1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Agata [3.3K]
3 years ago
5

Solve the following system of linear equations: 3x1+6x2+6x3 = -9 -2x1–3x2-3x3 = 3 If the system has infinitely many solutions, y

our answer may use expressions involving the parameters r, s, and t. O The system has at least one solution x1 = 0 x2 = 0 X3 = 0 O O
Mathematics
1 answer:
choli [55]3 years ago
6 0

Answer:

The set of solutions is \{\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}12\\-7-r\\r\end{array}\right]: \text{r is a real number}  \}

Step-by-step explanation:

The augmented matrix of the system is \left[\begin{array}{ccccc}3&6&6&-9\\-2&-3&-3&3\end{array}\right].

We will use rows operations for find the echelon form of the matrix.

  • In row 2 we subtract \frac{2}{3} from row 1. (R2- 2/3R1) and we obtain the matrix \left[\begin{array}{cccc}3&6&6&-9\\0&1&1&-7\end{array}\right]
  • We multiply the row 1 by \frac{1}{3}.

Now we solve for the unknown variables:

  • x_2+x_3=-7, x_2=-7-x_3
  • x_1+2x_2+2x_3=-2, x_1+2(-7-x_3)+2x_3=-2 then x_1=12

The system has a free variable, the the system has infinite solutions and the set of solutions is \{\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}12\\-7-r\\r\end{array}\right]: \text{r is a real number}  \}

You might be interested in
MAKE SURE TO SHOW YOUR WORK (please)
creativ13 [48]

Answer:

9.11 x 10^-28

Step-by-step explanation:

if you divide 9.11 x 10^-28 by 1.67 x 10^-24 you get .000546

if you divide 1.67 x 10^-24 by 9.11 x 10^-28 you get 1,833

therefore, 1.67 x 10^-24 is 1833 times greater than the other value

8 0
3 years ago
Read 2 more answers
How can the equation of a parabola be derived when given the focus and the directrix?
pickupchik [31]
The distance between any point (x0,y0) on the parabola and the focus (m,n) is the same as the distance between (x0,y0) and the directrix line ax+by+c. The distance between (x0,y0) and focus (a,b) is \sqrt((x-m)^2+(y-n)^2). The distance between (x0,y0) and ax+by+c is |ax0+by0+c|/\sqrt(m^2+n^2).  Equalize these two expressions.
4 0
3 years ago
Use the x-intercept method to find all real solutions of the equation.<br> x^3-8x^2+9x+18=0
meriva

Answer:

a. x=-1,3,\:or\:6

Step-by-step explanation:

The given equation is;

x^3-8x^2+9x+18=0

To solve by the x-intercept method we need to graph the corresponding function using a graphing calculator or software.

The corresponding function is

f(x)=x^3-8x^2+9x+18

The solution to x^3-8x^2+9x+18=0 is where the graph touches the x-axis.

We can see from the graph  that; the x-intercepts are;

(-1,0),(3,0) and (6,0).

Therefore the real solutions are:

x=-1,3,\:or\:6

8 0
3 years ago
Read 2 more answers
Four DVDs cost $84. If each DVD costs the same, how much does one DVD cost
nignag [31]

Answer:

one dvd costs $21

4 0
2 years ago
I need help solving polynomial in standard form​
tangare [24]

Step-by-step explanation:

standard form of

1 . = x⁴-2x ²+3

2. = 5m³- 3m²+ 9m -7

<em><u>plz</u></em><em><u> </u></em><em><u>mark</u></em><em><u> my</u></em><em><u> answer</u></em><em><u> as</u></em><em><u> brainlist</u></em><em><u> plzzzz</u></em><em><u> vote</u></em><em><u> me</u></em><em><u> also</u></em><em><u> </u></em><em><u>plzzzz</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u> Hope</u></em><em><u> this</u></em><em><u> will</u></em><em><u> be</u></em><em><u> helpful</u></em><em><u> for</u></em><em><u> you</u></em>

7 0
2 years ago
Other questions:
  • Similar triangles practice worksheet for problems 1-5 below identify if the triangles are similar or not
    14·1 answer
  • 12 picks in all . 1 out of 4 picks are orange . the rest are green . How many picks are orange ?
    5·1 answer
  • What is negative 65 times 5
    9·1 answer
  • Algebra question 2, Thanks if you help.
    8·1 answer
  • Anna makes 300 sandwiches for the company picnic. Half of the sandwiches are prepared with pimento cheese. Anna realizes that so
    12·2 answers
  • Find the mean of the picture below?
    15·1 answer
  • Write (4n^4)^2 without exponents
    9·1 answer
  • True or false: Two numbers are reciprocals of each other if they have different signs in front.
    10·2 answers
  • Write the product using exponents.<br> (-1/2)•(-1/2)•(-1/2)<br> Using exponents, the product is
    11·2 answers
  • Kim's softball team was playing in the championship game. When there were 444 innings left, the team was losing by a score of 17
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!