is (6,3) and (8,4) inverse or direct

Answer:

3. 2 or x=2

Step-by-step explanation:

I put your question into a math calculator and this was the answer. Good luck!

less than zero

Step-by-step explanation:

when the discriminant is less than zero, then it has no real solutions. this can be written as

b²-4ac<0 has no real solutions.

The angles of the rhombus are

             m∠ADC = 58°

             m∠BCD = 122°

What is a rhombus?

An example of a quadrilateral is a rhombus. It is a unique instance of a parallelogram in which the diagonals bisect each other at a 90° angle and all sides are equal.

The properties of a rhombus are:

From the figure,

In ΔDOC.

∠ODC = 180° - ( 90+61) = 29°

The diagonal bisects ∠ADC

So ∠ADC = 2∠ODC = 2 × 29° = 58°

Since the diagonal bisects the angle, ∠BCD = 2∠ACD

                                                                           = 2×61° = 122°

Therefore the angles of the rhombus are

             m∠ADC = 58°

             m∠BCD = 122°

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If A and B are similar matrices and v is an eigenvector of A, then v is also an eigenvector of B , similarly if u is an eigenvector of B then u is also eigenvector of A.

Suppose A and B are n×n matrices over R or C. We say A and B are similar, or that A is similar to B, if there exists a matrix P such that B =P⁻¹AP.

The eigenvalues are the roots of the

characteristic polynomial.

B =P⁻¹AP ⇔ PBP⁻¹ = A

If Av = λv , then PBP⁻¹v = λv ⇒ BP⁻¹v = P⁻¹λv

So, if v is an eigenvector of A, with eigenvalue λ, then P⁻¹v (which is non-zero since P is invertible) is an eigenvector of B with the same eigenvalue. If u is an eigenvector for B then P⁻¹v is an eigenvector for A. So, every eigenvalue of A is an eigenvalue of B and since you can interchange the roles of A and B in the previous calculations, every eigenvalue of B is an eigenvalue of A too. Hence, A and B have the same eigenvalues.

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Answer:

5 and 6

Step-by-step explanation:

The size of matrix cM is given as follows:

9 x 10.

When a matrix is multiplied by a constant, we have that every element in the matrix is multiplied by the constant. Hence, the dimension of the matrix remains constant.

The parameters for this problem are given as follows:

Hence the size of matrix cM is given as follows:

9 x 10.

(same size as the original matrix, as we simplify multiply each element in the matrix by the constant, hence the dimensions remain the same).

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Answer:

x < -18

Step-by-step explanation:

x/3 < -6

3 × x/3 < 3 × (-6)

x < 3 × (-6)

x < -3 × 6

x = -18

For the  trigonometric identity

11. If cos 27° = x, then the value of tan 63° interims of "x" is  x/√1 - x²

12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is  1/√3

13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2

14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) -  4 cos²45° is 0

15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is  30°

16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6

17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is  30°

18. The value of (sin 65°)/ (cos 25°) is 1

To solve the various   trigonometric identity;

11. Given: cos 27° = x

We know that cos (90 - θ) = sin θ

So, cos 63° = sin 27°

And sin 63° = √1 - cos²27°

Substituting cos 27° = x, we get

sin 63° = √1 - x²

Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.

= x/√1 - x²

12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get

7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ

⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)

⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ

⇒3 tan²Θ = 1

⇒ tan²Θ = 1/3

⇒ tanΘ = 1/√3

13. For tan 80° × tan 10° + sin² 70° + sin² 20°

⇒ tan 80° = cot (90 - 80)° = cot 10°

⇒  sin 70° = cos (90 - 70) = cos 20°

⇒ cot 10° × tan 10° +  cos 20° + sin² 20°

= 1 + 1 = 2

14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°

= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²

= (sin (90° - 43°)/cos43°)² +  (cos (90° - 47°)/sin)²  = 4(1/2)

= (cos 43°/cos 43°)² + (sin 47°/ sin   47°)² - 2

= 1 + 1 - 2 = 0

15. 2 (cos²Θ - sin²Θ) = 1

cos²Θ - sin²Θ = 1/2

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get

cos²Θ - (1 - cos²Θ) = 1/2

2cos²Θ = 3/2

cos Θ = √3/2(cos 30° = (√3)/2

= 30°

16. Given: 5 tan Θ = 4

We know that tan Θ = sin Θ / cos Θ

So, 5 sin Θ / cos Θ = 4

5 sin Θ = 4 cos Θ

Dividing both sides of the equation by 5, we get

sin Θ / cos Θ = 4/5

∴ sin Θ = 4/5 cos Θ

given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)

we substitute sin Θ = 4/5 cos Θ  into the equation

⇒(5 × 4/5 cos Θ  - 3 cos Θ)/(5 × 4/5 cos Θ  + 2 cos Θ)

= (4-3)/(4 + 2) = 1/6

17. Given: sin(x + 20)° = cos (x + 10)°

We know that sin(90 - θ) = cos θ

So, sin(x - 20)° = sin(90 - (3x + 10))°

⇒ (x - 20)° = (90 - (3x + 10))°

⇒ x - 20° = 90° - 3x + 10

⇒ 4 x = 120°

⇒ x = 120°/4

⇒ x = 30°

18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:

To solve this, we can use the following trigonometric identities:

sin(90 - θ) = cos θ

cos(90 - θ) = sin θ

We can also use the fact that sin²θ + cos²θ = 1.

Rewrite sin (65°) / cos (25°)

⇒ sin (65°) = cos (25°)

∴ cos (25°)/ cos (25°) = 1

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Answer:

ribeye steak dinner: 22.98

grilled salmon dinner: 8.94

Step-by-step explanation:

The cost of one ribeye steak dinner and one grilled salmon dinner is

574.48/18 = 31.92

The cost of six ribeye steak dinners and six grilled salmon dinners is

31.92 * 6 = 191.49

So the difference between 191.49 and 582.08 is for 23 - 6 = 17 ribeye steak dinners, then each ribeye steak dinner is (582.08 - 191.49)/17 = 22.98

Each grilled salmon dinner is 31.92 - 22.98 = 8.94

The general solution for the equation 5tan(θ) - 6cos(θ) = 0 is:

θ = sin⁻¹(2/3) + nπ, where n is an integer.

To determine the general solution of the trigonometric equation 5tan(θ) - 6cos(θ) = 0, we can use algebraic manipulation and trigonometric identities to simplify and solve for θ.

Starting with the given equation:

5tan(θ) - 6cos(θ) = 0

First, we can rewrite the tangent function in terms of sine and cosine:

5(sin(θ)/cos(θ)) - 6cos(θ) = 0

Next, multiply through by cos(θ) to eliminate the denominator:

5sin(θ) - 6cos²(θ) = 0

Using the identity sin²(θ) + cos²(θ) = 1, we can express cos²(θ) as 1 - sin²(θ):

5sin(θ) - 6(1 - sin²(θ)) = 0

Expanding and rearranging terms:

5sin(θ) - 6 + 6sin²(θ) = 0

Rearranging the equation:

6sin²(θ) + 5sin(θ) - 6 = 0

Now, we have a quadratic equation in terms of sin(θ).

We can solve this quadratic equation by factoring or using the quadratic formula.

However, since this equation is not easily factorable, we will use the quadratic formula:

sin(θ) = (-b ± √(b² - 4ac)) / 2a

For our equation:

a = 6, b = 5, c = -6

Plugging these values into the quadratic formula and simplifying, we get:

sin(θ) = (-5 ± √(5² - 4(6)(-6))) / (2(6))

sin(θ) = (-5 ± √(25 + 144)) / 12

sin(θ) = (-5 ± √169) / 12

sin(θ) = (-5 ± 13) / 12.

This gives us two possible solutions for sin(θ):

sin(θ) = (13 - 5) / 12 = 8/12 = 2/3

sin(θ) = (-13 - 5) / 12 = -18/12 = -3/2

Since the range of the sine function is -1 to 1, the second solution (-3/2) is not valid.

Now, to find the values of θ, we can use the inverse sine function (sin⁻¹) to solve for θ:

θ = sin⁻¹(2/3)

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Answer:

29. D

30. A

31. 15

32. -34

33. -241

34. -36

Step-by-step explanation:

The experimental probability that the next spin falls in a black region is given as follows:

0.205 = 20.5%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

205 out of the previous 1000 trials fell in the black region, hence the experimental probability is given as follows:

p = 205/1000

p = 0.205.

p = 20.5%.

The problem asks for the experimental probability that the next spin falls in a black region.

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Answer:

324 kilometres

What I did was do 36x10 which is 360

Then I did 360-36=24 because the question wants 9x36 not 10x36

Check the picture below.

r       = rate of the faster cyclist

r - 7 = rate of the slower cyclist

we know they both met 5 hours later, so the time each one has been cycling has been 5 hours for each.

let's say the faster cyclist on those 5 hours covered "k" kilometers, that means the slower one cover the slack, namely "255 - k" kilometers.

\({\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{Km s}{distance}&\stackrel{km/h}{rate}&\stackrel{hour}{time}\\ \cline{2-4}&\\ \textit{faster cyclist}&k&r&5\\ \textit{slower cyclist}&255-k&r-7&5 \end{array}\hspace{5em} \begin{cases} k=(r)(5)\\\\ 255-k=(r-7)(5) \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{using the 1st equation}}{k=5r}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{255-(5r) = (r-7)(5)} \\\\\\ 255-5r=5r-35\implies 255=10r-35\implies 290=10r \\\\\\ \cfrac{290}{10}=r\implies 29=r\hspace{5em}\stackrel{\textit{faster cyclist}}{\text{\LARGE 29}~\frac{km}{h}}\hspace{5em}\stackrel{\textit{slower cyclist}}{\text{\LARGE 22}~\frac{km}{h}}\)

Answer:

c. between 4&5 and -1&0

Step-by-step explanation:

The main belt is not located between these all planets.

What is orbit?

A route that an object in space follows around another is known as an orbit. A satellite is a thing that orbits the earth. An Earth- or moon-like natural satellite is one possibility. Moons are satellites that orbit many planets. A man-made satellite is also possible, such as the International Space Station.

The belt of asteroids is located between the orbits of Mars and Jupiter. The asteroids in this region, known as the main belt, are made up of small rocky bodies that orbit the sun in a region between about 2.2 and 3.2 astronomical units (AU) from the sun.

The distance from the sun to the Earth is about 1 AU, and the distance from the sun to Venus is about 0.7 AU, so the main belt is located beyond the orbits of both Venus and Earth.

The orbits of Saturn and Uranus are much farther out from the sun, at distances of about 9.5 and 19.2 AU, respectively, so the main belt is not located between these planets.

Hence, The main belt is not located between these all planets.

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Answer:

$976

Step-by-step explanation:

Straight time pay= $15.25(hourly rate) × 40(hours worked)= $610

Overtime Rate = 15.25×2= $30.50

Overtime Pay= $30.5 × 12 (Hours worked overtime)= $366

Total Pay= Basic wage + Overtime Wage = $976

Given:

The position coordinates of the subway stop, (x1, y1)=(-7,3).

The position coordinates of the house, (x2,y2)=(-2,9).

The distance between the house and the subway stop is,

Therefore, the distance between the house and the subway stop is 8 units.

Hence, option B is correct.

The average monthly wage for the entire workforce of the business is $7489.09.

The mathematical average of a group of two or more numbers is called the mean. There are two different sorts of means that can be calculated: the arithmetic mean and the geometric mean. The arithmetic mean is calculated by adding all of the numbers in a set and dividing by the total number of integers in the set.

Given, The six departments of a company consisting of 22, 32, 18, 16, 10, and 12 employees have equal monthly salaries of $7200, $7600, $6900, $8200, $7800, and $7400 respectively.

First, calculate the total monthly salary

22*7200 + 32*7600 + 18*6900 + 16*8200 + 10*7800 + 12*7200  dollars.

Total monthly salary = $823,800

Then divide this sum by the total number of employees  

 22 + 32 + 18 + 16 + 10 + 12

Total number of employees = 110

the mean monthly salary of all the employees  = \(\frac{Total salary}{total number of employee}\)

the mean monthly salary of all the employees  = 823800/ 110

the mean monthly salary of all the employees = 7489.0909

Therefore, the mean monthly salary of all the employees of the company is $7489.09.

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Here are the steps to simplify the expression \(\sf\:5x\sqrt{3x} - 2x\sqrt{3x} - x\sqrt{3x} \\\):

1. Combine like terms that have the same radical term \(\sf\:\sqrt{3x} \\\):

\(\sf\:(5x - 2x - x)\sqrt{3x} \\\)

2. Simplify the coefficients:

\(\sf\:2x\sqrt{3x} \\\)

Therefore, \(\sf\:5x\sqrt{3x} - 2x\sqrt{3x} - x\sqrt{3x}\) simplifies to \(\sf 2x\sqrt{3x} \\\).

Answer:

\(38 \div5 \\ \)

Answer:

The 2 factors are -2 and 18.

Step-by-step explanation:

xy = -36

Let y = 0.5x - 11 so

x(0.5x - 11) = -36

0.5x^2 - 11x + 36 = 0

0.5(x^2 - 22x + 72) = 0

(x - 4)(x - 18) = 0

x = 4, 18.

Try x = 18:-

The 2 numbers which are factors of -36 must be  -2 and 18 because they fit the requirement  that 0.5(18) - 11 = 9 - 11 = -2.

Answer:

\(\huge\boxed{\sf 18^{-3}}\)

Step-by-step explanation:

\(\displaystyle \frac{18^4}{18^7}\)

So, the expression becomes:

= \(18 ^{4-7}\)

= \(18^{-3}\)

\(\rule[225]{225}{2}\)

The ability of the twins to divide the oddly shaped plot into two Identical plots along the grid lines depends on the presence of a line of symmetry.

To determine whether the set of twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need to consider the characteristics of the plot and the conditions required for the division.

For the division to be possible, the plot needs to have a line of symmetry that can be used to create two identical halves. A line of symmetry divides an object into two equal and mirrored parts.

If the plot of land has a line of symmetry, the twins can divide it by drawing a line along the symmetry axis. This line should cut the plot into two equal halves, ensuring that both plots are identical.

However, if the plot does not have a line of symmetry, it may not be possible to divide it into two identical plots along the grid lines. In this case, the twins would need to consider alternative methods of division or compromise on the goal of having two identical plots.

To determine if the plot has a line of symmetry, the twins can examine its shape and characteristics. They can look for any symmetrical patterns, such as equal sides or mirrored shapes, that indicate the presence of a line of symmetry.

If the plot does not have an obvious line of symmetry, the twins might need to explore other options, such as dividing the plot into two equal areas based on other criteria, such as the length or width of each half.

the ability of the twins to divide the oddly shaped plot into two identical plots along the grid lines depends on the presence of a line of symmetry. If such a line exists, they can divide the plot by drawing a line along the symmetry axis. However, if the plot lacks symmetry, they may need to consider alternative methods of division or adjust their expectations.

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Note the full question may be :

To determine whether the twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need more specific information about the shape and dimensions of the plot. the shape of the plot (rectangular, triangular, irregular), the lengths of its sides, any existing grid lines or divisions within the plot.

Answer:

$20.298, round to $20.30

Step-by-step explanation:

The orginal price of the shorts are $19.90, and the tax is 0.02 (2%), so you multiple 19.90*0.02, which is $0.398, and then you add it to $19.90 to get $20.298.

Answer:

$0.39 cents

Step-by-step explanation:

2% of 19.9 is 0.398 but we will just say 39 cents :)

Answer:

The slope is -2 full equation is y = -2x -2

Answer:

The common denominator is 100 because they dont have a number lower so 20*5 is 100 and 25*4 gives you 100

i hope this helps<3

Answer:

a)64

b)96

Step-by-step explanation:

For this we calculate the number of rows, 32, as 2+3 is 5, and 160/5 is 32. Then we know that there are 32 rows, and in each row are 2 left seats and 3 right seats, so we multiply 32 by both numbers for the answers.  

Answer:

a64 b 96.

Step-by-step explanation:

.

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