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2 years ago

Find the solution set of the inequality: -3x + 8 < 15−3x+8<15

Mathematics

1 answer:

makkiz [27]2 years ago

3 0

Answer:

x=(8/3, infinity)

Step-by-step explanation:

-3x+8<15-3x+8

-3x+8<-3x+23

8<23

15-3x+8<15

23-3x<15

-3x<-8

x>8/3

Therefore, x=(8/3, infinity)

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For a random sample of 50 measurements on the breaking strength of cotton threads, the mean breaking strength was found to be 21

Vikentia [17]

Answer:

205.81 to 214.19

Step-by-step explanation:

Sample size (n) = 50

Sample mean weight (X) = 210 grams

Sample standard deviation (s) = 18 grams

Confidence coefficient (Z) at 90% = 1.645

The confidence interval for the true mean breaking strength of cotton threads of this type, at a 90% confidence level, is given by:

$CI=X \pm Z*\frac{s}{\sqrt n}\\CI=210 \pm 1.645*\frac{18}{\sqrt 50}\\CI = 210 \pm 4.19\\CI =205.81\ to\ 214.19$

The confidence interval is 205.81 grams to 214.19 grams.

6 0

3 years ago

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KonstantinChe [14]

Answer:

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5 0

2 years ago

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:

Swapping two rows
Multiplying a row by a nonzero number
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

Does the line passing through the points (−1,−5) and (2,1) intersect the line passing through the points (−1,−6) and (1,2)?

Serggg [28]

Answer:

Yes

Step-by-step explanation:

As long as the slopes of these two lines are not the same, they will intersect.

Given two points on a line, we can find the slope by taking the difference in the y coordinates and dividing it by the difference in the x coordinates.

Slope of 1st line: $\frac{-5-1}{-1-2} =\frac{-6}{-3} =\frac{1}{2}$

Slope of 2nd line: $\frac{-6-2}{-1-1} =\frac{-8}{-2}=4$

The slopes are not equal, therefore the lines intersect.

5 0

2 years ago

Multiply these polynomials.

maksim [4K]

When we multiply the polynomials we will get:
(5x^2+2x)(3x^2-7x+4)
=5x^2(3x^2-7x+4)+2x(3x^2-7x+4)
=15x^4-35x^3+20x^2+6x^3-14x^2+8x
=15x^4+(6x^3-35x^3)+(20x^2-14x^2)+8x
=15x^4-29x^3+6x^2+8x
The correct answer is C

4 0

3 years ago