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3 years ago

Find the inverse of the matrix , if it exists

Mathematics

1 answer:

Montano1993 [528]3 years ago

8 0

Answer:

So, option A is correct.

Step-by-step explanation:

To find the inverse of the matrix, the formula is:

$A^{-1} = 1/|A| * Adj A$

Inverse of the matrix exists if |A| does not equal to 0

|A| = 7 * 9 -( -2 * -10)

|A| = 63 - 20

|A| = 43

AS |A| ≠ 0

so inverse exist.

now finding Adj A

$Adj A$ = $\left[\begin{array}{cc}9&2\\10&7\end{array}\right]$

$\left[\begin{array}{cc}9/43&2/43\\10/43&7/43\end{array}\right]$

So, option A is correct.

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Tai went hiking with his friends. The beginning of the hiking path has an

Scilla [17]

Answer:

the first hike is going down negative(low) second hike is going up so positive (high)

Step-by-step explanation:

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3 years ago

An instructor gives her class the choice to do 7 questions out of the 10 on an exam.

Maksim231197 [3]

Answer:

(a) 120 choices

(b) 110 choices

Step-by-step explanation:

The number of ways in which we can select k element from a group n elements is given by:

$nCk=\frac{n!}{k!(n-k)!}$

So, the number of ways in which a student can select the 7 questions from the 10 questions is calculated as:

$10C7=\frac{10!}{7!(10-7)!}=120$

Then each student have 120 possible choices.

On the other hand, if a student must answer at least 3 of the first 5 questions, we have the following cases:

1. A student select 3 questions from the first 5 questions and 4 questions from the last 5 questions. It means that the number of choices is given by:

$(5C3)(5C4)=\frac{5!}{3!(5-3)!}*\frac{5!}{4!(5-4)!}=50$

2. A student select 4 questions from the first 5 questions and 3 questions from the last 5 questions. It means that the number of choices is given by:

$(5C4)(5C3)=\frac{5!}{4!(5-4)!}*\frac{5!}{3!(5-3)!}=50$

3. A student select 5 questions from the first 5 questions and 2 questions from the last 5 questions. It means that the number of choices is given by:

$(5C5)(5C2)=\frac{5!}{5!(5-5)!}*\frac{5!}{2!(5-2)!}=10$

So, if a student must answer at least 3 of the first 5 questions, he/she have 110 choices. It is calculated as:

50 + 50 + 10 = 110

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3 years ago

I need heeeeeelp please and thank you :)

Citrus2011 [14]

The answer the the question is A.

5 0

2 years ago

Mr. Jones wants to place a chimney on his roof. It is recommended that the chimney be set at a height of at least 30 feet. The h

Tom [10]

Absolute value of any number is always positive because it represent distance and distance will always positive.

To place chimney at least 30 feet , the distance along the width of the roof (x) will be x = 17.5 feet or x = 2.5 feet.

Since, The height of the roof is described by the function f(x)=−4/3|x−10| + 40

Since, minimum height is 30 feet.

So , substitute f(x)=30 in above expression.

30=−4/3|x−10| + 40

4/3|x−10| = 10

|x−10|=30/4

|x−10| = 7.5

Taking positive case,

x−10 = 7.5

x = 17.5 feet

Taking negative case,

x−10 = - 7.5

x = 10 - 7.5

x = 2.5 feet

Learn more:

brainly.com/question/14473339

7 0

2 years ago

The original price of a shirt was $20. It was decreased to $15. What is the percent decrease of the price of this shirt?

KIM [24]

Answer:

25%

Step-by-step explanation:

Price reduction = 20 - 15 = $ 5

Percent decrease of price = (5/20)*100 = 5*5 = 25%

6 0

3 years ago