Mathematics College

Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.
x + y - z = -2
2x - y + 3z = 9
x - 4y - 2z = 1

Answers

Answer 1

Answer:

x = 1 , y = - 1 , z = 2

Step-by-step explanation:

[tex]\begin{pmatrix}1&1&-1&-2\\ 2&-1&3&9\\ 1&-1&-2&1\end{pmatrix}\\\\\\= \begin{pmatrix}2&-1&3&9\\ 1&1&-1&-2\\ 1&-1&-2&1\end{pmatrix}[/tex]                          [tex][ \ swap \ R_1 \ and \ R_2 \ ][/tex]

[tex]=\begin{pmatrix}2&-1&3&9\\ 0&\frac{3}{2}&-\frac{5}{2}&-\frac{13}{2}\\ 1&-4&-2&1\end{pmatrix}[/tex]                        [tex][ \ R_2 = R_2 - \frac{1}{2} R_1 \ ][/tex]

[tex]=\begin{pmatrix}2&-1&3&9\\ 0&\frac{3}{2}&-\frac{5}{2}&-\frac{13}{2}\\ 0&-\frac{7}{2}&-\frac{7}{2}&-\frac{7}{2}\end{pmatrix}[/tex]                        [tex][ \ R_3 = R_3 - \frac{1}{2} R_1 \ ][/tex]

[tex]=\begin{pmatrix}2&-1&3&9\\ 0&-\frac{7}{2}&-\frac{7}{2}&-\frac{7}{2}\\ 0&\frac{3}{2}&-\frac{5}{2}&-\frac{13}{2}\end{pmatrix}[/tex]                      [tex][ \ swap \ R_2 \ and \ R_3 \ ][/tex]

[tex]=\begin{pmatrix}2&-1&3&9\\ 0&-\frac{7}{2}&-\frac{7}{2}&-\frac{7}{2}\\ 0&0&-4&-8\end{pmatrix}[/tex]                        [tex][ \ R_3 = R_3 + \frac{3}{7}R_2 \ ][/tex]

Therefore,

           [tex]-4z = - 8\\\\z = 2[/tex]

        [tex]-\frac{7}{2} y - \frac{7}{2}z = -\frac{7}{2}\\\\y + z = 1\\\\y + 2 = 1 \\\\y = 1 - 2 = - 1[/tex]

      [tex]2x - 1y + 3z = 9\\\\2x -1(-1) + 3(2) = 9\\\\2x + 1 + 6 = 9\\\\2x = 9 - 7\\\\2x = 2 \\\\x = 1[/tex]

Related Questions

Hello, please I bed urgent help with this math problem please

Answers

Answer:

option C

Step-by-step explanation:

[tex]4c^2 + 7c - 5 = 0 , \ where \ a = 4 , \ b = 7 , \ x = - 5[/tex]

[tex]c = \frac{- b \pm \sqrt{b^2 - 4ax }}{2a} \\\\c = \frac{- 7 \pm \sqrt{49 - ( 4 \times 4 \times - 5 )}}{2 \times 4} \\\\c = \frac{- 7 \pm \sqrt{49 + 80}}{8} \\\\c = \frac{- 7 \pm \sqrt{49 + 80}}{8} \\\\c = \frac{- 7 \pm \sqrt{129}}{8} \\\\[/tex]

Answer:

Option C

Step-by-step explanation:

Quadratic formula:

[tex]4c^{2} +7c-5=0[/tex]

[tex]a=4\\b=7\\x=-5[/tex]

[tex]c=\frac{-b\frac{+}{} \sqrt{b^2-4ax}}{2a}[/tex]

[tex]c=\frac{-7\frac{+}{}49-(4*4*-5) }{2*4}[/tex]

[tex]c=\frac{-7\frac{+}{}\sqrt{129} }{8}[/tex]

hope this helps....

please help. question in picture ​

Answers

Answer:

Step-by-step explanation:

cho tứ giác lồi ABCD và điểm S không thuộc mặt phẳng(ABCD). có bao nhiêu mặt phẳng qua S và hai trong số bốn điểmA B C D

Answers

Step-by-step explanation:

Có 7 mặt phẳng

5 mặt phẳng của hình chóp S.ABCD và (SAC), (SBD)

Cậu nên hỏi trên mấy web Việt Nam thì hơn tại đa số mấy người ở đây toàn nước ngoài ạ


In 8 days, a group of workers can plant 72 acres.
What is their rate in acres per day


Helppp fastttt

Answers

Answer:

Step-by-step explanation:

72/8 = 9 acres per day

9 x 8 = 72

So 9!




Hope this helps!

In grade 6, there are 40 students. There are 8 girls, find the percentage of the boys?

Answers

40 - 8 = 32
Therefore, there are 32 boys

(32/40)*100 = 80

Therefore, percentage of boys = 80%

Answer:

[tex]40 - 8 = 32 \\ \frac{32}{40} \times 100 \\ = 80\%[/tex]

Please answer question 4

Answers

Answer:

53

Step-by-step explanation:

how do i simplify 81^5 = 3x

Answers

Step-by-step explanation:

81/5=3x

x=81×1/5×3

x=81/15

Bill notes that his apple tree is 45 the size of his pear tree. His apple tree is 4 meters tall. How tall is the pear tree?

Answers

Answer:

11.25 m

Step-by-step explanation:

45 divide by 4

because the Apple tree is 45 the size of pear tree

Answer: 5

Step-by-step explanation:

David has available 240 yards of fencing and wishes to enclose a rectangular area.
(a) Express the area A of the rectangle as a function of the width W of the rectangle.
(b) For what value of W is the area largest?
(c) What is the maximum area?

Answers

Answer:

Below in bold.

Step-by-step explanation:

Perimeter = 2*width + 2*length

So

240 = 2w + 2l

120 = w + l

l = 120 - w

(a) Area = w*l

Substituting for l:

A = w(120 - w)

A = 120w - w^2

(b)

Finding the derivative:

A = 120w - w^2

A' = 120 - 2w

For a maximum area A' = 0, so:

120 - 2w = 0

2w = 120

w = 60 yards for maximum area.

(c)

Maximum area

= 120*60 - 60^2

= 3600 yd^2.

qual é a raiz quadrada de 84

Answers

9.16515138991 es la raíz cuadrada

The half life of Co-60 is 5.20 years. How many milligrams of a 1.00mg sample remains after 6.55 years

Answers

Answer:

For cobalt-60, which has a half-life of 5.27 years, 50% remains after 5.27 years (one half-life), 25% remains after 10.54 years (two half-lives), 12.5% remains after 15.81 years (three half-lives), and so on.

Step-by-step explanation:

You can figue out the rest.

What is the square root of 13?

Answers

Answer:

3.605551275

Step-by-step explanation:

What is the equation line of A?
What is the equation line of B?

Answers

Answer:

see below

Step-by-step explanation:

Line A is a horizontal line

It is of the form y = constant

y = 4

Line B is a vertical line

It is of the form x = constant

x = 8

A comet travels at an average speed of 273,000 km/h.
It takes 8 days for the comet to reach Earth.
Find the distance, in km, the comet travelled

Answers

Answer: 52,416,000 km

Step-by-step explanation:

If a comet travels 273,000 km/hr

1) Multiply 273,000 km by 24 hours to find how far the comet travels in one day

2) multiply the answer from 1 by 8 to determine how far it travels in 8 days

1) [tex]\frac{273,000 km}{hr}[/tex]*[tex]\frac{24 hr}{1 day}[/tex] = [tex]\frac{6,552,000km}{day}[/tex] (hours cancel out)

2)[tex]\frac{6,552,000km}{day}[/tex]*8 day= 52,416,000 km in 8 days

The comet approximately travelled 52,416,000km from when it began to travel to when it reached Earth. Hope this helped :)

Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)

Answers

Answer : 424.875 miles

The problem states that Brian can travel ‘27.5’ miles per gallon, and his tank can only hold ‘15.45’ gallons of fuel.

To find the miles he can travel, all you have to do is multiply the miles he can travel per gallon (27.5) by the gallons he has in the tank (15.45).

This gives you the answer of 424.875 miles.

Answer:

27.5 miles per gallon

1 full tank = 15.45 gallons

27.5 x 15.45 = 424.875 miles

rounded to the nearest 100th: 424.88 miles

nearest 10th: 424.9 miles

nearest whole #: 425 miles

Use the remainder theorem to find P(2) for P(x) = -x^3 + 4x^2 + 4

Answers

Answer:

12

Step-by-step explanation:

P(2)=-2³+4(2)²+4=-8+16+4=12

Which set of ordered pairs represent a function? O A {(1,0), (2,1), (2,3)} O B{(1,3), (1,4), (1,5)} O C{(1,5), (2,5), (3,5)} O D{(3, 1), (2, 2), (3, 3)}​

Answers

Answer:

C

Step-by-step explanation:

C is the only answer that doesnt share x-values

20 POINTS- Marlene surveyed her classmates asking them whether they prefer to vacation during spring break or summer and the type of vacation preferred. The results are shown in the table.
Marlene surveyed her classmates asking them whether they prefer to vacation during spring break or summer and the type of vacation preferred. The results are shown in the table.

A 4-column table with 5 rows titled Vacation Preferences. Column 1 has entries beach, big city, camping, skiing, total. Column 2 is labeled spring with entries 35, 7, 14, 4, 60. Column 3 is labeled summer with entries 10, 2, 8, 10, 30. Column 4 is labeled total with entries 45, 9, 22, 14, 90.

Complete each statments.
About ____% of the students surveyed prefer a spring camping vacation.
About ____% of the students surveyed prefer a big city vacation.

Answers

Answer:

The answers for edge 2021 is

Step-by-step explanation:

16 and 10

Create a number line to illustrate the following operations and find the solution.

Answers

Answer:

416

Step-by-step explanation:

26 times 16 is 416

how much greater is the volume of the refrigerator than the volume of the top part

Answers

Answer:

volume quantity is hjaj

Find the equation of the exponential function represented by the table below:
х
y
03
1
1
9
2 27
3
81

Answers

Answer:

$53.07

Step-by-step explanation:

Delta Math

Which expression is equivalent to
3V64k^12

Answers

Answer:

I think the answer is C

Step-by-step explanation:

Find the value of k, if (x - 2) is a factor of the polynomial p(x) = 2x2 + 3x - k​

Answers

Answer:

The value of k is 14.

Step-by-step explanation:

(x - 2) is a factor of the polynomial

[tex]x - 2 = 0 \rightarrow x = 2[/tex]

This means that [tex]p(2) = 0[/tex]

p(x) = 2x² + 3x - k​

[tex]p(2) = 2(2)^2 + 3(2) - k[/tex]

[tex]0 = 8 + 6 - k[/tex]

[tex]14 - k = 0[/tex]

[tex]k = 14[/tex]

The value of k is 14.

Find the greatest common factor of the
following monomials:
22x5
34x6

Answers

Answer:

22x5 = 1

34x6 = 2

Step-by-step explanation:

This might be the answer

Answer:

2x^5

Step-by-step explanation:what equals 22 is 2,11

what equals 34 equals 2,17 and 1,34 are the factors of 34x^6

The cost, in dollars, of a gym membership for n months can be described by the explicit equation Pn = 70 + 301. What does this equation tell us?​

Answers

Answer:

70 + 301 = 371

Step-by-step explanation:

This equation tells the gym

|x+2|+4=11
A) x=5,-9

Answers

Answer:

the mod always gives positive answers

so the answer will be

Step-by-step explanation:

x+2+4=11

x+6=11

x=11-6

x=5

answer is x is 5

Answer:

x=5,9

Step-by-step explanation:

|x+2|+4=11

|x+2| = 7

next you get two answers by adding two or subtracting two. SO the right answer should be 5 and 9. A is wrong . I DONT SEE THE OTHER ANSWER CHOICES BUT THIS IS WHAT I GOT.

if y=8, evaluate the following expression: 40-5y​

Answers

0
Explanation:
y = 8

40 - 5 x 8
40 - 40
= 0

Have a nice day

I need to find the value of x?

Answers

Answer:

x=20

Step-by-step explanation:

120=6x

120/6=6x/6

20=x

I’ll give brainliest to the first answer

Answers

Answer:

52

Step-by-step explanation:

4 1/2 x + 2x

Let x = 8

4 1/2 (8) + 2(8)

Change to an improper fraction

9/2(8) +2(8)

36+16

52

Slope is -1 and (3,2) is on the line

Answers

Y=Mx + c

Y=-x + c

To find c we replace the given points

2=-(3)+c

C=5

Final answer:

Y= -x+5

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