given that is a matrix with eigen pairs , and . find the matrix where . let , then , , ; , , ; , , .

The length of the diagonal of the square is d = 5√2.

Given that, the measure of the side of the square is 5.

We need to find the length of the diagonal of the square.

The diagonal of a square formula is d = a√2; where 'd' is the diagonal and 'a' is the side of the square.

Now, d = 5√2

Therefore, the length of the diagonal of the square is d = 5√2.

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Answer:

x = 65.26 degrees or x = 245.26 degrees.

Step-by-step explanation:

To solve the equation 4tan(x)-7=0 for 0<=x<360, we can first isolate the tangent term by adding 7 to both sides:

4tan(x) = 7

Then, we can divide both sides by 4 to get:

tan(x) = 7/4

Now, we need to find the values of x that satisfy this equation. We can use the inverse tangent function (also known as arctan or tan^-1) to do this. Taking the inverse tangent of both sides, we get:

x = tan^-1(7/4)

Using a calculator or a table of trigonometric values, we can find the value of arctan(7/4) to be approximately 65.26 degrees (remember to use the appropriate units, either degrees or radians).

However, we need to be careful here, because the tangent function has a period of 180 degrees (or pi radians), which means that it repeats every 180 degrees. Therefore, there are actually two solutions to this equation in the given domain of 0<=x<360: one in the first quadrant (0 to 90 degrees) and one in the third quadrant (180 to 270 degrees).

To find the solution in the first quadrant, we can simply use the value we just calculated:

x = 65.26 degrees (rounded to two decimal places)

To find the solution in the third quadrant, we can add 180 degrees to the first quadrant solution:

x = 65.26 + 180 = 245.26 degrees (rounded to two decimal places)

So the solutions to the equation 4tan(x)-7=0 for 0<=x<360 are:

x = 65.26 degrees or x = 245.26 degrees.

Since, P(male)*P(fail)= 0.33 and P(male and fail) = 0.33 , the two results are equal and independent.

What is Probability?

The possibility of outcome of any event is found by probability. as for an example whenever we toss a coin in the air, then what is the possibility that we get a head? Only based on possible outcomes we can answer this question. It is that part of events which deals with the results of random events. We can basically call it as prediction of any event that is based on study of previous record or the type and no of possible outcome.

Probability of happening of an event= Total no of favorable outcomes/                          Total no of outcomes

Here in this question;

P(male/fail)= P(male and fail)/P(fail)

                 = \(\frac{8/123}{(8+16)/123}\)

                 =\(\frac{8}{24} = \frac{1}{3} = 0.33\)

P(male) = \(\frac{33+8}{123} = \frac{41}{123} =\frac{1}{3} = 0.33\)

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Answer:

$20

Step-by-step explanation:

20% of 25 is 5

5 dollars off $25 is $20

Answer:

Carlotta needs 24 orange beads for her necklace.

Step-by-step explanation:

For each necklace, the ratio of blue beads to orange beads is 3 to 2. or 3:2

Total beads given to make a necklace is = 60

Let the number of orange beads be = x

The ratio is 2 orange beads out of 5 total beads

So, we can represent the ratio as:

x=24

Hence, Carlotta needs 24 orange beads for her necklace.

Blue beads needed =  

We can also check the ratio for blue beads to orange beads:

Divide by 4, we get

Divide by 3, we get

 ...... (the given ratio)

Therefore, Carlotta needs 24 orange beads for her necklace

Answer:

x = 0 , x = 2

Step-by-step explanation:

3x² = 6x ( subtract 6x from both sides )

3x² - 6x = 0 ← factor out 3x from each term

3x(x - 2) = 0

equate each factor to zero and solve for x

3x = 0 ⇒ x = 0

x - 2 = 0 ( add 2 to both sides )

x = 2

solutions are x = 0 , x = 2

Answer:

7) PQ = 46

8) QR = 46

9) PR = 92

Step-by-step explanation:

You are right on the first one (#5). Just make sure that the PQ and QR as drawn as equal. You can also represent this by drawing two short lines cutting PQ and QR which is the notation for equality of line segments.

You are right on #6. x is indeed 9

For #7, simply plug in the value of x in the equation 6x-8 which gives you

6 x 9 - 8 ==> 54 - 8 = 46

For #8 given that PQ = QR, QR must also be 46
If you wish you can verify by plugging in for x in 10x - 44 which evaluates to

10(9) - 44 = 90 -44 = 46

For #9 since PR = PQ + QR, just add the two values for PQ and QR giving 46 + 46 = 92

or, you could simply multiply any of the values by 2 giving 2 x 46 = 92

or,
you can add the two relations together and evaluate the result and plug in the value of x=9
(6x - 8) + (10x - 44) = 16x - 52 = 16(9) - 52 = 144 - 52 = 92

The quadratic regressiοn equatiοn fοr the given data pοints is y = 5x² - 20x + 7

A secοnd-degree equatiοn οf the fοrm ax² + bx + c = 0 is knοwn as a quadratic equatiοn in mathematics. Here, x is the variable, c is the cοnstant term, and a and b are the cοefficients.

Tο find the quadratic regressiοn equatiοn fοr the given data pοints, we need tο fit a quadratic equatiοn οf the fοrm y = ax² + bx + c tο the data.

We can start by using the three given pοints tο set up a system οf three equatiοns:

\((1,-8): a(1)^2 + b(1) + c = -8\\\\(2,-4): a(2)^2 + b(2) + c = -4\\\\(3,6): a(3)^2 + b(3) + c = 6\)

SimpIifying each equatiοn, we get:

a + b + c = -8 (equatiοn 1)

4a + 2b + c = -4 (equatiοn 2)

9a + 3b + c = 6 (equatiοn 3)

AIternativeIy, we can use technοIοgy such as a caIcuIatοr οr spreadsheet tο sοIve the system.

SοIving the system using technοIοgy, we get:

a = 5

b = -20

c = 7

Therefοre, the quadratic regressiοn equatiοn fοr the given data pοints is:

y = 5x² - 20x + 7

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Answer:

35%

Step-by-step explanation:

$28 less.

28 is 35% of 80. (28/80 = 0.35 which is 35%)

the percent markdown is 35%

Answer:

3

Step-by-step explanation:

-2=0+x

x¹=-2 (purple one)

4=2x-2

2x=6

x²=3 (green one)

Answer:

A and D

Step-by-step explanation:

The range, based on the solution, is between -2,147,483,648 and 2,147,483,647.

When the sample maximum as well as minimum are subtracted, the range of a collection of data seems to be the difference between the greatest and lowest values. It uses the same units as the data to express itself.

The distance between the greatest and smallest data sets in some kind of a set of numerical data is known as the range. The average of the greatest and smallest data points is the middle.

1 byte has 8 bits,

so 4 bytes have 32 bits.

Each bit can have 2 distinct states, so we have 2³² distinct combinations of bits (in 4 bytes) which correspond to 2³² distinct whole numbers.

Normally,

the range is 0 to 4,294,967,295 but if you want to allow negatives,

the range is -2,147,483,648 to 2,147,483,647

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Answer:

the answer is 19-2v combine like terms if not that then try this....

19-2y=0

-2y=-19

Then divide by -2

y=-19/-2

=9.5

Answer:

Cos 2theta = -3/5

Step-by-step explanation:

Given that;

tan theta = -2

tan theta = -2/1 = opp/adj

hyp^2 = (-2)^2+1^2

hyp = √4+1

hyp = √5

sin theta = opp/hyp

sin theta = -2/√5

Cos theta = adj/hyp

Cos theta = -2/√5

Cos 2theta = 1-2sin^2 theta

Cos 2theta = 1- 2(-2/√5)^2

Cos 2theta = 1- 2(4/5)

Cos 2theta = 1- 8/5

Cos 2theta = (5-8)/5

Cos 2theta = -3/5

Step-by-step explanation:

x > 5, both terms are positive

x < - 5, both terms are negative

This is not clear

If x>5

Hence..

If x<-5 terms are negative

If x=-5

Answer: A three-dimensional figure has a length, a width, and a height. A net is a two-dimensional pattern of a three-dimensional figure, that can be folded to form the figure. Identify the net that we could fold in order to create this 3D figure. Match the 3D figure to the right with its appropriate net, below.

Answer:

76ft^3

Step-by-step explanation:

Volume of a cube is Length x Width x Height, basically: 4 x 4 x 4 which is 64 ft^3. Add that to the small box gives you 64 + 12 or just 76 ft^3

Answer:

see below

Step-by-step explanation:

S+L = 22

L=2+3S

so S+2+3S =22

4S=22-2 = 20

S =5

L =17

Answer:

Step-by-step explanation:

Greetings from Brasil...

know that three-tenths = 0.3

then

0.3X = 15

3X/10 = 15

Answer:

see below

Step-by-step explanation:  5 23  8 03

the lenght of the longer leg of a right triangle is 9 ft longer than the lenght of the shorter leg x. The hypotenuse is 9 ft shorter than twice the lenght of the shorter leg.

shorter leg    = x

longer leg     = x + 9

hypotenuse  =  2x - 9

Pythagorean theorem  =    a² + b²  = c²

             shorter-leg² + longer-leg² = hypotenuse²

                         x²  +  (x+9)²  = (2x - 9)²                  solve for x

                  x² +  (x+9) (x+9)  =  (2x - 9)(2x - 9)

                 x² +  (x²+18x+81)  =  (4x² - 36x + 81)

                       (2x²+18x+81)  =  (4x² - 36x + 81)

                                          0 =   2x² -54x

                                          0 =  x(2x - 54)  

                           0 = x      and         0 = 2x -54  

                                                       54 = 2x

                                                      27 =  x

shorter leg    = 27        

longer leg     = 36

hypotenuse  =  45

divided all the values by 9 and you get a 3, 4, 5  right triangle, so the answer checks correct  

Answer:

Step-by-step explanation:

In this type of question , if the difference b/w the numerator and the denominator is 1 , then simply check the numerator . Whichever is big , it will be the larger .

In this question ,

           \(\frac{8}{9} \\\frac{7}{8} \\\\\)

here , we can see that 9 - 8 = 1  &  8 - 7 = 1

∵  8 > 7

∴   \(\frac{8}{9} > \frac{7}{8}\)

For common denominator , find its LCM : LCM(8,9) = 72

∴  Common denominator is 72 .

The total cost for X hours is the fixed cost of $15 plus the variable cost of $4 per hour which is equal to 4*X, so the total cost is 4*X + 15 

If Margie does not want to spend more than $27 then the inequality is 

4*X + 15 <= 27

4*X <= 12

X <= 3 

If Margie does not want to spend more than $27 then she cannot rent the bicycle for more than 3 hours 

Answer:

Step-by-step explanation:

let's every hour be x

first condition

therefore,

15

therefore

15+4x (as per our is x)

last condition

therefore,

15+4x≤27 (≤ is because as it says"does not want to spend more than $27"

few things about solving inequality

the direction of the inequality won't change

if

the direction of inequality will change

if

\(step - 1 \colon \: define\)

\(15 + 4x \leqslant 27\)

\(step - 2 \colon \: \\ subtract \:15 \: from \: both \: sides\)

\(15 - 15 + 4x \leqslant 27 - 15\)

\(4x \leqslant 12\)

\(step - 3 \colon \: \\ divide \: both \: sides \: by \: 4\)

\( \frac{4x}{4} \leqslant \frac{12}{4} \)

\(x \leqslant 3\)

\( \therefore \: she \: can \: rent \: the \: bicycle \: for \: 3 \: hours\)

Answer:

\(x=2\pm\sqrt{3}\)

\(y=\pm 2\sqrt{3}\)

Step-by-step explanation:

Since both equations are equal to y, you can set them equal to each other.

\(2x-4=(x-1)^2-5 \\\\\\2x-4=(x^2-2x+1)-4 \\\\\\2x-4=x^2-2x-3 \\\\\\x^2-4x+1=0 \\\\\\x=\dfrac{4\pm\sqrt{16-4}}{2}=\dfrac{4\pm2\sqrt{3}}{2}=2\pm\sqrt{3} \\\\\\y=2(2\pm\sqrt{3})-4=\pm 2\sqrt{3}\)

Hope this helps!

Answer:

x=5

Step-by-step explanation:

60+11x+13x =180° (sum of angles in a triangle )

60+24x=180

24x=180-60

24x=120

x=120/24

x=5

Therefore the angles are 60, 55, 65

Which shows that it is a scaleness triangle and an acute angle

The given information tells us that Terry's wins-to-races ratio is 2:3, but we cannot determine the exact number of races he has won without additional information about the total number of races he has participated in.

If the ratio of the number of times Terry has won to the number of races he has swum in is 2:3, we can set up a proportion to determine the number of races he has won.

Let's denote the number of times Terry has won as x, and the total number of races he has swum in as y. According to the given ratio, we have:

x/y = 2/3

To find the value of x, we need to solve for x when y is known. Since y represents the total number of races, we don't have that information in the given problem. Therefore, we cannot determine the exact number of races Terry has won without knowing the total number of races he has participated in.

The ratio tells us the relationship between the number of wins and the total number of races, but without knowing the denominator (total races), we cannot find a specific value for the numerator (number of wins). We can only determine the ratio between the two quantities.

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