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goblinko [34]
3 years ago
8

Let p: x < −3 Let q: x > 3 What is represented by p ∨ q?

Mathematics
1 answer:
I am Lyosha [343]3 years ago
7 0

Amphitrite1040Answer:

Amphitrite1040

Step-by-step explanation:

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Use Gaussian elimination to write each system in triangular form
Feliz [49]

Answer:

To see the steps to the diagonal form see the step-by-step explanation. The solution to the system is x =  -\frac{1}{9}, y= -\frac{1}{9}, z= \frac{4}{9} and w = \frac{7}{9}

Step-by-step explanation:

Gauss elimination method consists in reducing the matrix to a upper triangular one by using three different types of row operations (this is why the method is also called row reduction method). The three elementary row operations are:

  1. Swapping two rows
  2. Multiplying a row by a nonzero number
  3. Adding a multiple of one row to another row

To solve the system using the Gauss elimination method we need to write the augmented matrix of the system. For the given system, this matrix is:

\left[\begin{array}{cccc|c}1 & 1 & 1 & 1 & 1 \\1 & 1 & 0 & -1 & -1 \\-1 & 1 & 1 & 2 & 2 \\1 & 2 & -1 & 1 & 0\end{array}\right]

For this matrix we need to perform the following row operations:

  • R_2 - 1 R_1 \rightarrow R_2 (multiply 1 row by 1 and subtract it from 2 row)
  • R_3 + 1 R_1 \rightarrow R_3 (multiply 1 row by 1 and add it to 3 row)
  • R_4 - 1 R_1 \rightarrow R_4 (multiply 1 row by 1 and subtract it from 4 row)
  • R_2 \leftrightarrow R_3 (interchange the 2 and 3 rows)
  • R_2 / 2 \rightarrow R_2 (divide the 2 row by 2)
  • R_1 - 1 R_2 \rightarrow R_1 (multiply 2 row by 1 and subtract it from 1 row)
  • R_4 - 1 R_2 \rightarrow R_4 (multiply 2 row by 1 and subtract it from 4 row)
  • R_3 \cdot ( -1) \rightarrow R_3 (multiply the 3 row by -1)
  • R_2 - 1 R_3 \rightarrow R_2 (multiply 3 row by 1 and subtract it from 2 row)
  • R_4 + 3 R_3 \rightarrow R_4 (multiply 3 row by 3 and add it to 4 row)
  • R_4 / 4.5 \rightarrow R_4 (divide the 4 row by 4.5)

After this step, the system has an upper triangular form

The triangular matrix looks like:

\left[\begin{array}{cccc|c}1 & 0 & 0 & -0.5 & -0.5  \\0 & 1 & 0 & -0.5 & -0.5\\0 & 0 & 1 & 2 &  2 \\0 & 0 & 0 & 1 &  \frac{7}{9}\end{array}\right]

If you later perform the following operations you can find the solution to the system.

  • R_1 + 0.5 R_4 \rightarrow R_1 (multiply 4 row by 0.5 and add it to 1 row)
  • R_2 + 0.5 R_4 \rightarrow R_2 (multiply 4 row by 0.5 and add it to 2 row)
  • R_3 - 2 R_4 \rightarrow R_3(multiply 4 row by 2 and subtract it from 3 row)

After this operations, the matrix should look like:

\left[\begin{array}{cccc|c}1 & 0 & 0 & 0 & -\frac{1}{9}  \\0 & 1 & 0 & 0 &   -\frac{1}{9}\\0 & 0 & 1 & 0 &  \frac{4}{9} \\0 & 0 & 0 & 1 &  \frac{7}{9}\end{array}\right]

Thus, the solution is:

x =  -\frac{1}{9}, y= -\frac{1}{9}, z= \frac{4}{9} and w = \frac{7}{9}

7 0
3 years ago
Juanita is 13 years older than her cousin. The sum of their ages is no less than 103 years. Enter an inequality that can be used
Bond [772]
Please see below solution:

y = x + 13<span>
y + x ≥ 103
x + 13 + x ≥ 103
Inequality is:
2 x + 13 ≥ 103
2 x ≥ 103 - 13
2 x ≥ 90
x ≥ 90 : 2
x ≥ 45
<span>The youngest age Juanita`s cousin can be is 45.</span></span>

6 0
3 years ago
Lorenz total payment for his loan was $13,536.
Vera_Pavlovna [14]

Answer: $376

Step-by-step explanation:

Divide 13,536 by 36

13,536/36 = 376

6 0
3 years ago
Read 2 more answers
Pi x 36 - 16<br> Need help on this please answer appropriate.
Bad White [126]

Answer:

To do this question, we must first convert Pi to a decimal form, as shown below:

Pi = 3.14

So then our equation becomes:

3.14 x 36 - 16

We still need to remember PEMDAS.

Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.

So according to PEMDAS, we need to do 3.14 x 36, which equals 113.04

Now we have to do:

113.04 - 16 = 97.04

Our answer is 97.04

<u><em>Hope this helps - genius423</em></u>

4 0
3 years ago
Substitute a = 4, b = 1 and c = 5 into the expressions:<br> a + b - c
Soloha48 [4]

Answer:

a+b-c

4+1-5

5-5=0

THE ANSWER IS 0

3 0
2 years ago
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