Write the equation of the line passing through the points (−3,9) and (−9,3).
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Part 1
The equation of the line is enter your response here.

1. The length of x and y are 5 and 8.66 respectively

2. The area of the equilateral triangle is 9√3 cm²

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

sin30 = x/10

0.5 = x/10

x = 0.5×10

x = 5

sin60 = y/10

0.866 = y/10

y = 0.866 × 10

y = 8.66

2. The height of the triangle = √6²-3²

= √36-9

= √27

= 3√3

area = 1/2bh

= 1/2 × 6 × 3√3

= 9√3 cm²

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Answer: 24

Step-by-step explanation:

doing the math 30% of 80 is 24

The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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The correct statement regarding the triangles is given as follows:

Triangle ABC is similar to triangle A prime B prime C prime. because triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 4. and then rotating it about the origin by 180 degrees.

Similar triangles are triangles that share these two features presented as follows:

For this problem, we have that the transformations are given as follows:

The angle measures weren't changed, meaning that they are congruent, and thus the triangles are similar.

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1101000 is a binary number, which can be converted to its decimal equivalent as follows = 26 . all the options given is incorrect.

The binary number is to be transformed by appending three 0's to the end of the number. For example, 11101 is transformed to 11101000.

A binary number is a number that is written in the base 2 numbering system. In the base-2 system, there are only two digits used, 0 and 1, which are also referred to as binary digits or bits.

The decimal equivalent of a binary number can be found by using the following formula:

bn × 2ⁿ+ bn-1 × 2ⁿ-1 + ………+ b1 × 2¹ + b0 × 2⁰

Here, the binary number is to be transformed by appending three 0's to the end of the number. For example, 11101 is transformed to 11101000.

To find the relationship between the transformed number and the original number, we need to convert the given binary number to its decimal equivalent and compare it with the transformed number.11101 is a binary number, which can be converted to its decimal equivalent as follows:

11101 = 1 × 2⁴ + 1 × 2³ + 1 × 2¹ + 0 × 2⁰

= 16 + 8 + 2 + 0

= 26

The transformed number is 11101000. Here, we are appending three 0's to the end of the binary number, so its decimal equivalent will not change. Therefore, the decimal equivalent of the transformed number is also 26.

So, the transformed number is equal in value to the original number. Hence, the long answer of this question is:

The transformed number and the original number are related in such a way that the transformed number is equal in value to the original number.

Therefore, option (D) the transformed value is 1000 times the value of the original number is not correct.

Option (A) the transformed number is 3 times the value of the original number is also not correct.

Similarly, option (B) the transformed number is 4 times the value of the original number and option (C) the transformed number is 8 times the value of the original number are also not correct.

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Step-by-step explanation:

Maryam scores in paper 1 65% × 120

= 65/100 × 120

= 78 marks of full scores 120 marks

scores in paper 2 80% × 80

= 80/100 × 80

= 64 marks of full scores 80 marks

Trigonometric functions values of a 60-degree angle and a 30-degree angle are related to each other. The values of the sine, cosine, and tangent functions of a 60-degree angle are the same as the values of a 30-degree angle. However, the values of cosecant, secant, and cotangent functions of 60 degrees angle are opposite of 30 degrees angle.

This is because, in a right-angled triangle, the side opposite the 60-degree angle is twice the length of the side opposite the 30-degree angle. The six trigonometric functions values of an angle can be defined as ratios of the side lengths in a right-angled triangle with respect to the angle. A right-angled triangle can be used to understand and calculate the values of the six trigonometric functions.

For any given acute angle, the six trigonometric functions of the angle will always have the same ratio, regardless of the size of the triangle or the length of its sides. However, the values of the six trigonometric functions vary depending on the angle.In the case of a 60-degree angle and a 30-degree angle, these two angles are commonly used in trigonometry because they can be easily evaluated using special triangles. In a right-angled triangle with a 30-degree angle, the side opposite to the angle is half the length of the hypotenuse. Whereas, in a right-angled triangle with a 60-degree angle, the side opposite to the angle is twice the length of the side opposite to the 30-degree angle.In the special triangle, if the length of the shorter leg is 1, then the length of the hypotenuse is 2 and the length of the longer leg is √3. These are the ratios for a 30-degree angle and the same ratios for a 60-degree angle are: sin 60° = sin 30° = 1/2, cos 60° = cos 30° = √3/2, and tan 60° = tan 30° = √3/3. However, the values of cosecant, secant, and cotangent functions of 60 degrees angle are opposite of 30 degrees angle.

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Given:

Hayden \(1\dfrac{1}{2}\) minutes to complete each level of his video game.

He plays for \(10\dfrac{1}{4}\) minutes.

To find:

The number of levels he will complete.

Solution:

We have,

Required time for each level = \(1\dfrac{1}{2}\)

Total time = \(10\dfrac{1}{4}\)

The number of level is

\(n=\dfrac{\text{Total time}}{\text{Required time for each level}}\)

\(n=\dfrac{10\dfrac{1}{4}}{1\dfrac{1}{2}}\)

\(n=\dfrac{\dfrac{10(4)+1}{4}}{\dfrac{1(2)+1}{2}}\)

\(n=\dfrac{\dfrac{41}{4}}{\dfrac{3}{2}}\)

On further simplification, we get

\(n=\dfrac{41}{4}\times \dfrac{2}{3}\)

\(n=\dfrac{41}{6}\)

\(n=6.8333...\)

Number of levels must be a whole number. So, approx to value to the preceding whole number.

\(n\approx 6\)

Therefore, Hayden will complete 6 levels if he plays for \(10\dfrac{1}{4}\) minutes.

The Parallelogram Opposite Sides Theorem and the Parallelogram Opposite Sides Converse as a biconditional statement is, If the opposite sides of a parallelogram are equal in length, then the parallelogram is a rectangle and If the parallelogram is a rectangle, then the opposite sides are equal in length.

What is a parallelogram?

Parallelogram is a quadrilateral with opposite sides parallel and equal and opposite angle are equal.

The Parallelogram Opposite Sides Theorem and the Parallelogram Opposite Sides Converse can be stated as a biconditional statement as follows:

For any parallelogram, the opposite sides are equal in length if and only if the parallelogram is a rectangle.

In other words,

(1) If the opposite sides of a parallelogram are equal in length, then the parallelogram is a rectangle.

(2) If the parallelogram is a rectangle, then the opposite sides are equal in length.

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Answer:

Step-by-step explanation:

Your answer

A = 73

B= 33

C = 40

D = 40

Mark it as Brainlist answer. Follow me.

Part 1.

In this case, we have that

where x denotes the unknown number. Since the mixed number

our equation can be writen as

By multipliying both sides by 7, we have

and by dividing both sides by 12, we get

which means that

so, the missing number for the first question is 2/9

Part 2.

In this case, we have

which can be rewriten as

By multiplying by 3 both sides, we have

and by multiplying by 2 and dividing by 5 both sides, we get

so the answer to the second question is 10

Part 3.

In this case, we have

Answer:

sub to the students notice the best of luck in life is good and u don't know what to do

If the  box has the least possible surface area, then the dimension of box is a square base of 2 meters by 2 meters, and a height of 4 meters.

Let's call the side length of the square bottom "x" and the height of the box "h". Since the box has an open top, we don't need to worry about the surface area of the top. Therefore, we only need to consider the surface area of the bottom and sides.

The volume of the box is given as 32 cubic meters, so we can set up an equation:

Volume = x²h = 32

We want to minimize the surface area, which consists of the area of the bottom and the four sides. The area of the bottom is x², and the area of each side is xh. So, the total surface area is:

Surface Area = x² + 4xh

We can use the equation for the volume to solve for h in terms of x:

h = 32/x²

Substituting this expression for h into the equation for surface area gives:

Surface Area = x² + 4x(32/x²) = x² + 128/x

To minimize the surface area, we can take the derivative of this expression with respect to x and set it equal to zero:

d(Surface Area)/dx = 2x - 128/x² = 0

Solving for x, we get:

2x = 128/x²

x⁵ = 64

x = 2 meters

Substituting this value of x back into the equation for h gives:

h = 32/x² = 4 meters

Therefore, the dimensions of the box with the least possible surface area are:

Length = Width = x = 2 meters

Height = h = 4 meters

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Answer:

10.5

Step-by-step explanation:

I got this answer because since we don't have the minuend( first number of the subtraction problem) so we have to work with the numbers we have. We know that the sum is 8 and since this is a subtraction problem we will add 8 and 2.5 this leaves us with 10.5 so this is what the final rendering of the equation will look like, 10.5-2.5= 8.

Answer:

A

Step-by-step explanation:

using the cosine ratio in the right triangle

cos? = \(\frac{adjacent}{hypotenuse}\) = \(\frac{17}{27}\) , then

? = \(cos^{-1}\) ( \(\frac{17}{27}\) ) ≈ 51° ( to the nearest degree )

The matrix A does not eigenvector v corresponding to the given eigen value.

λ.A = [ -11  60 ]

v = [ 1   3λ ]

v is an eigenvector of A calculate corresponding eigenvalue,

A × v = λ × v

where A is the given matrix.

v is the given vector.

λ is the corresponding eigenvalue.

× denotes matrix multiplication.

Let's first calculate A × v we have,

A × v

= [-11 60] × [ 1 3λ]

= [-11-33λ    60+ 180λ]

Check A× v is equal to λ × v ,

λ × v =

λ × [ 1 3λ]

= [λ  3λ^2]

Set these two vectors equal to each other and get the following system of equations ,

-11-33λ = λ  __(1)

60+ 180λ = 3λ^2  ___(2)

From equation (1) we get,

⇒34λ = -11

⇒ λ = -11/34

Substituting this value of λ into the second equation, we have,

60+ 180λ = 3λ^2

⇒ 60 + 180(-11/34) = 3(-11/34)^2

⇒ (2040 -1980)/ 34 = 3(-11/34)^2

⇒ 60/34 = 3( 11/34)^2

⇒ 60 × 34 = 3 × 11 × 11

⇒20× 34 = 11 × 11

Which is not true.

so the value of λ does not satisfies both equations.

Therefore, v is not an eigenvector of A with corresponding eigenvalue λ.

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The above question is incomplete, the complete question is:

Check whether v is an eigen vector of A  if yes find the corresponding eigen value.

λ.A = [ -11  60 ]

v = [ 1   3λ ]

We know λ = v / f where

λ=wavelength

v=velocity

f=frequency

λ = 200 / 900

λ = 2/9 meters

Answer: The answer is option C: $17,925.00.

Step-by-step explanation: Using the simple interest formula:

I = Prt

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

We can find the interest earned over the 6 years:

I = P * r * t = $15,000 * 0.0325 * 6 = $2,925

Adding the interest to the principal, we get the balance at the end of the 6 years:

Balance = Principal + Interest = $15,000 + $2,925 = $17,925

Therefore, the answer is option C: $17,925.00.

Answer:

The functions that represent this situation are A and C.

Step-by-step explanation:

A geometric sequence goes from one term to the next by always multiplying or dividing by the same value.

In geometric sequences, the ratio between consecutive terms is always the same. We call that ratio the common ratio.

This is the explicit formula for the geometric sequence whose first term is k and common ratio is r

Answer:

no

Step-by-step explanation:

because more food less active

so if you eat more food, and you are less active you don't exercise off the weight

So you would gain weight not lose weight

Answer:

jonwjwjejejeken 20 ow91

The volume of the tent is approximately 700 cubic feet. To find the volume of the tent, we need to use the formula for the volume of a pyramid, which is:

Volume = (1/3) x Base Area x Height

Since the base of the pyramid is a square with sides measuring 60 inches, the base area is:

Base Area = 60 inches x 60 inches = 3600 square inches

The height of the pyramid is given as 84 inches.

Now, we can plug these values into the formula:

Volume = (1/3) x 3600 square inches x 84 inches
Volume = 1,209,600 cubic inches

To convert cubic inches to cubic feet, we need to divide by 12^3, which is 1728:

Volume = 1,209,600 cubic inches ÷ 1728 cubic inches per cubic foot
Volume = 700 cubic feet (rounded to the nearest cubic foot)

Therefore, the volume of the tent is approximately 700 cubic feet.

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Answer:

13

Step-by-step explanation:

The experimental probability would be the number of A’s you have out of the number of quizzes you took:

Experimental probability would be 6/18 which reduces to 1/3

The answer is 1/3

The constants that have to multiply to eliminate one variable from the system are 12 and 5.

The equations are

5x+13y = 232

12x + 7y = 218

Elimination Method

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables

Both x term and y terms, choose x terms  and apply the elimination method

The coefficient of x in the first equation is 5 and 12 in the second equation

Coefficient is a number that is being multiplied by the variable. 2x+6x+14. The 2x, 6x, and 14 are terms because they are being added together. 2 and x; 6 and x are factors because they are being multiplied together. 2 from 2x and 6 from 6x are the coefficients because they are being multiplied by the variable.

To make it the same

Prime factorization

Prime factorization is a process of writing all numbers as a product of primes.

5 = 5×1

12 = 2×2×3

LCM (5, 12 ) = 2×2×3×5 = 60

Multiply the first equation by 12 and the second equation by 5

60x + 156y = 2784

60x + 35y = 1090

Subtract equation 2 from equation 1

121y = 1694

Eliminated x term

The constants that we have to multiply to eliminate one variable from the system are 12 and 5

The complete question is:

Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together? 5x + 13y = 232

12x + 7y = 218

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Answer:

Step-by-step explanation:

You want the value of the piecewise function for various values of x.

The first step in evaluating a piecewise function is determining which domain is applicable to the value of x you have. Then you use the corresponding function, evaluating it in the usual way.

For x = -5, the applicable domain is x < -3, so the function is ...

  h(-5) = -4(-5) -18 = 20 -18

  h(-5) = 2

For x = 0, the applicable domain is -3 ≤ x < 1, so the function is ...

  h(0) = 1

For x = 1 or 4, the applicable domain is x ≥ 1, so the function is ...

  h(1) = 1 +2 = 3

  h(4) = 4 +2 = 6

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the second one is very easy because you are the sweetest person on earth

Answer :

A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

Step-by-step explanation :

We start by dividing the inequality by 3 to get

8 -4x < 2(x-5)

And we can divide by 2 to simplify further to

4 -2x < x-5

Now, we add 2x+5, which gives

9 < 3x

and then divide by 3 again:

3 < x

Hoped it help...