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4 years ago

A is a 3x3 matrix with det(A) = 4. Find det(adj(A)).

Mathematics

1 answer:

iris [78.8K]4 years ago

8 0

Answer:

The value of det(adj(A)) is 16.

Step-by-step explanation:

It is given that A is a 3x3 matrix with det(A) = 4.

We need to find the value of det(adj(A)).

We have a formula

$det(adj(A))=(det(A))^{n-1}$

where, n is order of the square matrix.

Substitute det(A) = 4 and n=3 in the above formula.

$det(adj(A))=(4)^{3-1}$

$det(adj(A))=(4)^{2}$

$det(adj(A))=16$

Therefore, the value of det(adj(A)) is 16.

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What method would be best to use 53=4(x-3)^2-11

Veronika [31]

Answer:

x = 7 , -1

Step-by-step explanation:

<u>SOLUTION :-</u>

$4(x-3)^2-11 = 53$

Add 11 to both the sides.

$=> 4(x-3)^2-11+11=53+11$

$=> 4(x-3)^2 = 64$

Divide both the sides by 4.

$=> \frac{4(x-3)^2}{4} = \frac{64}{4}$

$=> (x-3)^2 = 16$

Root square both the sides.

$=> \sqrt{(x-3)^2} = \sqrt{16}$

$=> x-3 = +4 \; or -4$

Here , x will have two values -

1) $x-3 = 4$

$=> x = 4 + 3 = 7$

2) $x - 3 = -4$

$=> x = -4 + 3 = -1$

<u>VERIFICATION :-</u>

When x = 7 ,

$4(x-3)^2 - 11 = 4(7 - 3)^2 - 11$

$= 4 \times 4^2 - 11$

$= 4 \times 16 - 11$

$= 64 - 11$

$= 53$

When x = -1 ,

$4(x-3)^2 - 11 = 4(-1 - 3)^2 - 11$

$= 4 \times (-4)^2 - 11$

$= 4 \times 16 - 11$

$= 64 - 11$

$= 53$

7 0

3 years ago

Totally blanking on how medians work

Elis [28]

<h3>Answer: FC = 16</h3>

===============================================

The three medians of this triangle are:

These segments go from one vertex to the midpoint of the opposite side.

The median we'll focus on is PF.

The point C is the centroid of the triangle. It's where the three medians intersect. It turns out that C divides PF such that CF is twice as long as PC

In other words,

CF = 2*PC

This means,

PF = PC+CF .... segment addition postulate

PF = PC+2*PC ... replace CF with 2*PC

PF = 3*PC .... combine like terms

So the median PF is three times the length of its portion PC

We're told that PF = 24

We can then find the following:

PF = 3*PC

24 = 3*PC

3*PC = 24

PC = 24/3

PC = 8

Then we double this to get the length of CF

CF = 2*PC

CF = 2*8

CF = 16

This is the same as FC because the order of the endpoints don't matter when it comes to naming a segment.

The final answer is 16.

5 0

3 years ago

Find the percent of change from 48 people to 71 people. Round to the nearest tenth of a percent if necessary.

kondaur [170]

Step-by-step explanation:

Here, the number of people has beed increased.

→ Number of people increased = 71 - 48

→ Number of people increased = 23

$\to \% \: change = \left ( \dfrac{23}{71} \times 100 \right ) \: \% \\$

$\to \% \: change = \left ( \dfrac{2300}{71} \right ) \: \% \\$

$\red{ \to \% \: change = 32.39 \: \%} \\$

Therefore, percentage change is 32.39 %.

4 0

3 years ago

What is the domain in the graph

masya89 [10]

There isn’t a graph shown

4 0

3 years ago

The expression represents the cost of Janelle’s cell phone bill, where m represents the number of minutes of use. 0.05m + 12 Wha

inn [45]

Answer:

The constant in the expression is 12

Step-by-step explanation:

The constant of the expression is the value that is independent of the number of minutes Janelle uses. The expression can be written as :

f(m)=0.05m +12

Example if m is 1 or 2

f(1) = 0.05(1) +12 = 12.05

f(2= = 0.05*2 +12 =0.1 +12 = 12.1

The value 12 is the minimum price of the bill indepent of the consumption of minutes of Janelle. She will always be charged this value.

8 0

4 years ago

Read 2 more answers