write the explicit formula for an, nth the term of the sequence 17,20,23

Answer:

x = 2.5

Step-by-step explanation:

           y = -3x + 14   -----------(I)

3x - 5y = -25 -------------------(II)

Substitute y = -3x + 14 in equation (II),

             3x -5 ( -3x + 14) = -25

          3x  + 5 * 3x - 5*14 = -25

            3x  + 15x - 70      = -25    {Combine like terms}

                        18x - 70   = -25  

Add 70 to both sides,

                                 18x = -25 + 70

                                 18x = 45

Divide both sides by 18,

                                    x = 45 ÷ 18

                                   x = 2.5

Answer:

The value of x in the solution to the system of equations is x = 7.

Here's the explanation and verification:

Solve for X in the first equation:

Y = -3X + 14

X = (Y - 14) / -3

Substitute this expression for X into the second equation:

3X - 5Y = -25

3((Y - 14) / -3) - 5Y = -25

Simplify this expression:

Y + 42 / 3 + 5Y = -25

6Y + 42 / 3 = -25

Solve for Y:

6Y = -25 - 42 / 3

6Y = -25 - 14

6Y = -39

Y = -39 / 6

Y = -6.5

Substitute this value of Y back into the expression for X that you found in step 1:

X = (Y - 14) / -3

X = (-6.5 - 14) / -3

X = (-20.5) / -3

X = 6.83

Round the answer to the nearest integer, so X = 7.

Verification:

Now that you have found the values of X and Y, you can verify that they are a solution to the system of equations by plugging them back into the original equations and seeing if they make both sides equal.

Y = -3X + 14

Plug in X = 7 and Y = -6.5:

-6.5 = -3 * 7 + 14

-6.5 = -21 + 14

-6.5 = -7

3X - 5Y = -25

Plug in X = 7 and Y = -6.5:

3 * 7 - 5 * -6.5 = -25

21 + 32.5 = -25

53.5 = -25

Both equations evaluate to true, so X = 7 and Y = -6.5 is a solution to the system of equations.

Answer:

271.2 meters

Step-by-step explanation:

See attached image.

Answer:

-4.23230, -4.232300, -4.2323000

Answer:

1) -4.23230 2)-4.232300 3)-4.2323000

Step-by-step explanation:

Where is my brainliest and my points :)

Answer:

Let x be the width of the pool. Then the length of the pool is 2x, since it is twice as long as it is wide.

The area of the pool is (2x)(x)=2x^2

The total area of the pool and the walkway is 2x^2+196 square feet.

We can set up the equation using this information:

2x^2 + 22x = 196

Where 22x is the area of the walkway, 22x = 2x * 2 = 4x

2x^2 + 4x = 196

2x^2 + 4x - 196 = 0

Using the quadratic formula to solve the equation above:

x = (-b ± √(b^2 - 4ac))/2a

x = (-4 ± √(4^2 - 42196))/2*2

x = (-4 ± √(16 - 1568))/4

x = (-4 ± √(-1552))/4

Since x is width of the pool, it cannot be a negative value, the x value that is negative must be rejected. Therefore x = (-4 + √1552)/4 = 8

The width of the pool is 8 feet and the length is 2x = 2*8 = 16 feet

Answer:

20 stones

Step-by-step explanation:

The perimeter of the garden is 10 feet.

He uses stones that are 1/2 foot long each to edge the garden.

The number of stones he will need can be gotten by simply dividing the perimeter of the garden by the length of each stone:

10 / 1/2 = 20 stones

He will need 20 stones.

Answer:

284.012

Step-by-step explanation:

Hope this awnsers your question!

Answer:

284.012

Step-by-step explanation:

Answer:

Isosceles Triangle

Step-by-step explanation:

Represents the vector f + g.  C.

The sum of two vectors, we simply add their corresponding components.

In this case,
f + g = (4 - 1, 3 + 0, 7 + 2) = (3, 3, 9)
So the resulting vector has components (3, 3, 9).
Now we need to find the graph that represents this vector.

Graphing a vector in three dimensions can be challenging, but we can use the following method:
Start at the origin (0, 0, 0) of the 3D coordinate system.
Move 3 units in the x-direction, 3 units in the y-direction, and 9 units in the z-direction.
Mark the endpoint of this displacement as the tip of the vector.

Option A has a similar direction, but it is longer than f + g.

Option B has the correct length, but it is pointing in the wrong direction.

Option D is pointing in the correct direction, but it is too short.

We only add the respective components of the two vectors to get their sum.

Thus, f + g = (4 - 1, 3 + 0, 7 + 2) = (3, 3, 9) in this situation.

The resultant vector has three (3), three (3), and nine (9).

We now need to identify the graph that this vector is represented by.

It might be difficult to graph a vector in three dimensions, however we can try the following approach:

Start at the 3D coordinate system's origin (0, 0, 0).

Move three units in the x, three units in the y, and nine units in the z directions.

Make a note of the vector's tip being the terminus of this displacement.

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Answer:

\(\frac{80-19.25}{6.75} = x\)

Step-by-step explanation:

Subtract $19.25 from the Amount Used for Payment ($80) to get the amount spent, then divide the amount of each sandwich to get the amount of sandwiches bought.

The measurement that is closest to the value of x, in centimeters, is given as follows:

14.3.

In this problem, we have a right triangle, in which the legs, which are the sides between the angle of 90º, are of 11.9 cm and 7.9 cm.

Then the hypotenuse x, which is the segment connecting both legs, is obtained using the Pythagorean Theorem.

The Pythagorean Theorem states that the measure of the hypotenuse squared is equals to the sum of the squares of the measures of each side.

Then the length of x is calculated as follows:

x² = 11.9² + 7.9²

x = square root of (11.9² + 7.9²)

x = 14.28.

Closest to 14.3, rounding to the nearest tenth, meaning that the third option is correct.  

We suppose that 11.9 cm and 7.9 cm are the measures of the legs.

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Work Shown:

The triangle has the given angles A = 45 and B = 89

Let's find angle C

A+B+C = 180

C = 180-A-B

C = 180-45-89

C = 46

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

Segment BA, or side c, is opposite angle C

Segment AC, or side b, is opposite angle B

So we have this known info:

Apply the law of sines to find c. Make sure your calculator is in degree mode.

sin(B)/b = sin(C)/c

sin(89)/15 = sin(46)/c

c*sin(89) = 15*sin(46)

c = 15*sin(46)/sin(89)

c = 10.7917406394501

c = 10.8

The area inside the curve r = 3 + sin(θ) is (5π)/2 square units.

Double integration is an important tool in calculus that allow us to calculate the area of irregular shapes in the Cartesian coordinate system. In particular, they are useful when we are dealing with shapes that are defined in polar coordinates.

To find the area inside this curve, we can use a double integral in polar coordinates. The general form of a double integral over a region R in the xy-plane is given by:

∬R f(x,y) dA

where dA represents the infinitesimal area element, and f(x,y) is the function that we want to integrate over the region R.

In polar coordinates, we can express dA as r dr dθ, where r is the distance from the origin to a point in the region R, and θ is the angle that this point makes with the positive x-axis. Using this expression, we can write the double integral in polar coordinates as:

∬R f(x,y) dA = ∫θ₁θ₂ ∫r₁r₂ f(r,θ) r dr dθ

where r₁ and r₂ are the minimum and maximum values of r over the region R, and θ₁ and θ₂ are the minimum and maximum values of θ.

To find the area inside the curve r = 3 + sin(θ), we can set f(r,θ) = 1, since we are interested in calculating the area and not some other function. The limits of integration can be determined by finding the values of r and θ that define the region enclosed by the curve.

To do this, we first note that the curve r = 3 + sin(θ) represents a cardioid, which is a type of curve that is symmetric about the x-axis. Therefore, we only need to consider the region in the first quadrant, where 0 ≤ θ ≤ π/2.

To find the limits of integration for r, we note that the curve intersects the x-axis when r = 0. Therefore, the minimum value of r is 0. The maximum value of r can be found by setting θ = π/2 and solving for r:

r = 3 + sin(π/2) = 4

Therefore, the limits of integration for r are r₁ = 0 and r₂ = 4.

The limits of integration for θ are simply θ₁ = 0 and θ₂ = π/2, since we are only considering the region in the first quadrant.

Putting it all together, we have:

Area = ∬R 1 dA

        = ∫\(0^{\pi /2}\) ∫0⁴ 1 r dr dθ

Evaluating this integral gives us:

Area = π(3² - 2²)/2 = (5π)/2

Therefore, the area inside the curve r = 3 + sin(θ) is (5π)/2 square units.

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Using double integrals, the area inside the curve r = 3 + sin(θ) is 0 units².

For the area inside the curve r = 3 + sin(θ), we can use a double integral in polar coordinates. The area can be expressed as:

A = ∬R r dr dθ

where R represents the region enclosed by the curve.

In this case, the curve r = 3 + sin(θ) represents a cardioid shape. To determine the limits of integration for r and θ, we need to find the bounds where the curve intersects.

To find the bounds for θ, we set the expression inside sin(θ) equal to zero:

3 + sin(θ) = 0

sin(θ) = -3

However, sin(θ) cannot be less than -1 or greater than 1. Therefore, there are no solutions for θ in this case.

Since there are no intersections, the region R is empty, and the area inside the curve r = 3 + sin(θ) is zero.

Hence, the area inside the curve r = 3 + sin(θ) is 0 units².

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Answer:

acute triangle

Step-by-step explanation:If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is an acute triangle.

Answer:

Step-by-step explanation:

d

Answer:

Step-by-step explanation:

The mass of a substance when given the density and volume can be found by using the formula

From the question

Density = 0.789 g/mL

volume = 200 mL

Substitute the values into the above formula and solve for the mass

That's

mass = 0.789 × 200

We have the final answer as

Hope this helps you

The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

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Answer:

The answer is 13x-7

Step-by-step explanation:

f(x) is x-7, and g(x) is 4x3. 4x3 can also mean 12x , because 4x3 is 4*x*3. So, f(x) can be replaced with x-7, and g(x) can be replaced by 12x. (x-7)+(12x) is 13x-7.

The numbers are 49 and 7 when both are positive and their sum is 56, is equal to the square of the other if they are both positive.

Given that,

We have to find the number that, if both are positive and their sum is 56, is equal to the square of the other if they are both positive.

We know that,

Let the numbers be x and y.

x=y²

x and y are positive

Sum is 56

x+y=56

Substitute x =y² in equation

y²+y=56

y²+y-56=0

y²+8y-7y-56=0

y(y+8)-7(y+8)=0

(y+8)(y-7)=0

y=7 and -8

The number are positive so y is 7.

Substitute x=y²

x=7²

x=49

Therefore, The numbers are 49 and 7 when both are positive and their sum is 56, is equal to the square of the other if they are both positive.

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Given that rates of the ingredients, the cost per unit of each ingredients can be calculated as follows,

Given the composition of each taco as, 1 tortilla, 0.25 pounds of beef, 0.125 pounds of beans, 0.0625 pounds of cheese, 1 ounce of Salsa.

Then the cost of taco (C) is calculated as the sum of the product of each ingredient per unit and number of units of that ingredient requires for 1 taco,

Thus, the cost of each taco is $1.17285 approximately.

The x-axis denotes blocks and the y-axis denotes the blocks per game .

Scatter - Plot : Scatter plots are an essential type of data visualization that shows relationships between variables . The variables are plotted on the x - axis and the y - axis .

Each of the points on a scatter plot is represented by a dot . It shows how strongly two variables are related .

In the given question , we have to label the axes ,

Labelling axes of a Scatter-Plot :

x-axis denotes blocks

y-axis denotes blocks per game

Hence , the x-axis denotes blocks and the y-axis denotes the blocks per game .

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Answer:

no

Step-by-step explanation:

Answer:

The concentration in both solutions is the same.

Step-by-step explanation:

Equilibrium> EQUAL

Answer:

The solution is the triplet: (a, b, c) = (-3, 0, 0)

Step-by-step explanation:

Let's start with the second equation, and solving for "a":

a - b = -3

a = b - 3

Now replace this expression for a in the third equation:

2 a + b = -6

2 (b - 3) +b = -6

2 b - 6 +b = -6

3 b = -6 +6

3 b = 0

b = 0

So if b = 0 then a = 0 - 3 = -3

now we can replace a= -3, and b = 0  in the first equation and solve for c:

2 a - b + c = -6

2 ( -3) - 0 + c = -6

-6+ c = -6

c = -6 + 6

c = 0

Our solution is a = -3, b= 0 , and c = 0 which can be expressed as (-3, 0, 0)

Answer:

$1.25

Step-by-step explanation:

Subtract $0.25 by $1.50

$1.50-$0.25=$1.25

The answer is, the correct statement are , 1. The matrix B² is positive definite if A is positive definite. ,2. A square matrix and its transpose have the same set of eigenvectors. , 3. A real square matrix has only real eigenvalues. , 4. The dimension of the row space of a matrix A with rank 4 is 4. , 5. The dimension of the null space of matrix A is 4.

the correct statements from the options provided:

1. The matrix B² is positive definite if A is positive definite.
2. A square matrix and its transpose have the same set of eigenvectors.
3. A real square matrix has only real eigenvalues.
4. The dimension of the row space of a matrix A with rank 4 is 4.
5. The dimension of the null space of matrix A is 4.

Please note that the statements regarding the values of x, dx, v, r, Av, and trace are incomplete or incorrect, so I have not included them in my answer.

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The function which represents the cost to drive a car from this agency miles x a day is :

C(x) = 15, if 0 ≤ x ≤ 200

      = 15 + 0.05x, if x > 200

Given that,

A car rental agency charges $15 a day for driving a car 200 miles or less.

The function can be written as,

C(x) = 15 if 0 ≤ x ≤ 200

If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.

C(x) = 15 + 0.05x, if x > 200

Hence the correct option is D.

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1. (A)  Section titles  (lines starting with %% followed by a space and then a title).

2. (B)  Automatically pause code execution at the start of each section when running a script. (This is not a purpose of code in the MATLAB Editor.)

3. All these functions operate element-wise on each element of the matrix X and return a matrix of the same size.

The source of the section headers in the resulting document when publishing a script from the MATLAB Editor is:

a. Section titles (lines starting with %% followed by a space and then a title).

The statement that is not true about the purpose of code in the MATLAB Editor is:

b. Automatically pause code execution at the start of each section when running a script. (This is not a purpose of code in the MATLAB Editor.)

3. The commands that return a matrix of the same size as x, given a non-scalar matrix X, are:

a. mean(x)

b. sin(x)

c. log(x)

d. sum(x)

e. std(x)

f. sqrt(x)

All these functions operate element-wise on each element of the matrix X and return a matrix of the same size.

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Step 1: Write out the expression to simplify

Step 2: Remove the bracket using distribution property

Step 3: Rewrite the resulting expression in order of degree and state the degree and the number of terms

The degree is 3 (third degree) as the highest power of the variable is 3, there are three terms in the expression

Hence, the expression is a cubic expression (degree 3) and a trinomial (3 terms)