(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

HELPPPPPPPPLSSSSS FASTTTUTS A TEST

Answers

Here, angle BGD is represent by 2.Here, the angle between BD and GD is 2. So, it is 2.

Hope you could get an idea from here.

Doubt clarification - use comment section.

Find the height of the trapezoid.
7 m
Area = 51 m2
10 m

Answers

The answer is 6

h = 2 A/a+b = 2 51/10+7 = 6

the lcm of 5 and 8 is??

Answers

The least common multiple of 5 and 8 is 40. This is because when you go by multiples of 5 and 8 the multiple that is the “smallest number” (LCM) of both numbers is 40. :)

Third-degree, with zeros of -4, -2, and 1, and a y-intercept of -11.

Answers

[tex]\begin{cases} x = -4\implies &x+4=0\\ x=-2\implies &x+2=0\\ x=1\implies &x-1=0 \end{cases}\qquad \implies (x+4)(x+2)(x-1)=\stackrel{y}{0}[/tex]

now, that's the equation or polynomial in factored form, hmmm we also know that it has a y-intercept of -11, namely, when x = 0  y = -11, well let's plug in a factor to it, that will reflect those values, namely say hmmm factor "a", so

[tex](x+4)(x+2)(x-1)=y\qquad \stackrel{\textit{adding "a" factor for vertical shift}}{a(x+4)(x+2)(x-1)}=y \\\\\\ \stackrel{\textit{we know that when x = 0, y = -11}}{a(0+4)(0+2)(0-1)=-11}\implies -8a=-11\implies a=\cfrac{-11}{-8}\implies a = \cfrac{11}{8} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\mathbb{FOIL}}{\cfrac{11}{8}(x^2+6x+8)}(x-1)=y\implies \cfrac{11}{8}(x^3+6x^2+8x-x^2-6x-8)=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{11}{8}(x^3+5x^2+2x-8)=y~\hfill[/tex]

An agent was able to sell a house and loth worth P2,300,000,00 if he was given a 5% commission.How much did he receive.
pls have solution :D​

Answers

Answer:

I am not sure what the P is.

2,300,000,00. X 5% = $115,000,000. Commission

Step-by-step explanation:

vnicn letter on the map indicates the location of the North China Plain?
AAA
o
О В
О С
OD
F

Answers

Answer:

The letter C

Step-by-step explanation:

North china plain runs along near the northern east border. It's territory has a noticeable river going through it, and is close to the Gulf of Jilin. A is most likely not correct, since North china plane doesn't go up that high the Yellow river. So it is safe to assume the answer is most likely C

The manager of a store increases the price of a popular product by 9​%. Let t be the original price of the product. The new price is t+0.09t. Write an equivalent expression by combining like terms. If the original price was ​$15.99​, estimate the new price by first rounding the original price to the nearest dollar.

Answers

Answer:

new equation : 1.09t = new price

Step-by-step explanation:

1.09(15.99) = 17.4291

it's about $17

Travis has hired Charlie and Dora to plant flowers. Dora can plant 150 flowers in the same time it takes Charlie to plant 120 flowers, which can be shown using the following relationship where d and c are the respective rates at which Dora and Charlie can plant flowers:

150 over d equals 120 over c

Also, Dora can plant 18 flowers more per day than Charlie.

How many flowers can Charlie plant per day?

Answers

Answer:

  72

Step-by-step explanation:

If the rates d and c are flowers per day, we have ...

  150/d = 120/c

  d -c = 18

__

Multiplying the first equation by cd/30, we have ...

  5c = 4d

Multiplying the second equation by 4 gives ...

  4d -4c = 72

Adding these equations together, we get ...

  5c +4d -4c = 4d +72

Simplifying and subtracting 4d leaves ...

  c = 72

Charlie can plant 72 flowers per day.

The midpoint M of ST has coordinates (5, 5). Point T has coordinates (9,5). Find the
coordinates of point S.

Answers

Answer:

5,5

Step-by-step explanation:

sin(83)cos(7) + cos(83)sin(7)

Answers

Answer:

1

Step-by-step explanation:

correct on edge

sin(83 radians) * cos(7 radians)) + (cos(83 radians) * sin(7 radians)) =

0.893996664

Answer:

hope it helps

List the pairs of congruent angles and the extended proportion that relates the corresponding sides for the similar polygons.

Answers

Answer:

<N=<T

<P=<Q

<O=<R

<M=<S

Step-by-step explanation:

they are in order since (N) is the first letter in one triangle then (T) has to be the corresponding angle.

(y-5)+0=(y-5)
Identify the property

Answers

Answer:

Identity property of addition

Step-by-step explanation:

I NEED MORE HELP PLZZ

Answers

Answer:

  1A: all real numbers

  1B: x = {-3, 0, +18}

  1C: (-3, 0) U [3, 18)

  2A: h(x) = -1/160x^2 +1/2x

  2B: focus: (40, -30); directrix: y = 50; axis of symmetry: x = 40

Step-by-step explanation:

1A:

The graph is attached. The domain is all real numbers.

__

1B:

The x-intercepts for x < 3 are the zeros of the quadratic:

  x^3 -9x = 0

  x(x^2 -9) = 0

  x(x +3)(x -3) = 0   ⇒   x = 0, -3, +3 . . . . x=3 is not in the domain of this piece

The x-intercepts for x ≥ 3 are the zeros of the log function:

  -log4(x -2) +2 = 0

  log4(x -2) = 2 . . . . . . add log4(x -2)

  x -2 = 4^2 . . . . . . . . . take the anti-log

  x = 2 +16 = 18 . . . . . . add 2

The x-intercepts of g(x) are x = {-3, 0, +18}.

__

1C:

The graph shows the function is positive on the intervals ...

  (-3, 0) U [3, 18)

__

2A:

The vertex of the curve is given as (40, 10). The vertical scale factor will make the function 0 at x=0.

  h(x) = a(x -40)^2 +10

  h(0) = 0 = a(-40)^2 +10 = 1600a +10

  a = -10/1600 = -1/160 = -1/(4·40)

The equation of the parabola is ...

  y = -1/(160)(x -40)^2 +10

In standard form, this is ...

  y = -1/160x^2 +1/2x

__

2B:

When we computed the leading coefficient (a) in Part A, we found it to be -1/(4·40). This corresponds to 1/(4p) where p=-40 is the focus to vertex distance. The negative sign means the focus is 40 units below the vertex, at (40, -30). The corresponding location of the directrix is 40 units above the vertex, at y=50.

Of course the axis of symmetry is the vertical line through the vertex: x = 40. These are shown in the second attachment.

Lamar is solving the equation x2−12x=−6 by completing the square. Which shows Lamar's next step and the solution to the equation?

Step 1: x^2 - 12x = -6

Step 2: x^2 - 12x + 36= -6 + 36

Answers

Completing the square is a process to find the solutions, or the x-values, to a quadratic equation. This method can only work if it is in the format: x^2 + bx = c
In this equation, the b value is -12 and the c value is -6. The process for completing the square goes like this:

x^2 + bx + (b/2)^2 = c + (b/2)^2

Now let’s solve the equation above using this method.

Step 1: x^2 - 12x + (-12/2)^2 = -6 + (-12/2)^2

Step 2: x^2 - 12x + (-6)^2 = -6 + (-6)^2

Step 3: x^2 - 12x + 36 = -6 + 36

Step 4: x^2 - 12x + 36 = 30

Now, to factor it. After doing the process until now, the left side of the equation can ALWAYS be in the format: (x + a)^2

Step 5: x^2 - 12x + 36 can be factored in this format as (x - 6)^2

Step 6: (x - 6)^2 = 30

Step 7: x - 6 = √30

Step 8: x = 6 ±√30

Q.

5! = ?

________________

Example :
4! = 4 × 3 × 2 × 1 = 24​

Answers

Answer:

5!=5*4*3*2*1=120

Step-by-step explanation:

n!=(n)(n-1)(n-2)...(3)(2)(1)

~Factorial

5!=5×4×3×2×1

=20×3×2×1

=60×2×1

=120×1

=120

help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast

Answers

Answer:

4

Step-by-step explanation:

The number in from of sin is the frequency

Answer:

4

Step-by-step explanation:

3. Twenty-five percent of Santa's elves
decorated the North Pole. If 150 elves
decorated, how many total elves live in
the North Pole?


Answers

600 elves

25% = 1/4
1/4 of the total = 150.
1/4 x 4 = 1 (total)
150 x 4 = 600
there are 600 elves

Prove the identity.
sin(x+y) / cosxcosy = tanx+tany

Answers

[tex]\dfrac{\sin(x+y)}{\cos x \cos y}\\\\\\=\dfrac{\sin x \cos y + \sin y \cos x}{\cos x \cos y}\\\\\\=\dfrac{\tfrac{\sin x \cos y}{\cos x \cos y} + \tfrac{\sin y \cos x}{\cos x \cos y}}{\tfrac{\cos x \cos y}{\cos x \cos y}}\\\\\\=\dfrac{\tan x + \tan y}1\\\\\\= \tan x + \tan y[/tex]

suppose Amaya wants to bake cookies that require 4.5 cups of flour for a recipe that makes 4 dozen cookies. how much flour would Amaya need to make 126 cookies?

Answers

Answer:

11.8125 cups of flour

Step-by-step explanation:

4 dozen = 48 cookies

126/48=2.625 batches of 48 cookies

2.625 x 4.5 = 11.8125 cups of flour




Help help help math math math

Answers

Answer:

1/4

Step-by-step explanation:

the x decreases by 1 the y decreases by 4

Answer:

-4

Step-by-step explanation:

Help help math math math

Answers

Answer:

10000

Step-by-step explanation:

you have four digits and each one of them can be 0-9, so 10 possibilities for each digit

10×10×10×10= 10,000

Answer:

160

Step-by-step explanation:

I believe the answer is 160 because it is a four-digit passcode, and 10 different numbers can be used ( 10 * 4 = 40, and 40 * 4 = 160).

It costs $6.50 per fidget popper. How much would it cost to get 8 fidget poppers.

Answers

Answer:

$52

Step-by-step explanation:

8*6.50

The factor that most heavily influences your credit score is
A. length of credit history
B. types of credit
C. amount owed
D. payment history

Answers

Answer:

D.payment history

Step-by-step explanation:

D:payment history because it shows your past credit history

A café has 60 tables. 35% of the tables have 2 chairs at each table. The remaining 65% of the tables have 4 chairs at each table. How many tables have 4 chairs?

Answers

The number of tables with 4 chairs are 39.

We have a café which has 60 tables. 35% of the tables have 2 chairs at each table. The remaining 65% of the tables have 4 chairs at each table.

We have to determine the number of tables having 4 chairs.

What is 10% of 250 ?

The 10% of 250 will be -

[tex]\frac{10}{100} \times 250[/tex] = 25

According to question, we have -

Percentage of tables with 2 chairs = 35%

Percentage of tables with 4 chairs = 65%

Total number of tables = 60

Therefore -

Number of tables with 2 chairs = [tex]\frac{35}{100} \times 60[/tex] = 21

Therefore, number of tables with 4 chairs will be = 60 - 21 = 39

Hence, the number of tables with 4 chairs are 39.

To solve more questions on Percentage, visit the link blow -

https://brainly.com/question/14196705

#SPJ2

There are 39 tables that have 4 chairs.

i.e. the number  of tables with 4 chairs is: 39.

Here, we have to find the number of tables that have 4 chairs, we first need to calculate how many tables have 2 chairs, and then subtract that number from the total number of tables.

Given that 35% of the tables have 2 chairs, we can calculate the number of tables with 2 chairs as follows:

Number of tables with 2 chairs = 35% of 60 tables

Number of tables with 2 chairs = 0.35 * 60

Number of tables with 2 chairs = 21 tables

Now, to find the number of tables with 4 chairs:

Number of tables with 4 chairs = Total number of tables - Number of tables with 2 chairs

Number of tables with 4 chairs = 60 tables - 21 tables

Number of tables with 4 chairs = 39 tables

So, there are 39 tables that have 4 chairs.

To learn more on percentage click:

brainly.com/question/13450942

#SPJ3

Potatoes are sold at $3.30 per 55 kg bag.
(a) Calculate the cost per kilogram.

(b) How much will 12 kg cost?

Answers

(a) $0.06 per kilogram
(b) $0.72 per 12 kg bag

Please look for the question in the picture.

Answers

Answer:

x = 8

Step-by-step explanation:

[tex]\frac{1}{4} x-\frac{3}{5} =1\frac{2}{5}[/tex]

[tex]\frac{1x}{4} -\frac{3}{5} =\frac{7}{5}[/tex]

[tex]\frac{1x}{4} =\frac{7}{5} +\frac{3}{5} \\[/tex]

[tex]\frac{1x}{4} =\frac{10}{5}[/tex]

Use cross multiplication.

[tex]5x=4*10[/tex]

[tex]5x=40[/tex]

[tex]\frac{5x}{5}=\frac{40}{5}[/tex]

[tex]x=8[/tex]

Hope this helps you.

Let me know if you have any other questions :-)

Hello There!

Question:-

[tex]\sf \longmapsto1/4x-3/5=1\dfrac{2}{5}[/tex]

We need to find the value of x.

Solution:-

Convert[tex] \dfrac{2}{5}[/tex] to improper fraction:-

[tex] \sf \longmapsto\dfrac{1}{4} x + \dfrac{ - 3}{5} = \dfrac{7}{5} [/tex]

Add 3/5 to both sides:-

[tex]\sf \longmapsto \: \dfrac{1}{4} x + \dfrac{ - 3}{5} + \red {\dfrac{3}{5}} = \dfrac{7}{5} + \red{\dfrac{3}{5}} [/tex]

On Simplification:-

[tex]\sf \longmapsto \: \dfrac{1}{4} x + \dfrac{ 3}{5} - \dfrac{3}{5} = \dfrac{7 + 3}{5} [/tex]

[tex]\sf \longmapsto \: \dfrac{1}{4} x - 0 = \cancel \dfrac{10}{5} [/tex]

[tex]\sf \longmapsto \dfrac{1}{4} x = 2[/tex]

Multiply both sides by 4 :-

[tex]\sf \longmapsto \: \red4 \times \bigg( \dfrac{1}{4} x \bigg) = \red 4 \times 2[/tex]

On Simplification:-

[tex]\sf \longmapsto \: \cancel 4 \times \dfrac{1}{ \cancel4}x = 4 \times 2[/tex]

[tex]\sf \longmapsto \: x = 8[/tex]

______________________________________

Henceforth,The value of x is :-

[tex] \boxed{ \huge\bf \: x = 8}[/tex]

________________________________

Please let me know if you have any questions.

~MisterBrian

Write an equation of the line passes through (4,1) and is parallel to y=-2x+7 .

Answers

Answer:

y= -2x+9

Step-by-step explanation:

First of all, since they need to be parallel, they must have the same slope to never intercept. Next, you can use a graphing calculator to test y-intercepts like desmos. You will find that 9 works, as it goes through (4,1) and never intercepts with the 1st line.

prove the identity.
(1-sin^2x)tanx=cosxsinx
Note that each Statement must be based on a Rule

Answers

[tex](1-\sin^2 x) \tan x \\\\=\cos^2 x \cdot \dfrac{\sin x}{\cos x}\\\\=\cos x \sin x[/tex]

(3x(3)+9X(2)+27X)/3X

Answers

3x | 3x^3+9x^2+27x |x^2+3x+9x

- 3x^3

-------

9x^2

- 9x^2

---------

27x

- 27x

--------

0

Answer:

x^2 + 3x + 9x

Hope you could get an idea from here.

Doubt clarification - use comment section.

The perimeter of a rectangle is 39.2 km, and its diagonal length is 14 km.
Find its length and width

Answers

Using the formulas to find its length =

P= 2 ( l + w )

d= w² + l²

There are 2 solutions for,

l = P / 4 + 1 / 4 √8d² - p²

= 39.2 / 4 + 1 / 4 × √8 × 14² - 39²

= 11. 2 km answer.

Using the formula to find its width =

w = p / 2 - l

= 39.2 / 2 - 11.2

= 8.4 km answer.

≈ the length of a rectangle is 11.2 km and the width is 8.4 km

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