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kobusy [5.1K]
3 years ago
15

Find the inverse of the matrices if they Exist. Use the algorithm introduced in the section. [1 0 -2 -3 1 4 2 -3 4]

Mathematics
1 answer:
KiRa [710]3 years ago
6 0

Answer:

\frac{1}{2} \left[\begin{array}{ccc}16&6&2\\20&8&2\\7&3&1\end{array}\right]

Step-by-step explanation:

Given is a matrix 3x3 as

\left[\begin{array}{ccc}1&0&2\\-3&1&4\\2&-3&4\end{array}\right]

|A| =2 hence inverse exists.

Cofactors are 16   20   7

                        6     8    3

                         2     2    1

Hence inverse =

\frac{1}{2} \left[\begin{array}{ccc}16&6&2\\20&8&2\\7&3&1\end{array}\right]

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Choose the correct simplification of the expression (d^3)^5
marin [14]

(d^3)^5 is equal to d^(3^5), which is equal to d^243.

6 0
3 years ago
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Julie, a police officer, has the following work pattern. She works 3 days, has 4 days off, then works 4 days, then has 3 days of
zalisa [80]

Answer:

See below.

Step-by-step explanation:

For each day number, Y means working, and N means off

Day

1   Y

2   Y

3   Y

4   N

5   N

6   N

7   N

8   Y

9   Y

10   Y

11   Y

12   N

13   N

14   N

15   Y

16   Y

17   Y

18   N

19   N

20   N

21   N

22   Y

23   Y

24   Y

25   Y

26   N

27   N

28   N

29   Y

30   Y

31   Y

32   N

33   N

34   N

35   N

36   Y

37   Y

38   Y

39   Y

40   N

41   N

42   N

43   Y

44   Y

45   Y

46   N

a. Today is day 1. 30 days from today is day 31.

She works on day 31, so she does work 30 days from today.

b. 45 days from today is day 46. She is off on day 46, so she will be off 45 days from today.

8 0
3 years ago
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Solve the equation by factoring. 8x^2+10x-7=0<br><br> What is the solution set?
nydimaria [60]

Answer:

\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}

Step-by-step explanation:

Given: 8x² + 10x - 7 = 0

<u>When factoring trinomials of the form ax² + bx + c</u>:

  • multiply the leading coefficient and the last term.
  • find the product factors that add to give you the coefficient of the middle term.
  • rewrite the polynomial with those factors replacing the middle term.

1. Split the middle term:

⇒ 8 × -7 = -56 [multiply the leading coefficient and the last term]

⇒ 14, -4 [find the product factors that add to the middle term's coefficient]

⇒ 8x² + 14x - 4x - 7 = 0 [rewrite with those factors replacing the middle term.]

2. Factor by grouping:

⇒ 8x² + 14x - 4x - 7 = 0 [factor out 2x]

⇒ 2x(4x + 7) - 4x - 7 = 0 [factor out -1 or the negative sign]

⇒ 2x(4x + 7) -1(4x + 7) = 0 [factor out 4x + 7]

⟹ (4x + 7)(2x - 1) = 0

3. Separate into 2 cases:

  1. 4x + 7 = 0
  2. 2x - 1 = 0

 

<u><em>Case 1:</em></u>

⇒ 4x + 7 = 0 [subtract 7 from both sides]

⇒ 4x + 7 - 7 = 0 - 7

⇒ 4x = -7 [divide both sides by 4]

⇒ 4x ÷ 4 = -7 ÷ 4

⟹ x = \bold{-\dfrac{7}{4}}

<u><em>Case 2:</em></u>

⇒ 2x - 1 = 0 [subtract 1 from both sides]

⇒ 2x - 1 + 1 = 0 + 1

⇒ 2x = 1 [divide both sides by 2]

⇒ 2x ÷ 2 = 1 ÷ 2

⟹ x = \bold{\dfrac{1}{2}}

Solutions:

\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}

Learn more about quadratic equations here:

brainly.com/question/27750885

brainly.com/question/27739892

brainly.com/question/27638369

7 0
2 years ago
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A chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people
Anastaziya [24]

Answer:

\frac{1}{4} lbs/person

Step-by-step explanation:

Here is the complete question: Find the rate of change for the situation:

A chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people.

Given: 1st situation, A chef cook 9 lbs chicken for 36 people.

           2nd situation, chef cook 17 lbs chicken for 68 people.

∴ 1st situation, weight of chicken per person= \frac{9\ lbs}{36\ person} = \frac{9}{36}

  Weight of chicken per person= \frac{1}{4} lbs/ person

2nd situation, weight of chicken per person= \frac{17\ lbs}{68\ person} = \frac{17}{68}

Weight of chicken per person= \frac{1}{4} lbs/ person

In both the situation chef cook same amount of chicken per person, which is \frac{1}{4} lbs/ person

∴ Rate of change is \frac{1}{4} lbs/ person

5 0
3 years ago
Will mark brainliest <br> Number 1 and 3
Keith_Richards [23]

Answer: Q1=20 Q2=39

Step-by-step explanation:

For question one all you have to do is multiply 20x35x8 giving you 5600. For question two just multiply 39x7x8 giving you 2184. Beat of luck.

8 0
2 years ago
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