1. Sоlvе fоr X: -243 -9(10 + х)

To find the eigenvalues and eigenvectors of a 2x2 matrix, follow these steps:

Calculate the characteristic equation by subtracting the identity matrix I multiplied by the scalar λ from matrix A, and set the determinant of this resulting matrix equal to zero. The characteristic equation is given by det(A - λI) = 0.Solve the characteristic equation to find the eigenvalues (λ).

Let's assume we have a 2x2 matrix A:

  | a  b |

A = | c d |

To find the eigenvalues, we need to calculate the characteristic equation:

det(A - λI) = 0,

where I is the 2x2 identity matrix and λ is the eigenvalue.

A - λI = | a-λ b |

| c d-λ |

The determinant of this matrix is:

(a-λ)(d-λ) - bc = 0,

which simplifies to:

λ² - (a+d)λ + (ad - bc) = 0.

This quadratic equation gives us the eigenvalues.

Solve the quadratic equation to find the values of λ. The solutions will be the eigenvalues.

Once you have the eigenvalues, substitute each value back into the equation (A - λI)v = 0 and solve for v to find the corresponding eigenvectors.

For each eigenvalue, set up the homogeneous system of equations:

(A - λI)v = 0,

where v is the eigenvector.

Solve this system of equations to find the eigenvectors corresponding to each eigenvalue.

To find the eigenvalues and eigenvectors of a 2x2 matrix, follow the steps mentioned above. The characteristic equation gives the eigenvalues, and by solving the corresponding homogeneous system of equations, you can determine the eigenvectors.

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A particular plant root grows 2.5 inches per month.  The plant root is growing at a rate of 2.5 inches per month.

The given information states that the plant root grows at a rate of 2.5 inches per month. This means that for each month that passes, the length of the plant root increases by 2.5 inches.
The rate of growth per month indicates how much the plant root is extending in length within a specific time frame. In this case, the rate of growth is constant at 2.5 inches per month, implying that the plant root consistently adds 2.5 inches to its length every month.
This growth rate can be visualized as a linear relationship, where the length of the plant root increases by 2.5 inches for each unit of time (month) that passes. The consistent growth rate of 2.5 inches per month allows us to predict the future length of the plant root based on the number of months elapsed.

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The value of x when f(x) of 8 according to the graph is; 4.

In order to determine a point's coordinates in a coordinate system, you must do the opposite. Start at the point and move in a vertical line in either an upwards or downwards direction to the x-axis. Here is the x-coordinate for you. Next, repeat the process while following a horizontal line to determine the y-coordinate.

According to the graph;

To determine the value of x when f(x) = 8.

We must plot a line of the equation; y = 8.

This y = 8 line produces a horizontal line.

The point at which the horizontal line, y = 8 intersects the given graph has an x coordinate.

Ultimately, this point has x coordinates of 4, making 4 the value of x when f(x) = 8.

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Answer:

(6, - 5 )

Step-by-step explanation:

Given a point (x, y ) on the function then the corresponding point on the inverse is (y, x )

Given

(- 5, 6 ) lies on h(x) , then

(6, - 5 ) lies on \(h^{-1}\) (x)

False. The statement is not entirely accurate. While significantly different sample variances can impact the assumptions of a t-test, it does not necessarily mean that a t-test cannot be conducted.

In traditional t-tests, there is an assumption of equal variances between the compared groups or populations. This assumption is known as the assumption of homogeneity of variances. If the sample variances are significantly different, it violates this assumption.

However, there are alternative versions of the t-test that can be used when the variances are not equal, such as the Welch's t-test or the modified t-test. These tests do not assume equal variances and can be applied when the variances are significantly different.

Therefore, it is possible to conduct a t-test even when the sample variances are significantly different, using appropriate modifications to the test. However, it is essential to consider the validity and appropriateness of the chosen test based on the specific circumstances and assumptions of the data.

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The probability that the student chosen will be a boy who watched tennis yesterday is 1/8.

Given that 56 students were asked if they watched tennis yesterday, 20 of the students are boys, 17 girls watched tennis yesterday and 32 students did not watch tennis yesterday and out of all these one students is to be chosen at random.

We have to find the probability that the student chosen will be a boy who watched tennis yesterday.

Total number of students is 56.

The total number of girls is 56-20=36

Girls who didn't watch tennis is 36-17=19

Number of the boys who did not watch the game is 32-19=13

Number of boys watching a tennis match is 20-13=7

Now, we will find the probability that the student chosen will be a boy who watched tennis yesterday.

Probability=Number of boys watching a tennis match/Total number of students
Probability=7/56

Probability=1/8

Hence, the probability that the student chosen will be a boy who watched tennis yesterday when 56 students were asked if they watched tennis yesterday is 1/8.

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Answer:

slope = \(\frac{2}{7}\)

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \(\frac{2}{7}\) x + \(\frac{3}{4}\) ← is in slope- intercept form

with slope m = \(\frac{2}{7}\)

The linear equation to find the temperature T at an elevation x on the mountain, where x is in thousands of feet will be T = (-9/2)x +103.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that, it is 76 degrees at the 6000-foot level of a mountain and 49 degrees at the 12000-foot level of the mountain.

As we know the linear equation in the slope-intercept is found as,

y =mx + b

Replace m with the c,y with the T, and b with the k as

T = cx + k

From the given data,

76 = c(6) + k

76 = 6c + k

⇒ k = 76 - 6c

For condition 2,

49 = c(12) + k

49 = 12c + k

Substitute the value of k in the above equation,

49 = 12c + (76 - 6c)

49 = 12c + 76 - 6c

49 - 76 = 6c

6c = -27

c=-9/2

Put the value of c in the equation,

K = 76 -6c
K = 76 -6(9/2)

K = 76+27

k = 103

Put the value of c and k in the equation below,

T = cx + k

T  = (-9/2)x+103

Thus, the linear equation to find the temperature T at an elevation x on the mountain, where x is in thousands of feet will be T = (-9/2)x +103.

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In a given scenario where 8% of the employees needed corrective shoes, 15% needed major dental work and 3% needed both corrective shoes and major dental work, the probability that an employee selected at random will need either corrective shoes or major dental work is 0.20.

Therefore, the answer is 0.20.

The probability that the employees needed corrective shoes = 0.08

The probability that the employees needed major dental work = 0.15

The probability that the employees needed both corrective shoes and major dental work = 0.03

Therefore the probability that the employees needed only corrective shoes = 0.08 - 0.03

= 0.05

And the probability that the employees needed only major dental work = 0.15 - 0.03 = 0.12

The probability that an employee selected at random will need either corrective shoes or major dental work is obtained by the summation of probabilities of needing only corrective shoe or needing only major dental work or needing both.

P = 0.05 + 0.12 + 0.03

P = 0.20

This can be solved easily by Venn diagram.

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Answer:

-4≤x<5

Hope This Helps!!!

Answer:

-1 = -1

Step-by-step explanation:

y = mx + b

y=-3  x=0 and m=2/5

-3 = (2/5)0 + b

Since 2/5(0) is 0, b must be -3.

So the equation is y = (2/5)x - 3

Add the slope to the given point and you get (5, -1)

-1 = (2/5) 5 - 3

-1 = 2 - 3

-1 = -1

A segment MN has endpoints M(-7.-6) and N(7,7). Find the coordinates of partition point P that divides the segment into a 5:2 ratio. ​

___________________________

Find the coordinates of partition point P that divides the segment into a 5:2 ratio. ​

5:2 means that it is divided into 7, and we do not move two positions from (7,7)

X axis

7- (-7) = 14

14/7 = 2

7-2*2 = 3

Y axis

7-(-6)= 13

13/7 =

7 - 2* (13/7) = 49/7 - 26/ 7 = 23/7 = 3 2/7

______________________________

Answer

(3, 3 2/7)

Answer:

15,300 ft or 2.9 miles

Step-by-step explanation:

Distance = Rate * Time (but rate and time must be in the same units)

convert hours to minutes

1 hr * 60 min/hr = 60 min

then

D = 255 ft/min * 60 min

D = 15,300 ft

if you want miles, convert ft to miles (5280 ft per mile)

15,300 ft * 1 mi/5280 ft

2.9 mi

Answer? the answer is A

Step-by-step explanation:

is A

Answer:

Step-by-step explanation:i don’t know the report but 2+4 is 6.00

Answer:

WY = 8

Step-by-step explanation:

We solve for above question using the Trigonometric function of Sine

sin θ = Opposite/Hypotenuse

Opposite = WY = x

Hypotenuse = 9

θ = 63°

Hence,

sin 63° = x/9

Cross Multiply

x = sin 63° × 9

x = 8.0190587177

Approximately x = 8

Therefore, WY = 8

The Greek mathematicians started using the symbol pi (π) for as long as 4000 years in mathematical world.

A Short History of Pi

Even if we counted the number of seconds in those 4000 years and round the value of pi (π) to so many places, we would still only be estimating the true value of pi. Pi has been known for over 4000 years. Below is a quick summary of the discovery of.

By multiplying the radius of a circle by three, the ancient Babylonians determined its area, yielding the number pi = three. About 1900–1680 BC Babylonian tablets show a value of 3.125 for, which is a more accurate estimate.

The Rhind Papyrus, which dates to around 1650 BC, sheds light on ancient Egyptian mathematics. The calculation used by the Egyptians to determine a circle's area yielded a result that was around 3.1605 for.

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A. There are 37 terms in the sum.

B. The sum of the given series is 7,696.

A. Using arithmetic sequences, We can observe that each term in the sum is obtained by adding 11 to the previous term. Therefore, the nth term can be expressed as:

\(a_n = 10 + 11(n-1)\)

We want to find the number of terms in the sum up to \(a_n\) = 406. Setting \(a_n\)= 406 and solving for n, we get:

406 = 10 + 11(n-1)

396 = 11(n-1)

n = 37

Therefore, there are 37 terms in the sum.

B. We can use the formula for the sum of an arithmetic series:

\(S_n = n/2 * (a_1 + a_n)\)

where \(S_n\) is the sum of the first n terms, \(a_1\) is the first term, and\(a_n\) is the nth term.

In this case, we have:

\(a_1\)= 10

\(a_n\)= 406

n = 37

Substituting these values, we get:

\(S_{37}\) = 37/2 * (10 + 406)

\(S_{37}\) = 18.5 * 416

\(S_{37}\) = 7,696

Therefore, the sum of the given series is 7,696.

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Step-by-step explanation:

Area of a triangle = 1/2 base * height

 for these triangles    area = 1/2 14 * 12.12  = 84.84 cm^2

     and there are four of these       four * 84.84 = 339.36 cm^2

Answer and Step-by-step explanation:

Yes, the three side lengths could form a triangle.

To find out if the sides can form a triangle, you take the lowest side lengths and add them together. If they are greater than the longest side, then they can form a triangle. If it is equal or less than the longest side, then it CAN NOT form a triangle.

7.8 + 10.4 > 13

18.2 > 13

So, the answer is Yes.

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Answer:

44/15 converted into a mixed number   = 2(14/15)

Step-by-step explanation:

44/15 =     2.9333333...... = 2( 14/15)

so it is the number 2 and   (0.93333)

Lets see how is  the  decimal is in fraction

0.93333  is a mixed recurrent number  and in fraction is  14/15

14/15 = 0.93333.....

With recurring  mixed  decimal :

For the top part:

Take the non-repeating and the repeating(93) and subtract the non repeating(9)

93-9= 84

For the bottom part: for  every repeating decimal,you put a 9  And for every non repeating decimal,you put a zero

so one 9 and one zero (90)

84/90  = 14/15  = 0.93333....

Answer:

see the attached  picture

Step-by-step explanation:

The geometric term that can be used to describe the crossing sign shown is intersecting lines.

In geometry, intersecting lines are two lines that cross one another at a location known as the point of intersection. It is possible to use the point of intersection to solve issues concerning angles, segments, and geometric shapes because it is the sole point that both lines share.

Two pairs of opposite angles that are equal to one another are formed when two lines connect, giving rise to four angles.

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The distance between the ship and the base of the lighthouse can be calculated using trigonometry. By applying the tangent function to the angle of depression, we can determine that the ship is approximately 54.49 feet away from the base of the lighthouse.

To determine the distance between the ship and the base of the lighthouse, we can use trigonometry. The angle of depression of 15° represents the angle formed between the horizontal line from the top of the lighthouse and the line of sight to the ship in the ocean. We can consider the height of the lighthouse (158 ft) as the opposite side of the right triangle, and the distance between the ship and the base of the lighthouse as the adjacent side.

Using the tangent function, we can set up the equation tan(15°) = opposite/adjacent, where the opposite side is 158 ft and the angle is 15°. Rearranging the equation, we have tan(15°) = 158/adjacent. Solving for the adjacent side, we find that the ship is approximately 545.51 feet away from the base of the lighthouse.

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Answer:

I think it's 31

Step-by-step explanation:

Answer:

x = 31°

Step-by-step explanation:

The two triangles seem to be identical.

All angles of a triangle must add up to 180° to make a triangle.

So, 53° + 96° = 149°

Subtract 149° from 180°

180° - 149° = 31°

So x = 31°

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Answer:

THERE IS NO DARN SHAPE MAN

Step-by-step explanation:

Answer:

7/12

Step-by-step explanation:

Total = 10W+14R

probability of red = R/total

10+14 = 24 so total = 24

R = 14

14/24

reduce (divide by two on the top and bottom)

14/2

-------

24/2

= 7/12

A segment's length is unaffected by a dilatation when it travels through the centre of one. Before and after the dilatation, the segment has the same length.

A segment's length is unaffected when it travels through the centre of a dilatation. This is so that the segment's length is unaffected by the dilation factor and the centre of dilation serves as a fixed point. The section retains its original length regardless of the scale factor that was applied during the dilation. This is such that the segment itself is unaffected by the dilation, which instead expands or contracts other places around the segment's centre.

However, the length of segments that do not travel through the centre of dilatation changes. The dilation factor determines the size of this shift. The segment stretches or elongates if the dilation factor exceeds 1. The length of the segment grows by a specific multiple in direct proportion to the dilation factor.

The section shrinks or contracts, on the other hand if the dilation factor is less than 1. The section gets a little bit shorter because the length drop is proportionate to the dilation factor. Points closer to the centre of dilation have less change in length, and the effect is more prominent the further the segment is from the centre.

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