if 2 is added to denominator and nemerator it becomes 9/10 and 3 is substracted from nemerator and denominator it becomes 4/5 find the fraction​

Given:

The matrix is:

[tex]A=\begin{bmatrix}\cos x&-\sin x\\\sin x&\cos x\end{bmatrix}[/tex]

To show:

[tex](A^{-1})^{-1}=A[/tex]

Solution:

If a matrix is:

[tex]M=\begin{bmatrix}a&b\\c&d\end{bmatrix}[/tex]

Then,

[tex]M^{-1}=\dfrac{1}{ad-bc}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}[/tex]

We have,

[tex]A=\begin{bmatrix}\cos x&-\sin x\\\sin x&\cos x\end{bmatrix}[/tex]

Using the above formula, we get

[tex]A^{-1}=\dfrac{1}{(\cos x)(\cos x)-(-\sin x)(\sin x)}\begin{bmatrix}\cos x&\sin x\\-\sin x&\cos x\end{bmatrix}[/tex]

[tex]A^{-1}=\dfrac{1}{\cos^2x+\sin^2x}\begin{bmatrix}\cos x&\sin x\\-\sin x&\cos x\end{bmatrix}[/tex]

[tex]A^{-1}=\dfrac{1}{1}\begin{bmatrix}\cos x&\sin x\\-\sin x&\cos x\end{bmatrix}[/tex]

[tex]A^{-1}=\begin{bmatrix}\cos x&\sin x\\-\sin x&\cos x\end{bmatrix}[/tex]

Now, the inverse of [tex]A^{-1}[/tex] is:

[tex](A^{-1})^{-1}=\dfrac{1}{(\cos x)(\cos x)-(\sin x)(-\sin x)}\begin{bmatrix}\cos x&-\sin x\\\sin x&\cos x\end{bmatrix}[/tex]

[tex](A^{-1})^{-1}=\dfrac{1}{\cos^2x+\sin^2x}\begin{bmatrix}\cos x&-\sin x\\\sin x&\cos x\end{bmatrix}[/tex]

[tex](A^{-1})^{-1}=\dfrac{1}{1}A[/tex]

[tex](A^{-1})^{-1}=A[/tex]

Hence proved.

Answer:

15.87 %

Step-by-step explanation:

z = (.9-1)/.1 = -1

z score of -1 = .1587

The probability that a randomly selected small size package has a weight of less than 0.9 pounds is 15.87 %

We have given that,

A store sells ground meat in small, medium, and large sizes. The weights of the small size packages have a mean weight of 1 pound and a standard deviation of 0.1 pounds. If the distribution of weights for the small-size packages of ground meat is approximately normally distributed

[tex]Z = \frac{x - \mu}{\sigma}[/tex]

Z = standard score

x = observed value

[tex]\mu[/tex] = mean of the sample

[tex]\sigma[/tex] = standard deviation of the sample

z = (0.9-1)/0.1 = -1

z of -1 = 0.1587

Therefore the value of the z-score is 0.1587.

To learn more about the Z-score visit:

https://brainly.com/question/25638875

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Answer:

D.

Step-by-step explanation:

.

Step-by-step explanation:

— If the arc AB has length 3.2 cm, calculate (a) the length of the radius, (b) ... the length of the radius, (b) the length of the arc BC. r 0.8 rad С o r A .

Answer:

a) ∠ADB is 55°

b) ∠ABD is 45°

Step-by-step explanation:

a) In the cyclic quadrilateral ABCD, we have;

Segment AB = Segment BC

∠ABC = 70°

Therefore, ∠ADC = 180° - 70° = 110° (Opposite angles are supplementary)

∠ADC + ∠CDP = 180° (Sum of angles on a straight line)

∴ ∠CDP = 180° - ∠ADC

∠CDP = 180° - 110° = 70°

∠DCP = 180° - 70° - 30° = 80°, (Angle sum property)

Similar to ∠DCP = ∠DAB = 80° (Exterior angle of a cyclic quadrilateral)

∠CAB = ∠ACB = (180° - 70°)/2 = 55° (Base angles of isosceles triangle ΔABC)

∠ADB = ∠ACB = 55° (Inscribed angle of a circle subtended by the same chord)

∠ADB = 55°

b) ∠ABD = 180° - ∠DAB - ∠ADB

∴ ∠ABD = 180° - 55° - 80° = 45°

∠ABD = 45°

Answer:

Step-by-step explanation:

Answer:

The second one

Step-by-step explanation:

Obejctive: Real Wolrd Algebra.

X represent number of pound peaches sold and Y represent the total cost of the peaches. We can represent this as

[tex]y = 2x[/tex]

If someone sell something, they cant get negative profit from it, and if no one buy it, it doesnt mean that it will decrease the seller profit.

Using that knowledge, let go through each answer.

The first one is wrong, Real Numbers include negative numbers and you can't negatively sell something so that means you cant lose profit for not selling something( In some instances, you can but for this sake of the problem, you cant).

The second one is right It is possible that you dont sell nothing and gain no money from it. So y and xcan be zero. it also possible you sell something and get money from it.

The third one is wrong, it is possible that you sell something and get profit from it.

The fourth one is wrong, x can be any real number as long its greater than zero. Y can be any real number as long as it greater than zero, but it doesnt have to be a interger( counting number). What if you sell 1.3 pounds of peaches, you will get 2.6

Answer:

3124/999

Step-by-step explanation:

x = 3. 127 127 ....... -------------(I)

127 -----> 3 digits are repeating. so multiply both sides by 1000

(I)*1000             1000x = 3127.127127......

                                 x =       3.127127......        [Now subtract}

                           999x = 3124

x = 3124/999

Answer:

[tex]Probability = \frac{5}{36}[/tex]

Step-by-step explanation:

The samples are

{ ( 1 , 1) , ( 1 , 2 ) , ( 1 , 3 ) , ( 1 , 4 ) , ( 1 , 5) , ( 1 , 6 )

  ( 2 , 1 ) , ( 2  2 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 2 , 5 ) , ( 2 , 6 )

  ( 3 , 1 ) , ( 3 , 2 ) , ( 3 , 3 ) , ( 3 , 4 ) , ( 3 , 5 ) , ( 3 , 6 )

 ( 4 , 1 ) , ( 4 , 2 ) , ( 4 , 3 ) , ( 4 , 4 ) , ( 4 , 5 ) , ( 4 , 6 )

( 5 , 1 ) , ( 5 , 2 ) , ( 5 , 3 ) , ( 5 , 4 ) , ( 5 , 5 ) , ( 5 , 6 )

 ( 6 , 1 ) , ( 6 , 2 ) , ( 6 , 3 ) , ( 6 , 4 ) , ( 6 , 5 ) , ( 6 , 6 ) }

Total number of samples = 36

Samples with a sum of 8 = { ( 2 , 6 ) , ( 3 , 5 ) , ( 4 , 4 ) , ( 5 , 3 ) , ( 6 , 2 ) }

Total number of sample with sum 8 = 5

Therefore,

          [tex]Probability \ of \ sum \ of \ 8 = \frac{5}{36}[/tex]          

Answer:

[tex]A) - \frac{1}{4} + \frac{2}{3} \\ \frac{ - 3 + 8}{12} \\ = \frac{5}{12} [/tex]

[tex]B) \frac{1}{2} - \frac{3}{5} - \frac{1}{2} \\ \frac{5 - 6 - 5}{10} \\ = \frac{ - 6}{10} [/tex]

[tex]C) \frac{3}{4} of \frac{2}{9} \\ \frac{3}{4} \times \frac{2}{9} \\ \frac{6}{36} = \frac{1}{6} [/tex]

[tex]D) \frac{2}{5} \times \frac{7}{12} \\ = \frac{14}{60} = \frac{7}{30} [/tex]

Answer:

4 pounds

Step-by-step explanation:

take 20% off the original price. 20(0.20)= 4

So that's a discount of 4 pounds and the sale price is 16 pounds.

The savings is 4 pounds on 1 shirt.

Answer:

Step-by-step explanation:

Following is the sample space for all the possible outcomes when 2 standard 6-sided dice are rolled simultaneously:

1 2 3 4 5 6

1 1,1 1,2 1,3 1,4 1,5 1,6

2 2,1 2,2 2,3 2,4 2,5 2,6

3 3,1 3,2 3,4 3,4 3,5 3,6

4 4,1 4,2 4,3 4,4 4,5 4,6

5 5,1 5,2 5,3 5,4 5,5 5,6

6 6,1 6,2 6,3 6,4 6,5 6,6

Therefore the sample space for the multiplication of the two values in each possible outcome:

elements of the set are:

1*1=1

1*2=2

1*3=3

...........

2*1=2

2*2=4

2*3=6

.............

so on...

Therefore the complete set:

S={ 1, 2, 3, 4, 5, 6, 2, 4, 6, 8, 10, 12, 3, 6, 9, 12, 15, 18, 4, 8, 12, 16, 20, 24, 5, 10, 15, 20, 25, 30, 6, 12, 18, 24, 30, 36 }

9.75 ft is the answer

[tex]By \: Pythagoras \: Theorem, \\ \boxed{ {hyotenuse}^{2} = {base}^{2} + {height}^{2} } \\ \\ here \\ hypotenuse = 12ft \\ base = 7 ft\\ height = x\ \\ \\ \ {12}^{2} = {7}^{2} + {x}^{2} \\ \implies144 = 49 + {x}^{2} \\ \implies {x}^{2} = 144 - 49 \\ =95 \\ x = \sqrt{95 } \\ = 9.75 ft\\ \\ \\ [/tex]

Answer:

-28[tex]w^{2}[/tex]

Step-by-step explanation:

-24[tex]w^{2}[/tex] + (-4[tex]w^{2}[/tex]) =

a negative plus a negative is a negative.

if you owe me 24 dollars and then I loan you another 4 dollars then you are in the negative 28 dollars to me.

Both 'w' have same exponent, making them like terms

Answer:

37500

Step-by-step explanation:

3% of 1250000

That is (3/100)*1250000

The answer is 37500

Answer:

{2,3,4}

Step-by-step explanation:

The range are simply the f(x) values

The range are the x values

To get the x values, we simply get x from each f(x)

So we have;

1-2x = -3

1+ 3 = 2x

2x = 4

x = 4/2

x = 2

Secondly;

1-2x = -5

1 + 5 = 2x

2x = 6

x = 6/2

x = 3

lastly;

1-2x = -7

1 + 7 = 2x

2x = 8

x = 8/2

x = 4

So the domain values are;

{2,3,4}

Answer:

459270

Answer:

then why are you asking?

Step-by-step explanation:

okay

Answer:

-3 <x <-1

Step-by-step explanation:

|x + 2| < 1

There are two solutions, one positive and one negative ( remember to flip the inequality for the negative)

x+2 <1    and  x+2 > -1

Subtract 2 from each side

x+2-2 < 1-2  and  x+2-2 > -1-2

x < -1      and       x >-3

-3 <x <-1

Answer:

150 km

Step-by-step explanation:

Put the minutes into hours 120min is 2 hours.

Distance = speed * time

Distance = 75 * 2

Distance = 150

Answer:

150 kilometers

Step-by-step explanation:

if the bus is going 75 kilometers an hour and they traveled for 120 minutes (exactly 2 hours) then you would just multiply 75 by 2 to get 150 kilometers total.

Answer:

- Reflected over the x-axis  

- Compressed by a factor of 0.4.

- Translated 2 units left

Step-by-step explanation:

Given

[tex]y = \sqrt[3]{x}[/tex]

[tex]y' = -(0.4)\sqrt[3]{x-2}[/tex]

Required

The transformation from y to y'

First, y is reflected over the x-axis.

The transformation rule is:

[tex](x,y) \to (x,-y)[/tex]

So, we have:

[tex]y = \sqrt[3]{x}[/tex] becomes

[tex]y' = -\sqrt[3]{x}[/tex]

Next, it was compressed by a scale factor of 0.4

The rule is:

[tex]y' = k * y[/tex]

Where k is the scale factor (i.e. k = 0.4)

So, we have:

[tex]y' = 0.4 * -\sqrt[3]{x}[/tex]

[tex]y' = -(0.4)\sqrt[3]{x}[/tex]

Lastly, the function is translated 2 units left;

The rule is:

[tex](x,y) \to (x-2,y)[/tex]

So, we have:

[tex]y' = -(0.4)\sqrt[3]{x - 2}[/tex]

Answers:

-reflected over the x-axis

-translated 2 units right

-compressed by a factor of 0.4

Answer:

1: the number of years since 2008 2. t is greater than or equal to 0 3. negative values 4. continuous

Step-by-step explanation:

1. t usually represents time

2. t must be greater than 0 as you can not go backward in time

3. the range must be positive as you can not have negative bobcats

4. its continuous because its a quadratic equation

1. no. of bobcats since 2008

2. greater than equal to 0

3 negative values

4. discrete because no. of bobcats cannot be broken into fraction.

Point F

Point E

These lie in the second quadrant.

Answer:

sinA = ± [tex]\sqrt{1-cos^2A}[/tex]

Step-by-step explanation:

Using the Pythagorean identity

sin²A + cos²A = 1 ( subtract cos²A from both sides )

sin²A = 1 - cos²A ( take the square root of both sides )

sinA = ± [tex]\sqrt{1-cos^2A}[/tex]

Answer:

33 jóvenes prefieren el basquetbol.

Step-by-step explanation:

Hay 165 jóvenes.

De estos, 20% prefieren el basquetbol.

¿cuantos prefieren el basquetbol?

20% de 165, entonces:

[tex]20\% = \frac{20}{100} = 0.2[/tex]

[tex]0.2*165 = 33[/tex]

33 jóvenes prefieren el basquetbol.