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expeople1 [14]
3 years ago
9

Can someone please explain Linear Inequalities to me?​

Mathematics
2 answers:
Arisa [49]3 years ago
8 0

A linear inequality is similar to a linear equation ( y=2x+5) where there is a relation between 2 variables and when plotted on the graph it is always a straight line, taking the example given earlier, y=2x+5 when plotted on a graph would give us this line ( added as attachment), a linear equations or inequalities do not have a power above, like x^2+3x+9=y is not a linear equation as there is a power above 1, in this case 2 involved, coming to linear inequalities, only the '=' symbol is replaced with \geq, \leq,. so instead of y=2x+5, a linear <u>inequality</u> would be :-

y\leq 2x+5\\ y\geq 2x+5\\ y2x+5

Now all of these have seperate meanings, starting with the first one it states y is less than or equal to 2x+5, second is y is greater than or equal to 2x+5, third is y is less than 2x+5 and lastly the fourth is y is greater than 2x+5. All 4 of these inequalities are graphed on the graph similarly to the original equation ( y=2x+5) however shading the right area according to the inquality is important.

In the graphs attached below, there is a solid line for \leq,\geq but a dashed line for <,> this is because the value of y in the first 2 equations may be equal to 2x+5, it may be on the line or any where in the shaded regions, however in the second too it cannot be on the line but it can only be in the shaded region hence the line is dashed

I hope I made sense for you, let me know if anything confused it, i'll elaborate it further

Zarrin [17]3 years ago
6 0
Ok so an equation like y<_x+2 is not completely equal. a linear inequality is like that but just graphed, so basically a graphed unequal equation (<_ means equal to or greater) i hope this helped!
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Answer:

B i think

Step-by-step explanation:

i think its B because all the other ones don'e look right. hope its correct. :)

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3 years ago
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Solve for XX. Assume XX is a 2×22×2 matrix and II denotes the 2×22×2 identity matrix. Do not use decimal numbers in your answer.
sveticcg [70]

The question is incomplete. The complete question is as follows:

Solve for X. Assume X is a 2x2 matrix and I denotes the 2x2 identity matrix. Do not use decimal numbers in your answer. If there are fractions, leave them unevaluated.

\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]· X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right] =<em>I</em>.

First, we have to identify the matrix <em>I. </em>As it was said, the matrix is the identiy matrix, which means

<em>I</em> = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

So, \left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]· X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right] =  \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

Isolating the X, we have

X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]= \left[\begin{array}{cc}2&8\\-6&-9\end{array}\right] -  \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

Resolving:

X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]= \left[\begin{array}{ccc}2-1&8-0\\-6-0&-9-1\end{array}\right]

X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]=\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]

Now, we have a problem similar to A.X=B. To solve it and because we don't divide matrices, we do X=A⁻¹·B. In this case,

X=\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]⁻¹·\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]

Now, a matrix with index -1 is called Inverse Matrix and is calculated as: A . A⁻¹ = I.

So,

\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]·\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

9a - 3b = 1

7a - 6b = 0

9c - 3d = 0

7c - 6d = 1

Resolving these equations, we have a=\frac{2}{11}; b=\frac{7}{33}; c=\frac{-1}{11} and d=\frac{-3}{11}. Substituting:

X= \left[\begin{array}{ccc}\frac{2}{11} &\frac{-1}{11} \\\frac{7}{33}&\frac{-3}{11}  \end{array}\right]·\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]

Multiplying the matrices, we have

X=\left[\begin{array}{ccc}\frac{8}{11} &\frac{26}{11} \\\frac{39}{11}&\frac{198}{11}  \end{array}\right]

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Make 2 sets of data 8 numbers each between 1 and 25. Then calculate the median and IQR for each data set.
vlada-n [284]

The median of the data set will be 15.5. The data set is in between the 1 to 25.

<h3>What is median?</h3>

Median is such a number for the arranged data set in ascending or descending order, such that to its left and to its right belong the same number of observations.

The data set between the number is;

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25

The value of IQR for data set is;

First Quartile Q1 = 6.5

Second Quartile Q2 = 13

Third Quartile Q3 =19.5

The median of the data set is;

\rm Median= \frac{15+16}{2}  \\\\ Median= 15.5

Hence, the median of the data set will be 15.5.

To learn more about median refer:

brainly.com/question/21396105

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2 years ago
Suppose Mahkah makes a Native American lunch in a pot that is shaped like a right cylinder. If
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The pot can hold 5.23 quarts

Step-by-step explanation:

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Diameter of the pot = 8 in

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Height = 6 in

⇒ Volume of the pot = πr²h = 3.14 × 4² × 6

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  • Step 2: Convert inches to quarts.

1 in³ = 0.017316 liquid quarts

⇒ 301.44 in³ = 301.44 × 0.017316 = 5.23 quarts

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For the polynomial x5 – 2x6 + 3, which of these statement(s) is true? Select all that apply A. The polynomial is a trinomial. B.
Evgen [1.6K]

Answer:

A, B and D

Step-by-step explanation:

A. The polynomial is a trinomial.

A trinomial refers to a polynomial with three terms. This option is correct.

B. The degree of the polynomial is 6.

Degree refers to the highest power in the polynomial. This option is correct.

C. The leading coefficient is 1

This is false. The leading coefficient is the coefficient of the variable bearing  the degree of the polynomial. This is wrong.

D. Written in standard form, the polynomial is –2x6 + x5 + 3.

This is correct.

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3 years ago
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