z - 3w = -3
In matrix form, this is
[tex]\begin{bmatrix}2&-1&2&1\\1&2&-3&1\\3&-1&-1&2\\-2&3&2&-3\end{bmatrix}\begin{bmatrix}x\\y\\z\\w\end{bmatrix}=\begin{bmatrix}-3\\12\\3\-3\end{bmatrix}[/tex]
which we can strip down to the augmented matrix,
[tex]\left[\begin{array}{cccc|c}2&-1&2&1&-3\\1&2&-3&1&12\\3&-1&-1&2&3\\-2&3&2&-3&-3\end{array}\right][/tex]
Now for the row operations:
• swap rows 1 and 2
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\2&-1&2&1&-3\\3&-1&-1&2&3\\-2&3&2&-3&-3\end{array}\right][/tex]
• add -2 (row 1) to row 2, -3 (row 1) to row 3, and 2 (row 1) to row 4
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&-7&8&-1&-33\\0&7&-4&-1&21\end{array}\right][/tex]
• add 7 (row 2) to -5 (row 3), and row 3 to row 4
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&16&-2&-24\\0&0&4&-2&-12\end{array}\right][/tex]
• multiply through rows 3 and 4 by 1/2
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&8&-1&-12\\0&0&2&-1&-6\end{array}\right][/tex]
• add -4 (row 4) to row 3
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&0&3&12\\0&0&2&-1&-6\end{array}\right][/tex]
• swap rows 3 and 4
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&-1&-6\\0&0&0&3&12\end{array}\right][/tex]
• multiply through row 4 by 1/3
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&-1&-6\\0&0&0&1&4\end{array}\right][/tex]
• add row 4 to row 3
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&0&-2\\0&0&0&1&4\end{array}\right][/tex]
• multiply through row 3 by 1/2
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]
• add -8 (row 3) and row 4 to row 2
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&0&0&-15\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]
• multiply through row 2 by -1/5
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&1&0&0&3\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]
• add -2 (row 2) and 3 (row 3) and -1 (row 4) to row 1
[tex]\left[\begin{array}{cccc|c}1&0&0&0&-1\\0&1&0&0&3\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]
Then the solution to the system is (x, y, z, w) = (-1, 3, -1, 4).
3/4 + 20 (2/5 x 4/7)
Answer:
i believe the answer is 5.3
Please help me, by completing this proof!
Answer:
Step-by-step explanation:
Statement Reasons
1). Line PQ is an angle bisector of ∠MPN D). Given
2). ∠MPQ ≅ ∠NPQ A). Definition of angle bisector
3). m∠MPQ = m∠NPQ F). Definition of congruent
angles.
4). m∠MPQ + m∠NPQ = m∠MPN C). Angle addition postulate
5). m∠MPQ + m∠MPQ = m∠MPN G). Substitution property of
equality
6). 2(m∠MPQ) = m∠MPN B). Distributive property
7). m∠MPQ = [tex]\frac{1}{2}(m\angle MPN)[/tex] E). Division property of equality
Help please! it’s due soon
Answer:
33. That means (A) can be any number and b times any number wilo get 0 so any numbr will do
34.It is wrong because if x equals 40 anything multiply that will be more than that and so isnt a good reasoning
I WILL GIVE BRAINLEST FAST PLEASE ANSWER THE QUESTION IN THE IMAGE
Answer:
Cannot be determined
Step-by-step explanation:
We only know one angle and we could only compare one set of sides.
We do not have enough information to determine if the triangles are similar
A research report claims that 20% of all individuals use Firefox to browse the web. A software company is trying to determine if the proportion of their users who use Firefox is significantly different from 0.2. In a sample of 200 of their users, 26 users stated that they used Firefox.
Required:
Using this data, conduct the appropriate hypothesis test using a 0.01 level of significance.
Answer:
Reject H0
Step-by-step explanation:
Z = -2.474873734
survey (positive) 26
n (total) 200
p 0.2
p /point est. 0.13
POPULATION(min) 4000
np >= 5 ? YES 40
n(1-p) >= 5 ? YES 160
Sample is valid
Confidence Level - "P" values
99% 2.58
Confidence Interval - "P" values
(0.0686 , 0.1914 )
Reference=0.2 Reject H0
1+9+40-40+40+10x2 equals what?
Answer:
70
Step-by-step explanation:
1+9+40-40+40+10*2
----------------------- 20
10+40-40+40+20
50 (-40+40 cancels out to 0) +20
50+20= 70
(Following PEMDAS)
Multiply, add, subtract.
if you were to instead go through it left to right, you would get 120, which is incorrect.
Find the minimum turning point of y = x^2 + x - 12
Answer:
(x+4)(x-3)
Step-by-step explanation:
x^2+x-12
=x^2+(4-3)x-12
=x^2+4x-3x-12
=x (x+4)-3 (x+4)
=(x+4)(x-3)
Answer:x=6
Step-by-step explanation:
Find the distance between (6,6) & (-6,2)
Round your answer to the nearest 100th
Answer:
65
Step-by-step explanation:
show your work and practic
given the recursive formula below, what are the first four terms of the sequence
Answer:
c
Step-by-step explanation:
The first four terms are 17, 15, 13, and 11.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(n):
f(1) = 17
f(n) = f(n - 1) - 2 if n > 1
Now,
The first term is 17.
The second term.
f(2) = f(2 - 1) - 2
= f(1) - 2
= 17 - 2
= 15
The third term.
= f(3 - 1) - 2
= f(2) - 2
= 15 - 2
= 13
The fourth term.
f(4) = f(4 - 1) - 2
= f(3) - 2
= 13 - 2
= 11
Thus,
The terms are 17, 15, 13, 11
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ2
Solve 7 ( x + 1 ) + 2 = 5x + 15
Answer:
x = 3
Step-by-step explanation:
7(x + 1) + 2 = 5x + 15
~Simplify left side
7x + 7 + 2 = 5x + 15
~Combine like terms
7x + 9 = 5x + 15
~Subtract 9 to both sides
7x = 5x + 6
~Subtract 5x to both sides
2x = 6
~Divide 2 to both sides
x = 3
Best of Luck!
Which expression is equivalent to the following complex fraction?
Answer:
The correct choice is option B. y+1/y-1
Step-by-step explanation:
Find the greatest number of students to whom 45 soccer balls and 60 tennis balls can be equally divided.
Answer:
15 studentsStep-by-step explanation:
Find GCF of 45 and 60:
45 = 3*3*560 = 2*2*3*5GCF(45,60) = 3*5 = 15
Find Greatest common multiple or GCF
[tex]\\ \sf\longmapsto 45=3\times 3\times 5[/tex]
[tex]\\ \sf\longmapsto 60=2\times 2\times 3\times 5[/tex]
Now
[tex]\\ \sf\longmapsto GCF=3\times 5=15[/tex]
please help brainliest to correct answer
Answer:
Question for number 3 is -3
Question for number 4 is 6
Step-by-step explanation:
Brainless please
a company has decreased the weight of its boxes of macaroni by 8 %. if the new weight of the box is 13.1ounces, what was the original weight of the box?
Answer:
실례합니다 ?
Step-by-step explanation:
이것이 무엇을 의미하는 질문입니까?
회사는 마카로니 상자의 무게를 8% 줄였습니다. 상자의 새 무게가 13.1온스인 경우 상자의 원래 무게는 얼마였습니까? 오른쪽 ?
Answer:
x*0.92 = 13.1
x = 14.24
Step-by-step explanation:
Х
30°
Calculate the size of angle x.
angle x =
I
If one Angle is = 30
And the other two angles are equal
Given: x = l
ATQ
⇒30+x+l= 180
⇒x + x = 180-30
⇒2x = 150
⇒x = 150/2
⇒x = 75
Therefore x = 75
And the angles are 30, 75 and 75
Must click thanks and mark brainliest
What is the range of the function in the graph?
Answer:
b=70
Step-by-step explanation:
The range is the value that the output takes
In this graph, the output is constant at 70
The output value is b
b=70
Kara ate 2 7/9 of the raisins she packed. Which box shows the decimal equivalent of the amount of raisins she ate? Box A: 2.777 etc Box B: 2.79 Box C: 2.999 etc.
Answer: Box A, 2.777
=======================================================
Explanation:
When using a calculator or long division, you should find that
7/9 = 0.7777...
where the 7s go on forever
So we can say that 7/9 = 0.777 approximately. You could argue that the last '7' would round up to an '8' and we could say 7/9 = 0.778; however, I'll stick to the first value so that it matches with the answer.
Since 7/9 = 0.777, this means 2 & 7/9 = 2 + 7/9 = 2 + 0.777 = 2.777 which is box A.
Answer:
A
Step-by-step explanation:
Please help me please! I really need it! Thank you so much!!!!!!!!!!! Sorry Quality is really bad
Answer:
7[tex]\frac{5}{6}[/tex]
Step-by-step explanation:
- 2[tex]\frac{1}{3}[/tex] - ( - 10[tex]\frac{1}{6}[/tex] ) = - 2[tex]\frac{1}{3}[/tex] + 10[tex]\frac{1}{6}[/tex] = - 2[tex]\frac{2}{6}[/tex] + 10[tex]\frac{1}{6}[/tex] = ( 10 - 2 ) + ( [tex]\frac{1}{6}[/tex] - [tex]\frac{2}{6}[/tex] ) = 8 - [tex]\frac{1}{6}[/tex] = 7 + ( [tex]\frac{6}{6}[/tex] - [tex]\frac{1}{6}[/tex] ) = 7[tex]\frac{5}{6}[/tex]
Which Expression is equivalent to -2(x + 6) 2x + (-12) 2x + 12 2x + 6
Answer:
-2x -8
Step-by-step explanation:
(a) If y varies directly as x, and y=24 when x=16, find y when x=12.
(b) In a formula, z varies inversely as P. If Z is 200 when P is 4, find z when P is 10.
Answer:
(a) 18
(b) 80
Step-by-step explanation:
(a) let y=kx
so, 24=16k
or, k=24/16 or, k=3/2
now, putting x=12
y=kx
or, y=(3/2)×12
or, y=3×12/2
or, y=36/2
or, y=18
(b) let P=k/z
so, 4=k/200
or, k=800
when P = 10
P=k/z
or, 10=800/z
or, z=800/10
or, z=80
Describe who is responsible for the cost and efficiency variances for direct materials, direct labor, and manufacturing overhead
Answer:
The materials price variance is usually the responsibility of the purchasing manager. The materials quantity and labor efficiency variances are usually the responsibility of production managers and supervisors.
What is the median to 17,19, 20, 21, 22, 25, 29, 30, 32, 35
Answer:
23.5
Step-by-step explanation:
The median is the middle value when the numbers are put in order from smallest to largest
17,19, 20, 21, 22, 25, 29, 30, 32, 35
There are 10 numbers
17,19, 20, 21, 22, 25, 29, 30, 32, 35
The middle is between 22 and 25
(22+25)/2 = 47/2 =23.5
Solve. Justify your responses. Given:a║b and c║d, m∠ 4=35° Find: m∠1, m∠2, and m∠3
Answer <1 = 145
< 2= 35
<3 = 35
PLS MARK BRAINLIESTSTEPS BELOWStep-by-step explanation:
<1 + <4 = 180 (supplementary since you can find corresponding side and straight angle)
<1 = 180-35
=145 degrees
<2 =<4 corresponding angles
<2 = 35 degrees
<3 = 35 degree (corresponding to <2)
Maximum and minimum value
Answer:
Maximum: 1
Minimum: -1
Step-by-step explanation:
To solve this, we can find the derivative of the function and then solve for when the derivative is equal to 0, finding the local maximum and minimum values in this function. Then, we can compare those points to the endpoints of the interval to find the maximum and minimum.
Using the Quotient Rule, we can say that
(f/g) ' = (f'g - fg')/(g²)
[tex]\frac{2x}{x^2+1}dx = \frac{\frac{d}{dx}(2x) * (x^2+1) - \frac{d}{dx} (x^2+1) * (2x) }{(x^2+1)^2} \\= \frac{2 *(x^2+1) - (2x)*(2x)}{(x^2+1)^2} \\[/tex]
Since we just need to solve for 0, we can disregard for the bottom part, resulting in
2(x²+1)-(2x)(2x) = 0
2x²+2-4x² = 0
2-2x² = 0
add 2x² to both sides to isolate the x² and its coefficient
2x² = 2
divide both sides by 2
x²=1
x = ±1
Therefore, we have 4 possible values for the maximum and minimum over this interval:
-2, -1, 0, 1
Trying each of these numbers into f(x),
f(-2) = -4/5
f(-1) = -2/2 = -1
f(0) = 0/1 = 0
f(1) = 2/2 = 1
Therefore, the maximum and minimum values of the function over the given interval are 1 and -1 respectively
An automobile manufacturer has given its car a 46.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 150 cars, they found a mean MPG of 46.5. Assume the population standard deviation is known to be 1.1. A level of significance of 0.05 will be used. State the null and alternative hypotheses.
Answer: See explanation
Step-by-step explanation:
The null hypothesis H0: The null hypothesis states that there is no relationship between the two things that are being considered.
The alternative hypothesis is contradictory to H0 and it explains that there is a relationship between the two selected variables.
Based on the question, the null hypothesis H0 is that the rating of car is equal to 46.7 miles per gallon. μ = 46.7 MPG
The alternative hypothesis Ha is that the rating of the car is not equal to 46.7 Miles per gallon. μ ≠ 46.7 MPG
r-(-4x - (y + y)); use x = -4, and y = -3 evaluate
Answer:
insert values of x and y
r - ( -4(-4) - ( -3-3))
r - ( 16 +6 )
r - 22
Doneeeeeeeeeeeeeeeeee3
A certain positive integer has exactly 20 positive divisors.
What is the largest number of primes that could divide the integer?
thx for the help in advance
9514 1404 393
Answer:
3
Step-by-step explanation:
20 has at most 3 proper factors greater than 1: 2×2×5. Each of these can represent a prime factor of the number of interest, and is 1 more than that prime's power. That is, the number of interest (n) will have at most 3 prime factors p, q, r, and will be ...
n = p·q·r^4
_____
For some prime factorization ...
[tex]\displaystyle n=\prod_{k=1}^m{p_k^{q_k}}[/tex]
The total number of divisors of n is ...
[tex]\displaystyle\prod_{k=1}^m{(q_k+1)}[/tex]
Find the measure of angle x in the figure below:
A triangle is shown. At the top vertex of the triangle is a horizontal line aligned to the base of the triangle. The angle formed between the horizontal line and the left edge of the triangle is shown as 57 degrees, the angle formed between the horizontal line and the right edge of the triangle is shown as 61 degrees. The angle at the top vertex of the triangle is labeled as y, and the interior angle on the right is labeled as 67 degrees. The interior angle on the left is labeled as x.
35°
47°
51°
62°
Your answer iss...
It is 51º
Write the quadratic function f(x) = x2 - 2x - 8 in factored form.
A) f(x) =(x - 4)(x - 2)
B) f(x) =(x + 4)(x - 2)
C) f(x) =(x - 4)(x + 2)
D) Rx) =(x + 4)(x + 2)
Answer:
Hello,
answer C
Step-by-step explanation:
[tex]f(x)=x^2+2x-8\\\\=x^2-4x+2x-8\\\\=x(x-4)+2(x-4)\\\\=(x-4)(x+2)\\\\Answer\ C[/tex]
12 workers take 4 hours to complete a job. How long would it take 15 workers to complete the job?
Answer:
3.75
Step-by-step explanation:
