(8 pts)
7. Solve the following system using a matrix and converting the matrix to reduced row
echelon form, without introducing any fractions.
3x - 2y + 5z = -7
x – y + 3z = -5
4x + y + z = 6

Answers

Answer 1

Answer:

{x,y,z} = {-22/13,29/13,6/13} 

Answer 2

Write the system as the following augmented matrix:

[tex]\left[ \begin{array}{ccc|c} 3 & -2 & 5 & -7 \\ 1 & -1 & 3 & -5 \\ 4 & 1 & 1 & 6 \end{array} \right][/tex]

Swap rows 1 and 2 :

[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 3 & -5 \\ 3 & -2 & 5 & -7 \\ 4 & 1 & 1 & 6 \end{array} \right][/tex]

Eliminate the x coefficient from the last two rows by add -3 (row 1) to row 2, and -4 (row 1) to row 3 :

[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 3 & -5 \\ 0 & 1 & -4 & 8 \\ 0 & 5 & -11 & 26 \end{array} \right][/tex]

Eliminate the y coefficient from the first and last rows by adding row 2 to row 1, and -5 (row 2) to row 3 :

[tex]\left[ \begin{array}{ccc|c} 1 & 0 & -1 & 3 \\ 0 & 1 & -4 & 8 \\ 0 & 0 & 9 & -14 \end{array} \right][/tex]

Eliminate the z coefficient from the second row by adding 4 (row 3) to 9 (row 2) :

[tex]\left[ \begin{array}{ccc|c} 1 & 0 & -1 & 3 \\ 0 & 9 & 0 & 16 \\ 0 & 0 & 9 & -14 \end{array} \right][/tex]

Eliminate the z coefficient from the first row by adding row 3 to 9 (row 1) :

[tex]\left[ \begin{array}{ccc|c} 9 & 0 & 0 & 13 \\ 0 & 9 & 0 & 16 \\ 0 & 0 & 9 & -14 \end{array} \right][/tex]

Then the solution to the system is (x, y, z) such that

9x = 13 and 9y = 16 and 9z = -14

or

x = 13/9 and y = 16/9 and z = -14/9


Related Questions

Please help me with this question and how to break even!

Answers

Answer:

The blogger needs at least 189subscribers to break even

2
Which of the following is equal to 4
+31;
?
3
2
WIN
04 3
X 3.
1
14 2
X
3 7
14
X
72
3
42 2
X
3 31

Answers

Answer:

1428485748586384858858

I will give brainliest

Answers

Answer:

Equations 1 & 3 are correct.

Explanation:

Equation 2's actual answer is -8, and Equation 4's actual answer is positive 7.

Answer:

1 and 3 are correct

Step-by-step explanation:

i will give you brainly if help

Answers

Answer:

i think its D im not sure tho

Step-by-step explanation:

= Homework: Mo...
Ben bowled 122 and 188 in his first two games. What must he bowl in his third game to have an average of at least 160?
HOM

Answers

Answer:

i think its 195 but i am not for sure correct me if i am wrong

Step-by-step explanation:

it would 170
if you want to find the average of something you want to add up all the numbers and then divide that number by the amount of number there is
so for this i did (122+188+170)/3 which equals 160

Helpppp for a math exammm

Answers

Answer:

2. angle A is congruent to angle X

Step-by-step explanation:

Given f '(x) = (2 - x)(6 - x), determine the intervals on which f(x) is increasing or decreasing. (2 points)
Decreasing (-∞, 2); increasing on (6, ∞)
Decreasing (2, 6); increasing on (-∞, 2) U (6, ∞)
Decreasing (-∞, 2) U (6, ∞); increasing on (2, 6)
Increasing (-∞, -2) U (-6, ∞); increasing on (-2, -6)

Answers

Answer:

Decreasing (2, 6); increasing on (-∞, 2) U (6, ∞)

Step-by-step explanation:

To determine where [tex]f(x)[/tex] is increasing or decreasing, we set [tex]f'(x)=0[/tex] and check for the intervals.

We see that [tex]f'(x)=0[/tex] when either [tex]x=2[/tex] or [tex]x=6[/tex]. Therefore, we'll need to check the intervals [tex](-\infty,2)[/tex], [tex](2,6)[/tex], and [tex](6,\infty)[/tex]

For the interval [tex](\infty,2)[/tex], we can pick [tex]x=0[/tex] . This means that[tex]f'(0)=(2-0)(6-0)=(2)(6)=12>0[/tex], showing that [tex]f(x)[/tex] increases on the interval [tex](-\infty,2)[/tex]

For the interval [tex](2,6)[/tex], we can pick [tex]x=4[/tex]. This means that [tex]f'(4)=(2-4)(6-4)=(-2)(2)=-4<0[/tex], showing that [tex]f(x)[/tex] decreases on the interval [tex](2,6)[/tex]

For the interval [tex](6,\infty)[/tex], we can pick [tex]x=7[/tex]. This means that [tex]f'(7)=(2-7)(6-7)=(-5)(-1)=5>0[/tex], showing that [tex]f(x)[/tex] increases on the interval [tex](6,\infty)[/tex]

Therefore, [tex]f(x)[/tex] is increasing on [tex](-\infty,2)\cup(6,\infty)[/tex] and is decreasing on [tex](2,6)[/tex].

Which of the following integers is less than -23?
a) o
b) -13
c) 13
d) -25

Answers

Answer:

i think d) -25 is answer

Step-by-step explanation:

good luck

Answer:

d) -25

Step-by-step explanation:

Because -25 is less than -23 . as it is negative integers

Amare runs 1\10 mile in 2\3 minute. What is his speed in miles per minute? Show your work

Answers

Answer:

60

Step-by-step explanation:

will give brainliest due in 20 min

Answers

Answer:

25 is the area of ABCD

Step-by-step explanation:

5×5 = 25

Evaluate the expression: (–2)2 + (–42) + (18 – 23).

Answers

Hey there!

(-2)2 + (-42) + (18 - 23).

= -2(2) - 42 + 18 - 23

= -4 - 42 + 18 - 23

= -46 + 18 - 23

= -46 + (-5)

= -46 - 5

= -51

Therefore, your answer is: -51

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Which algebraic sentence means "a number x plus 2 is at most 25"?

Answers

Answer:

x + 2 [tex]\leq[/tex] 25

Step-by-step explanation:

The given algebraic sentence means is x + 2 ≤ 25

What is Mathematical inequalities?

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

ATQ

x + 2 ≤ 25

To learn more about inequalities from here

https://brainly.com/question/20383699

#SPJ2

Evaluate.

{3+[−5(2−4)÷2]}⋅3

−27
−13
18
24

Answers

2-4 is -2 and -5 times -2 is 10 divided by 2 is 5 and 5 +3 is 8. and 8 times 3 is 24. PEMDAS

Answer:

→24

Step-by-step explanation:

Evaluate: {3+[−5(2−4)÷2]}⋅3

= {3+[-5(2-4)÷2]}.3

= {3+[-5(-2)÷2]}.3

= {3+[10÷2]}.3

= {3+[10÷2]}.3

= {3+[10÷2]}.3

= {3+[10/2]}.3

= {3+[5]}.3

= {3+5}.3

= 8.3

= 8*3

= 24 Ans.

2) 13 years back my mother age was thrice my age and 2 years back she was twice my age then find a) The present age of my mother b) my present age​

Answers

Answer:

age of the Father is 46 and age of the son is 24

Step-by-step explanation:

13 years ago x was thrice y's age, or

(x - 13) = 3(y - 13); or

x - 3y = -26

2 years ago, x was twice y's age, or

(x - 2) = 2 (y - 2); or

x - 2y = -2

Subtracting equation 1 from 2:

x - 2y - (x - 3y) = -2 - (-26)

or y = 24

Help. How to solve this equation.

Answers

Step-by-step explanation:

x-8/2 = x-5/5

5(x-8) = 2(x-5)

5x-40 = 2x-10

3x= 30

x = 10

Answer:

x = 10

Step-by-step explanation:

[tex]\frac{x-8}{2}[/tex] = [tex]\frac{x-5}{5}[/tex] ( cross- multiply )

5(x - 8) = 2(x - 5) ← distribute parenthesis on both sides

5x - 40 = 2x - 10 ( subtract 2x from both sides )

3x - 40 = - 10 ( add 40 to both sides )

3x = 30 ( divide both sides by 3 )

x = 10

HELP ME! I WILL GIVE BRAINLIEST

Answers

Answer:

#1 matches with the pizza scenario

#2 matches with the present scenario

#3 matches with the Sarah scenario

Step-by-step explanation:

Look for keywords at the end of the questions and if they go hand and hand (such as in 7 hours / yield 20 servings) then they go together as a pair

Can y’all please help me answer this, this My last question

Answers

Answer:

x ft is the answer since X = 10

so it means 10 ft

Please help me
I don’t know what to do for this and it’s really confusing

Answers

Answer:

Midpoint: (0, 5/2) or (0, 2.5)

Step-by-step explanation:

The diagonal BD is made of the points B(4,7) and D(-4,-2)

to find the midpoint of these points you add the two x coordinates and divide by two --> (4+-4)/2=0/2=0

Then you add the y coordinates and divide by 2 --> (7+-2)/2=5/2 or 2.5

Then you've got your midpoint.

hopefully I've understood the question correctly - hope this helps!

Fill in the blanks so the left side of each is a perfect square trinomial. That it complete the square

x^ 2 -2x+?=(x-?)^ 2

the question mark are the empty boxes for the numbers

Answers

Answer:

1

Step-by-step explanation:

Look at the LHS: you have the square of x, then you have 2 times x, times -1. to complete a square you just need to add the square of -1, that is 1. That becomes

[tex]x^2-2x +1 = (x-1)^2[/tex]

Save You More offers a buy one/get one free item each week. Customers who purchase only one of the items must pay the regular
price. The limit is one deal per customer. Is the relation (# sale items purchased, price) a function? Why or why not?

A)
B
It is a function because the input can be either 1 or 2 items, but the output
will always be the same price.
It is not a function because the input can be either 1 or 2 items, but the
output will always be the same price.
It is a function because the input will always be the same price, but the
output can be either one or two items.
D
It is not a function because the input will always be the same price, but the
output can be either one or two items.

Answers

Answer:

It is a function because the input can be either 1 or 2 items, but the output

will always be the same price.

Step-by-step explanation:

Answer:

A. It is a function because the input can be either 1 or 2 items, but the output

will always be the same price.

Step by Step Explanation :

A function is for every single input but the output is always the same. So, let's make a scenario. If someone bought ' 1 ' then paid the marked cost and if you bought 2 then paid the marked cost BUT with " One Buy One Free. " So, it is in fact a function.

PLEASE HELP DUE RIGHT NOW!!!

Answers

Answer:

linear

Step-by-step explanation:

From a hot-air balloon, Mariana measures a 40° angle of depression to a landmark that's 1165 feet away, measuring horizontally. What's the balloon's vertical distance above the ground? Round your answer to the nearest hundredth of a foot if necessary.​

Answers

Here is the set up:

Let h = balloon's vertical distance.

sin(40°) = h/1165

sin(40°)(1165) = h

748.847565

748.85 feet = h

Done.

The balloon's vertical distance above the ground is 1388.40 feet to the nearest hundredth.

What is division?

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

From a hot-air balloon,

Mariana measures a 40° angle of depression to a landmark that's 1165 feet away, measuring horizontally.

Let h be the vertical distance.

Use tanθ = perpendicular / base

Here, perpendicular = 1165 feet and base = h and θ = 40°

Substituting the values,

tanθ = perpendicular / base

tan40° = 1165 / h

h = 1165 / tan40

h = 1165 /  0.839095

h = 1388.40059 feet.

h ≈ 1388.40 feet to the nearest hundredth.

Therefore, vertical distance is 1388.40 feet

To learn more about the division;

https://brainly.com/question/13263114

#SPJ5

Compare the decimal by writing <,> or = on the space provided.
1). 501.019_______501.901
2). 65.561________65.651
3). 0.2134________0.03124
4). 0.500_________0.5
5). 0.004_________0.0004







pa answer Po please ​

Answers

Answer:

1. <  2. < 3. > 4. = 5. >

Step-by-step explanation:

2 2/6 is equivalent to what?​

Answers

The answer is 2.3333333333

On which number line -9 and its opposite shown?

Answers

Answer:C TRUST MEEE

Step-by-step explanation:

mark as brainliest

A tiled floor measures 1 ⅔ by 2 ⅔ feet. What is the area of the floor?

Answers

let's firstly convert the mixed fractions to improper fractions and then multiply.

[tex]\stackrel{mixed}{1\frac{2}{3}}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}}~\hfill \stackrel{mixed}{2\frac{2}{3}}\implies \cfrac{2\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{8}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{3}\cdot \cfrac{8}{3}\implies \cfrac{40}{9}\implies 4\frac{4}{9}[/tex]

pls help im gonna fail geometry:(

(4 points) Given two lengths of a triangle 2.2 ft. and 3.2 ft. which inequality will give all the
possible lengths of the third side, s?
A 2.2 ft < s <3.2 ft tabclft < s < 5.4 ft
B 2.2 ft < s < 5.2 ft
1326

Answers

B for Benjamin Franklin

Answer:

its ether a or d

Step-by-step explanation:

ps (id like to tell you the exact answer but that would be considered plagerism and i dont want anyone to receive the consenquesnces of that. I hope you understand and that this helps you)

Please help for brainliest!!:)

Answers

Answer:

d)

Step-by-step explanation:

we know, that i = sqrt(-1)

so, i² = -1

i³ = -i

i⁴ = -i × i = - -1 = 1

i⁵ = i⁴×I = 1×i = i

and the cycle begins again for any higher exponents.

so, we find out what i^n is, by dividing n by 4 and look at the remainder.

remainder = 0, i^n = 1

remainder = 1, i^n = i

remainder = 2, i^n = -1

remainder = 3, i^n = -i

so, what is 139 in this regard ?

139 ÷ 4 = 34

remainder 3

so, i¹³⁹ = -i

a) 322 ÷ 4 = 80

remainder 2. not equivalent.

b) 304 ÷ 4 = 76

remainder 0. not equivalent.

c) 221 ÷ 4 = 55

remainder 1. not equivalent.

d) 239 ÷ 4 = 59

remainder 3. this IS equivalent.

I NEED HELP WITH THIS PLEASE HELP ME

Answers

Answer:

  1a: f(x) = x³ -6x² +9x -4

  1b: no breaks; the function is defined everywhere

  2a: (-∞, 5]

  2b: y = -3; y = -1

  2c: x → -∞, y → -3; x → ∞, y → -1

Step-by-step explanation:

1A:

The factored form of f(x) is ...

  f(x) = (x -4)(x -1)²

  f(x) = (x -4)(x² -2x +1) = x³ -2x² +x -4x² +8x -4

  f(x) = x³ -6x² +9x -4

__

1B:

The function h(x) is defined for all values of x to be either f(x) or g(x). The function f(x) is a polynomial function, so has no breaks in its domain. The function g(x) is defined for all values of x, so has no breaks in its domain.

There are no breaks in the domain of h(x).

__

2A:

See the attachment for a graph.

  -∞ < y ≤ 5 . . . . range of f(x)

__

2B:

The asymptote as x → -∞ is the asymptote of the exponential function. The exponential term has an asymptote of y=0, but shifting it down 3 units means the asymptote is 0 -3:

  x → -∞, y → -3 . . . . asymptote is y = -3

The asymptote as x → ∞ is the asymptote of the rational expression. That is the ratio of the leading terms: -x²/x² = -1.

  x → ∞, y → -1 . . . . asymptote is y = -1

__

2C:

See part B.

factorise the quadratic expression
pls help me I'll give brainliest
x²+8x-48​

Answers

[tex]x^2+8x-48\\\\=x^2 + 12x -4x -48\\\\=x(x+12) -4(x+12)\\\\=(x-4)(x+12)[/tex]

Other Questions
Answer all pleaseeeeee explain how political parties connect citizens to their government and provide examp real or made up. 2+2+4+6+9+2+4+5+7+0+10+3 In Super Mario Bros., you become Mario and your friend is Marios younger brother Luigi. Your job is to race through Mushroom Kingdom to save Princess Toadstool and avoid the enemy, Bowser. You can jump from and to different objects, picking up coins and other items to help you on your journey through the levels. What game genre (or combination of genres) best describes this game?A. strategy simulationB. action adventureC. RPGD. sports action If you are soaking wet and the water on your clothes evaporates, you will feel cold. Explain the cooling effect in the terms of kinetic theory. Jordan has a part-time job which pays $75 a week. He has already saved $55 toward the purchase of a $400could use to find the minimum number of weeks Jordan must work to have enough money to buy the iPhone. Write a poem about a motto What is the name of the agreement that established that the senate would have two members per state, and representation in the house of representatives would be based on population? Can anyone solve and explain part b Find the perimeter of both ( they have the same perimeter) Which of the following statements is true about the Yalta and Potsdam conferences?and if anyone knows the rest of the answers that'd be amazing!100 points! please answer quickly! Monarch butterflies have brightly colored orange wings with black patterns on them, making them easily visible to birds that eat butterflies and moths, yet birds rarely eat the monarchs. Likewise, the monarch caterpillars are brightly striped yellow and white and black, and they also are rarely eaten by birds, although some wasps will attack them and feed them to their young. What can be inferred from these observations? A. Monarchs must threaten and attack birds, but not wasps. B. Monarchs have a way of discouraging bird predation that does not involve hiding. C. Monarchs' wings are so colorful that most birds must find them difficult to eat. D. Monarchs lay more eggs than other less conspicuous butterflies. last one someone help please. The amount of milk in a carton is modeled by the equation y = 64 - 4x. The number of ounces of milk leftis represented by y. The number of servings of milk poured from the carton is represented by x.4.) How many ounces of milk are in an unopened carton? 5.) How many ounces of milk are in each serving? No links please. All of the following nations were represented at the Berlin conference except which one? a) Berlin b) Congo c) Portugal b) France A Code of Ethics is an organizational doctrine for public and private behavior.. true or false?? why was there a debate between the federal and state governments over the funding of transportation improvements? 1.Which expression is equivalent to 5(3x + 1)(x 2)(x 3)? what is a return message Pls answer this question Yesterday, 5/6 of the 120 students in a contest gave their speeches. How many students gave their speeches.