What is the 8th term in the geometric sequence described by this explicit
formula?
an=6x3(n-1)

The point (9, -7) is the only solution to the system of linear inequalities given.

To determine which point would be a solution to the system of linear inequalities, let's substitute the given points into the inequalities and see which point satisfies both inequalities.

The system of linear inequalities is:

y > -4x + 6

y > (1/3)x - 7

Let's test each given point:

For the point (9, -7):

Substituting the values into the inequalities:

-7 > -4(9) + 6

-7 > -36 + 6

-7 > -30 (True)

-7 > (1/3)(9) - 7

-7 > 3 - 7

-7 > -4 (True)

Since both inequalities are true for the point (9, -7), it is a solution to the system of linear inequalities.

For the point (-12, -2):

Substituting the values into the inequalities:

-2 > -4(-12) + 6

-2 > 48 + 6

-2 > 54 (False)

-2 > (1/3)(-12) - 7

-2 > -4 - 7

-2 > -11 (False)

Since both inequalities are false for the point (-12, -2), it is not a solution to the system of linear inequalities.

For the point (12, 1):

Substituting the values into the inequalities:

1 > -4(12) + 6

1 > -48 + 6

1 > -42 (True)

1 > (1/3)(12) - 7

1 > 4 - 7

1 > -3 (True)

Since both inequalities are true for the point (12, 1), it is a solution to the system of linear inequalities.

For the point (-12, -7):

Substituting the values into the inequalities:

-7 > -4(-12) + 6

-7 > 48 + 6

-7 > 54 (False)

-7 > (1/3)(-12) - 7

-7 > -4 - 7

-7 > -11 (True)

Since one inequality is true and the other is false for the point (-12, -7), it is not a solution to the system of linear inequalities.

In conclusion, the point (9, -7) is the only solution to the system of linear inequalities given.

For similar question on inequalities.

https://brainly.com/question/28755685  

#SPJ8

The height of the scyscraper will be equal to H=251.66 meters

The branch of mathematics set up a relatioship between the angle and the sides of the right angle triangle is called as trigonometry.

Here we have the following data:-

The height of the observer's eye=1.63 meters

The angle which eye is making withe the building=33

The horizontal distance = 385 meters

So the height of the building is calculated as:-

\(Tan\theta=\dfrac{P}{B}\\\\\\tan\theta=\dfrac{H-1.64}{385}\\\\ \\\\tan33=\dfrac{H-1.64}{385}\\\\\\\\\)

H=251.66 meters

hence height of the scyscraper will be equal to \(H=251.66\ meters\)

To know more about Trigonometry follow

https://brainly.com/question/24349828

#SPJ1

Answer:251.7

Step-by-step explanation:

Answer:

x=4

y= 5

Step-by-step explanation:

6x+y=29

3x-y=7

Let's add them together

9x = 36

x= 4

Then put 4 back in the equation for x

6(4) + y =29

24 + y = 29

y= 5

Answer:

A and E

Step-by-step explanation:

Hello!

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

b:7

42:7

6

Hope it helps!

~SparklingFlower

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

Step-by-step explanation:

given

b = 42

given expression,

b ÷ 7 or can be written as b/7

so a/q

42/7 = 6

therefore, 6 is the correct answer.

HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE

As a result, the x-coordinate of the point on the curve closest to the origin is 2.

Coordinates are a pair of integers that are used to locate a point or object in a two-dimensional plane. A point's location on a 2D plane is defined by two integers called the x-coordinate and the y-coordinate. The distance of a point from the y-axis scaled with the x-axis is known as its abscissa or x coordinate. The ordinate is the distance of a point from the x-axis scaled with the y-axis. Coordinates are the abscissa and ordinate combined. To find the coordinates of a point in a coordinate system, do the inverse. Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate.

Here,

The x-coordinate of the point on the curve that is closest to the origin can be found by minimizing the distance between the point on the curve and the origin. The distance between two points (x1, y1) and (x2, y2) is given by the Pythagorean theorem:

d = √((x2 - x1)^2 + (y2 - y1)^2)

For the origin and a point on the curve, we have x1 = y1 = 0, so the distance between the origin and a point (x, y) on the curve is:

d = √(x^2 + y^2)

Using the equation of the curve, we have y = 2 * √(9 - x), so the distance can be expressed as:

d = √(x^2 + (2 * √(9 - x))^2)

= √(x^2 + 4(9 - x))

= √(x^2 + 36 - 4x)

To find the x-coordinate of the point that minimizes d, we can use calculus. Setting the derivative of d with respect to x equal to zero and solving for x, we obtain:

d' / dx = 2x - 4 = 0

x = 2

So the x-coordinate of the point on the curve that is closest to the origin is 2.

To know more about coordinate,

https://brainly.com/question/29189189

#SPJ4

Answer:

B

Step-by-step explanation:

To go from B' to B , perform the inverse operation

That is the translation rule is (x - 4, y - 5 ) , then

B'(7, - 4 ) → B (7 - 4, - 4 - 5 ) → B (3, - 9 ) → option B

The length of the base of the triangle is 3/2 meters.

To find the length of the base of the triangle, we can use the formula for the area of a triangle, which is given by the formula:

Area = (1/2) * base * height.

We are given that the area of the triangle is 3/10 square meters, and the height is 2/5 meters. Let's denote the length of the base as b.

Plugging in the given values into the formula, we have:

(1/2) * b * (2/5) = 3/10.

To solve for b, we can simplify the equation:

b * (2/5) = (3/10) * 2.

Multiplying both sides of the equation by 5/2 to isolate b, we get:

b = (3/10) * 2 * (5/2).

Simplifying further, we have:

b = (3/10) * 5 = 15/10 = 3/2.

In summary, using the formula for the area of a triangle and the given values, we find that the length of the base of the triangle is 3/2 meters.

For more such question on triangle. visit :

https://brainly.com/question/17335144

#SPJ8

A statement that creates a list is my_nums= [5,10,15]. This is also known as array.

An array is a grouping of identically typed elements that are stored in adjacent memory locations and may each be separately referred to using an index to a special identifier. There is no need to declare five distinct variables when declaring an array of five integer values (each with its own identifier).

The three types of arrays are index, multidimensional and associative array.

my_nums= [5,10,15] is an array that stores multiples of 5.

To learn more about array visit the link:

https://brainly.com/question/13261246

#SPJ1

A statement that creates a list is my_nums= [5,10,15]. This is also known as array.

What is an array?

An array is a data structure consisting of a collection of elements (values or variables), each identified by at least one array index or key. An array is a combination of a set of elements which are all of the same data type, organized in a particular way. Arrays are used to store multiple values in a single variable, structure data, and access data more efficiently. Arrays are generally used to represent data in a structured way, and they can be used to perform various mathematical operations and other calculations. Arrays are also useful for sorting and searching data in a predetermined order.

What are three types of array?
The three types of array are index, multidimensional and associative array.
my_nums= [5,10,15] is an array that stores multiples of 5.

To learn more about array visit the link:
https://brainly.com/question/29641515
#SPJ1

Answer:

See below

Step-by-step explanation:

This is a system of equations. That means you are trying to find the point that makes both lines true at the same time.

To do this you have to solve for one variable at a time. Luckily, these equations already have one variable that will cancel. If you add 2x and -2x, you get 0. I'm going to line these up like a vertical math problem to show you how it works.

-2x + 3y = 12

2x +3y = 0                    Add together

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

0x + 6y = 12                Simplify by removing the 0x

6y =12                        Divide both sides by 6 to solve for y

y = 2

Plug 2 in for y in one of the original equations.

2x + 3(2) = 0

2x + 6 = 0                   Subtract 6 from both sides

2x = -6                        Divide by 2 to solve for x

x = -3

The point that makes both lines true is (-3,2). This is where the lines intersect.

The angle x in the diagram is 98 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.

Therefore, let's find the angle of x using the angle relationships as follows:

The size of the angle x can be found as follows:

82 + x = 180(same side interior angles)

Same side interior angles are supplementary.

Hence,

82 + x = 180

x = 180 - 82

x = 98 degrees

learn more on angles here: brainly.com/question/24195209

#SPJ1

(a) The general solution to the differential equation y" + 4y = x sin(2x) is y(x) = c₁cos(2x) + c₂sin(2x) + (Ax + B) sin(2x) + (Cx + D) cos(2x), where c₁, c₂, A, B, C, and D are arbitrary constants. (b) The solution to the differential equation y' = 1 + 3y³ is given by y(x) = [integral of (1 + 3y³) dx] + C, where C is the constant of integration. (c) The general solution to the differential equation y" - 6y = 0 is \(y(x) = c_1e^{(√6x)} + c_2e^{(-√6x)}\), where c₁ and c₂ are arbitrary constants.

(a) To solve the differential equation y" + 4y = x sin(2x), we can use the method of undetermined coefficients. The homogeneous solution to the associated homogeneous equation y" + 4y = 0 is given by y_h(x) = c₁cos(2x) + c₂sin(2x), where c₁ and c₂ are arbitrary constants. Finally, the general solution of the differential equation is y(x) = y_h(x) + y_p(x), where y_h(x) is the homogeneous solution and y_p(x) is the particular solution.

(b) To solve the differential equation y' = 1 + 3y³, we can separate the variables. We rewrite the equation as y' = 3y³ + 1 and then separate the variables by moving the y terms to one side and the x terms to the other side. This gives us:

dy/(3y³ + 1) = dx

(c) To solve the differential equation y" - 6y = 0, we can assume a solution of the form \(y(x) = e^{(rx)}\), where r is a constant to be determined. Substituting this assumed solution into the differential equation, we obtain the characteristic equation r² - 6 = 0. Solving this quadratic equation for r, we find the roots r₁ = √6 and r₂ = -√6.

To know more about differential equation,

https://brainly.com/question/31483896

#SPJ11

Answer:

60 kilograms

Step-by-step explanation:

Given the probability distribution for the angle x of a tree blowing from the vertical, we can see that the probability density function (PDF) is zero for values of x less than or equal to 0. Therefore, we need to calculate the area under the PDF curve for values of x greater than 4.

Using integration, we can find that the area under the curve for x > 4 is approximately 0.7315. This means that the probability of the tree's angle, from the vertical, being greater than 4 degrees is 0.7315 or about 73.15%.

Therefore, there is a high probability that the tree's angle, from the vertical, will be greater than 4 degrees.

To learn more about probability : brainly.com/question/32004014

#SPJ11

Answer:

x=1 y= 7

x=2 y= 10

x=3 y= 13

Step-by-step explanation:

y=3x+4

y=3(1)+4

=7

y=3(2)+4

=-10

y=3(3)+4

=13

Using statistical concepts, it is found that:

From their concepts above, we have that the mean and the range are influenced by outliers.

In this problem, the outlier is at the low end, of 15, hence:

More can be learned about statistical concepts at https://brainly.com/question/24732674

#SPJ1

Answer:

Infinite Solutions

Step-by-step explanation:

6x+6=6(x+1)

6x+6=6x+6

If both sides of the equations are equal, it will ALWAYS be infinite solutions:)

Answer:

Infinite solutions.

Step-by-step explanation:

You have to distribute the 6 to the x and the 1. You'll then realize that both sides have 6x+6, and since 6x-6x=0 and 6-6=0,  If you solve this your answer would be 0=0 this means the problem has an infinite number of solutions.

The answer is option A. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity.

Probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is 0.0229.Round to four decimal places as needed.Based on the calculations the elevator does not appear to be safe.The solution for the given problem is as follows:

Given that, the maximum capacity of the elevator is 1884 lb - 12 passengers.

We can write as below:

Maximum capacity per person=1884/12=157lb.

And, weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.Thus, Z = (157-165) / (32 / √12) = -1.7321Then, P(Z > -1.7321) = 0.9586

Hence, the probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is:P(Z > -1.7321) = 1 - P(Z < -1.7321) = 1 - 0.0229 = 0.9771 (rounded off to 4 decimal places).This probability is greater than 5% and therefore, the elevator does not appear to be safe.

To know more about randomly:

https://brainly.com/question/13319968

#SPJ11

Answer:

1*2(3-2n) = 2(n-2)

Thanks for giving question. I am working my way up to brainliest and Master Answerer

Answer:

Step-by-step explanation:

7

Answer:

1=b

2=f

3=d

4=e

5=a

6=b

So tough question dud

Answer

The answer is 16/3

Step-by-step-explain

F(x) = ⅓ • 4ˣ, F(2)

F(2) = ⅓ • 4²

F(2) = ⅓ • 16

F(2) = 16/3

Thus, The answer is 16/3

-TheUnknownScientist

Answer:

Step-by-step explanation:

16/3

I hope it's helpful

The denominator of the next term in the given Geometric Sequence is 162.

We have been given the following Geometric Sequence whose first four terms are as follows: 1/2, 1/6, 1/18, 1/54

To find the denominator of the next term in the given Geometric Sequence, we need to find the common ratio between consecutive terms of the sequence.

This can be done by dividing any term in the sequence by its previous term or any term after it by its previous term. Therefore, let's divide the second term by the first term:

{1/6}/{1/2} = 1/6. 2/1 = 3

Thus, the common ratio between consecutive terms of the sequence is 1/3.

Now we can use the formula for the nth term of a geometric sequence, where a1 is the first term and r is the common ratio between consecutive terms. This formula is given by:

aⁿ = a₁ rⁿ⁻¹

We need to find the denominator of the next term in the sequence, i.e. the term with index n=5.

We can see that the first term is 1/2 and the common ratio is $1/3. Therefore, the fifth term can be calculated as follows:

a₅ = 1/2 1/3⁴ = 1/2 1/81

= 1/162

Therefore, the denominator of the next term in the given Geometric Sequence is 162.

To learn about Geometric Sequences here:

https://brainly.com/question/30303755

#SPJ11

Answer:

x = 54

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.