Solve for the short leg of the 30-60-90 triangle.

s is an eigenvalue of A.

Eigenvalues are a unique collection of scalar values connected to a set of linear equations that are most likely seen in matrix equations. The characteristic roots are another name for the eigenvectors. It is a non-zero vector that, after applying linear transformations, can only be altered by its scalar component.

A =[tex]\left[\begin{array}{ccc}a_{11} &a_{12} &\\a_{21} &a_{22} &\\&\end{array}\right][/tex][tex]\left[\begin{array}{ccc}f1\\f2&\\\end{array}\right][/tex]

[tex]f_{1} = a_{11} + a_{12}[/tex]

[tex]f_{2} = a_{21} + a_{22}[/tex]

We see that if (A - sI) is unique, then s is an eigenvalue of A. ( I is the identity matrix). Keep in mind that if every column in A adds up to s, then the total of the resultant vector is zero when s is subtracted from one item.

We know that the image of a matrix is the span of its column vectors. Since all the column vectors are members of the above-mentioned subspace, the image of the transformation is contained in this subspace. Thus, the rank of our n x n matrix is less than n. Thus, (A - sI) is singular.

Thus, s is an eigenvalue of A.

Transposition preserves eigenvalues (this is actually a profound statement, in a way). If A has columns adding to s, then A^T has rows adding to s. Let v be the column vector of 1's.

A^T * v = s * v.

Thus, s is an eigenvalue of A^T

Thus, s is an eigenvalue of A.

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The selling price of a used book at the store where the owner buys a used book for $1.50 and resells the used book at a price of 400% the price at which he buys the used book is $6.00

The selling price of an item is the price which is displayed on the item on the shelves of a store. The selling price is often different from the price at which the item is bought, or produced, which is often lesser than the price at which the item is sold.

The amount at which the owner buys each used books = $1.50

The amount at which the owner of the used book store sells the books = 400% of the amount he paid for the books

400% of an amount x is equivalent four times the amount. (4 × x)

The price at which the owner sells a used book at his store, P, is therefore;

P = 400% × $1.50 = 400/100 × $1.50 = $6.00

The price of a used book at the store is $6.0

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The measure of three angles of triangle are 45°, 55° and 80°.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Let the smallest angle of triangle be x.

One angle the triangle measures 10° greater the smallest angle, that is x+10°

The third angle measures 10° less than twice the smallest angle.

The third angle is 2x-10°

Now, x+2x-10°x+10°=180°

⇒ 4x=180°

⇒ x=45°

So, 2x-10°=80° and x+10°=55°

Therefore, the measure of three angles of triangle are 45°, 55° and 80°.

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Answer:

2/-5

Step-by-step explanation:

The 4ml of this solution, this patient will need in a day.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that 80 kg patient needs a medication X in the amount of 0.25 mg/kg/day.

The medication comes in a liquid solution of 50 mg for every 10 ml therefore,

0.25 x 80 = 20mg/day

50/10 = 5mg/ml

Then the patient need in a day;

20/5= 4ml

Theefore, The solution, this patient will need in a day is 4 ml.

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Answer:

not enough information

Compound interest equation:

Find equations for each case below.

1) P = 1200, r = 0.09, n = 1, t = 15

2) P = 1200, r = 0.12, n = 4, t = 15

3) P = 1200, r = 0.12, n = 12, t = 15

4) P = 1200, r = 0.15, n = 2, t = 9

Answer:

continue the streak:)

Step-by-step explanation:

fluffytopfluffytopfluffytopfluffytopfluffytopfluffytopfluffytopfluffytopfluffytop

hoped this helped:)

brainliest for the brains lol

All the statements are true.

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

Y = mx + b, where m is the slope and b is the y-intercept, is the slope equation utilizing the equation of a line.

A. The triangles drawn between each pair of points are similar.

B. The ratio of y2-y1/x2-x1  will be the same for Tavion and Jess.

C. Both students should find a slope of .

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The value of the number will be;

⇒ 5/2

A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.

Given that;

The rational number is,

⇒ 2.5

Now,

Since, The rational number is,

⇒ 2.5

Hence, We get;

⇒ 2.5 = 25/10

          = 5/2

Thus, The value of the number = 5/2

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The coordinates of S(x₁, y₁)=(3/2 , 5) if F(0, 2) and G(2,6) and the lines divided in the ratio 1:3

Finding the ratio by which a line segment is divided by a point internally or externally in coordinate geometry is done using the Section formula. The centroid, incenter, and ex center of a triangle are determined using it. Finding systems' centers of mass, equilibrium locations, etc. are all done using this method in physics. Finding the ratio by which a line segment is divided by a point internally or externally in coordinate geometry is done using the Section formula. The centroid, incenter, and ex center of a triangle are determined using it.

Given,

F(0, 2) and G(2, 6)

And also given that the points S lies on the way along FG then:

The lines divides the ratio,

1:3= m:n

Here we have to find the coordinates of S, we get:

S(x₁, y₁)=((mx₁+n x₂)/(m+ n), (my₁+n y₂)/(m+ n))

=((1(0)+3(2))/4 , (1(2)+3(6))/4)

=(6/4 , 20/4)

=(3/2 , 5)

S(x₁, y₁)=(3/2 , 5)

Therefore, the coordinates of S(x₁, y₁)=(3/2 , 5).

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Answer:

----------------------------------

Given

We need to find the point S(x, y) which makes FS = 1/3 FG.

Each coordinate of S is at 1/3 FG distance from F.

Find values of x and y:

So the point S is at (2/3, 10/3).

The reduced fraction of 0.245 is 49/200.

What is the greatest common factor (GCF)?

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, the numbers 12, 20, and 24 share the components 2 and 4. Since four is the largest, we refer to the GCF of 12, 20, and 24 as four. Frequently, GCF is used to identify common denominators.

We have,

0.245

Write 0.245 as  

0.245 / 1

Multiply both the numerator and denominator by 10 for each digit after the decimal point.

0.245/1

=   0.245 x 1000 / 1 x 1000

=  245 / 1000

In order to reduce the fraction find the Greatest Common Factor (GCF) for 245 and 1000. Keep in mind a factor is just a number that divides into another number without any remainder.

The factors of 245 are: 1  5  7  35  49  245

The factors of 1000 are: 1  2  4  5  8  10  20  25  40  50  100  125  200  250  500  1000

The Greatest Common Factor (GCF) for both 245 and 1000 is: 5

Now to reduce the fraction we divide both the numerator and denominator by the GCF value.

245/ 1000

= 245 ÷ 5 /1000 ÷ 5

=  49 / 200

The decimal part is: 0.245 = 245/1000

Full simple fraction breakdown: 245/1000

= 49/200

Hence, the reduced fraction of 0.245 is 49/200.

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Answer:

Step-by-step explanation:

I'd say c.) table b only. Because it's a straight line which I think is positive but i'm not sure about the association between the variables part. If wrong I'm sorry.

Answer:

B: y=2/3-5x

Step-by-step explanation:

15x+3y=2

-15x.     -15x

3y=2-15x

/3 /3. /3

y=2/3-5x

so B is the correct answer

hopes this helps please mark brainliest

Answer:

D

Step-by-step explanation:

Based on the information provided, it appears that the correct answer would be option D: y=2 - 15x. This can be determined by solving the given equation for y by isolating the y-term on one side of the equation. To do this, you can subtract 15x from both sides of the equation, resulting in y = 2 - 15x.

Here is the complete process for solving the equation:

Begin by subtracting 15x from both sides of the equation:

15x + 3y = 2

-15x -15x

This simplifies to:

3y = 2 - 15x

Now, divide both sides by 3 to isolate the y-term:

3y/3 = (2 - 15x)/3

This simplifies to:

y = 2/3 - 15x/3

Finally, since 3 is a common factor, we can simplify the right side of the equation further by dividing both the numerator and the denominator by 3:

y = 2/3 - 15x/3

y = (2/3) / (3/3) - (15x/3) / (3/3)

y = (2/3) / 1 - (15x/3) / 1

y = 2/3 - 15x/3

y = 2/3 - 5x

Therefore, the equivalent equation is y = 2/3 - 5x, which is option D.

Answer:

No solution.

Step-by-step explanation:

You would multiply -2 to the 2nd equation and you would get -8x+2y=-2 and you would add that to 8x-2y=2 and when you would add all of them would eliminate or cross each other out, showing no solution.

Answer:

  7x -(12¾)

Step-by-step explanation:

You want the algebraic expression for "12¾ less than the product of 7 and a number x".

The product of 7 and x is represented as ...

  7x

If you want 12¾ less than that, then you subtract 12¾.

  7x -12¾ . . . . . . . the desired expression

__

Additional comment

A "product" is what we call the result of multiplication. The operation of multiplication can be indicated several ways. If there is no ambiguity, the most common way to show multiplication is to write the values next to each other without any symbol.

  7x . . . . 7 times x

Sometimes, it is helpful to put the values in parentheses:

  (7)(x)

A multiplication symbol can be used, if desired.

  7·x

  (7)×(x)

When showing multiplication using the symbol ×, care must be taken to differentiate it from the symbol x, especially if confusing these symbols will give a different result than desired. (Sometimes, when the symbol × is unavailable, an 'x' is used instead.)

Occasionally, you will see a dot on the baseline used as a multiplication symbol. Likewise, you may see a centered dot intended as a decimal point.

  7.x . . . . . 7 times x

  7·3x . . . . 7 and 3 tenths times x (maybe)

When different numbers are involved, the use of a baseline dot for multiplication, and a centered dot for a decimal point can be confusing.

  7.3.x . . . . could be (7)(3)(x) or (7.3)(x)

  7·3.x . . . . could be (7)(3)(x) or (7.3)(x)

In general, a notation should be chosen so as to reduce any ambiguity to a minimum and communicate in a way that the audience understands.

When a mixed number is involved, as above, it can be useful to enclose it in parentheses, so it is not confused with the product of an integer and a fraction. The font used to express the fraction can be chosen to help reduce the ambiguity.

the cost of 145 refrigerators is $16954.82 and fixed cost rate per refrigerator is $116.92

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

A company manufactures small refrigerators. The total cost to manufacture 57 refrigerators is $6665.

manufacture 1 refrigerator is $6665/57 = $116.92

So to make 145 refrigerators the money will spent is $116.92*145= $16954.82

The fixed cost arte per refrigerator is $116.92

Hencve the cost of 145 refrigerators is $16954.82 and the fixed cost rate per refrigerator is $116.92

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Speed

1500 m/sec

Time 20 seconds

Given speed and time, you can calculate distance.

Distance = Time * Speed

Distance = 1500 * 20

Distance = 15000 * 2

Distance travelled by the sonar = 30,000 meters

Since its bouncing off the ocean floor and returning, divide by 2 to find one way distance.

Depth 15,000 meters

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

Answer:

[tex]y+5=-\frac{2}{3}(x-5)[/tex]

Step-by-step explanation:

The slope of the line is [tex]\frac{-1-(-5)}{-1-5}=-\frac{2}{3}[/tex].

Using the point [tex](5,-5)[/tex], the equation is [tex]y+5=-\frac{2}{3}(x-5)[/tex].

From the explanations, we can say that for the research experiment;

A Her results were not typical. She should have called on females fewer than 10 times since most of the data is centered around 10.

Since the teacher is conduction the experiment to see if she  was more likely to call on boys or girls in class, it means that there may have been some bias in the research.

The reason for the purposed bias comes from the  she is also a female. However,  it is not only just about genders only but which student was closer and as such if the teacher is female it’s more likely for a female student to be closer to her eye view whereas the boys may be in the back as usual and so 23 shows a typical expectation.

Now, looking at the options, we can say that the correct one is certainly.

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Answer:

-11 in top left, 5 in top right, -12 in bottom left, and -2 in bottom right.

Step-by-step explanation:

4C is the matrix C with all its elements multiplied by 4. Same logic applies for 3D. Then subtract each element of 3D from its counterpart of 4C which gives you the final answer. A big shortcut however if you have a TI-84 Plus Graphing Calculator is to use second x^-1 for matrices to edit the matrices and do matrix operations.

The total carbon dioxide that the country would emit over the course of the 6 year period is 661,505 kilotons.

The formula that can be used to determine the emission each year is:

Emission in the first year x(1 - rate of decrease)^number of years

Emission in the first year = 120,000

Emission in the second year = 120,000 x (1 - 0.034)^1 = 115,920

Emission in the third year = 120,000 x (1 - 0.034)^2 = 111,978.72

Emission in the fourth year = 120,000 x (1 - 0.034)^3 = 108,171.44

Emission in the fifth year = 120,000 x (1 - 0.034)^4 = 104,493.61

Emission in the sixth year = 120,000 x (1 - 0.034)^5 = 100,940.83

Sum of emissions from the first year to the sixth year = 661,505

This illustrates the concept of exponential decrease.

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Answer:

Below

Step-by-step explanation:

If they are similar the ratios of their sides are similar

11 is similar to 43    as   8 is similar to OP

Set up a ratio of this statement:

11/43  =  8/OP      then OP = 8 * 43/11 = 31.3 units  

The counter example for the system of equation is given by x + y = 1 ,

-x - y = 1 has the result 0 = 2 but ( 0, 2 ) is not the solution of the equation. It proves statement is false.

As given in the question,

Form the given system of equations , using elimination method to get the solution of the equation which shows the result 0 = 2 is as follow:

a. x + y = 1

- x - y = -1

0 = 0

Not the required result.

b. x + y = 1

  x - y = 1

 2x = 2

Not a required result.

c. x + y = 1

  - x - y = 1

     0 = 2

Required result.

Analyze : substitute x = 0 and y = 2 in any one equation

0 + 2 = 1

or -0 -2 = 1

Both the equations proves that statement is false.

d. x + y = -1

  -x -y = -1

   0 = -2

Not a required result.

Therefore, the system of equation of option c.  x + y = 1 , -x - y = 1 has the result 0 = 2 and proves it is the false statement.

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The answer would be (C) 20.

Answer:

The 2nd quartile, also known as the median, is the middle value of a dataset, or the value that separates the lower half of the data from the upper half. In a box-and-whisker plot, the 2nd quartile is represented by the line in the middle of the box.

In the given box-and-whisker plot, the 2nd quartile is 12.5, which is the middle value of the data set. This can be determined by looking at the scale on the x-axis and finding the value that is in the middle of the box.

Option B, 12.5, is the correct answer.

Step-by-step explanation:

Answer:

it is easy 56 and 45 and 567

The sale price of the shirt can be found by calculating 30% of the original price, which in this case would be $22.40 x 0.30 = $6.72. Thus, the sale price of the shirt would be $22.40 - $6.72 = $15.68.

Answer:

7.065

Step-by-step explanation:

So, to find the area of a circle you need to use "A =  π r2"

First, we have to find out the radius of the circle, so cut the diameter in half, that will equal 1.5 ft

then, you put 3.14 (pi) into a calculator

then put (1.5 x 1.5) which is 1.5 to the second power.

the equation put together will be 3.14 (1.5 x 1.5)

So the answer will be 7.065