10, 15, 24, 24, 25, 30 What is the mode?

The sum of the sequence based on the function Sn = ( -1 )n + 1 will be -6.

The formula for finding the nth term in an arithmetic sequence given as:

= a + (n - 1)d

Here, Sn is given as ( -1 )n + 1. This is used to illustrate the sum in the sequence. Based on the function given, let's assume that n = 5. Therefore, the 5th term will be:

= (-1)n + 1

= (-1)5 + 1

= (-1)6

= -6

Here is the complete question:

Find the 5th term of a sequence given the function Sn = ( -1 )n + 1.

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The northerly component of the wind blowing at 15 m/s from the South East is approximately 10.605 m/s.

To determine the northerly component of a wind blowing from the South East, we need to consider the direction from which the wind is coming and its magnitude.

A wind blowing from the South East means it is coming from the South East direction towards the opposite direction, which is the North West. Since the wind is coming from the South East, we can say it has a southeasterly direction.

To find the northerly component, we need to break down the wind vector into its north and east components. The northerly component represents the part of the wind that is directed towards the north.

If we assume that the wind is blowing at an angle of 45 degrees with respect to the North, we can use trigonometry to find the components. Since the wind is blowing at 15 m/s, we can consider it as the hypotenuse of a right triangle.

The northerly component can be found using the sine of the angle:

Northerly Component = Wind Speed * sin(Angle)

Northerly Component = 15 m/s * sin(45°)

Using the value of sin(45°) (which is √2 / 2 ≈ 0.707), we can calculate the northerly component:

Northerly Component ≈ 15 m/s * 0.707

Northerly Component ≈ 10.605 m/s

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Answer:12 yes 14 no 16 yes

Step-by-step explanation:its hard to explain

just plug the value in

12.

17 + 5 < 13

22 < 13

false

14.

10/2>6

5>6

false, you are correct

16.

-5 =< 0

it just has to be less OR equal

so it's true, it is a solution

Answer:

first and third expressions

Step-by-step explanation:

using the rule of exponents

\(\frac{a^{m} }{a^{n} }\) = \(a^{m-n}\)

then

\(\frac{3^{\frac{4}{9} } }{3^{\frac{2}{9} } }\)

= \(3^{\frac{4}{9}-\frac{2}{9} }\) ← first expression

= \(3^{\frac{2}{9} }\) ← third expression

Using the Pythagoras theorem, the height of the ladder that it reaches up to wall is 8 feet.

Given that,

Distance of the base of the ladder from the wall = 6 feet

Total height of the ladder = 10 feet

When we consider this as a right angled triangle,

hypotenuse = 10 feet

one leg = 6 feet

Using Pythagoras theorem,

other leg = √(10² - 6²) = 8 feet

Hence the required distance is 8 feet.

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Answer:  D

Step-by-step explanation:

To have a proportional relationship, the value of y divide by x has to have the same constant value and if you were to graph it, it has to go through the origin.

A is not proportional because it is not going through the origin.

B is also not proportional because it is also not going through the origin.

Now to find out if C is proportional divide the y value by x so see if they all have a constant change.

8/2 =4

16/4 = 4

24/8 = 3

32/ 12 = 2.6  

This is also not proportional .

D. 3/2 = 1.5

   6/4 = 1.5

 12/ 8 = 1.5  

 18/12 = 1.5  

This represents a proportional relationship  because they all have a constant change

The proportional relationship between x and y will be given by option D.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

Let's check all the options:

Option A because the line has intercept.

Option B because the line is zero.

Option C:

The slope is given as,

Slope = (16 - 8) / (4 - 2) = 4

Slope = (24 - 16) / (8 - 4) = 2

Slope = (32 - 24) / (12 - 8) = 2

Option D:

The slope is given as,

Slope = (6 - 3) / (4 - 2) = 3/2

Slope = (12 - 6) / (8 - 4) = 3/2

Slope = (18 - 12) / (12 - 8) = 3/2

The proportional relationship between x and y will be given by option D.

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9514 1404 393

Answer:

Step-by-step explanation:

1. In general, restrictions on rational functions refer to values of the variable that make the denominator zero. The function will be undefined in that case. On a graph, such a location will show up as a "hole" or a vertical asymptote.

__

2. If ±2 are excluded from the domain, we expect factors of (x-2)(x+2) in the denominator. That is, the denominator will have a factor of (x²-4). (There may be other factors that do not have real zeros.)

__

3. A rational expression is a fraction the same as any other. The usual rules of addition, subtraction, multiplication, and division apply. For addition and subtraction, it can be useful to identify a common denominator. For multiplication and division, that is not so essential.

Answer:

Well, I can't say which of the following combinations, because I can't see what you see. But I will list some equivalent ratios & hope one fits. If it doesn't, maybe type in the comments what the choices are & I can help more.

Step-by-step explanation:

2:5

4:10

6:15

8:20

10:25

12:30

14:35

The value of d in the image that shows the two parallel lines that are crossed by the transversal is determined as: 125°.

In geometry, a transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects a pair of parallel lines, it creates various angles and relationships between those angles.

The image attached below shows the two parallel lines which are crossed by the transversal, where angle d and 125° are vertical angles.

Since they are vertical angles, they will be equal or congruent to each other. Therefore, the value of d = 125°

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Answer:

hello your question is incomplete attached below is the complete question

answer : 2/13    6/13

               6/13    3/13

Step-by-step explanation:

Firstly we will calculate the orthogonal basis L in R^2

attached below is the detailed solution

also assuming β to be the standard ordered basis

hence the matrix A of the reflection in the Line L in R2 =

2/13    6/13

6/13    3/13

The matrix A of the reflection in line L is given by  \(\rm A = \begin{bmatrix}\dfrac{2}{13} & \dfrac{6}{13}\\ \dfrac{6}{13} & \dfrac{3}{13}\end{bmatrix}\)  and this can be determined by first evaluating the value of \(\rm R^2\) by using the given data.

The orthogonal basis L in \(\rm R^2\) is given by:

\(r = [u_1,u_2] =\left[\dfrac{1}{\sqrt{39} }\binom{6}{3}, \dfrac{1}{\sqrt{39} }\binom{3}{-6}\right]\)

\(\rm T(u_1)=u_1\)

\(\rm T(u_2)=0\)

\(\rm [T]_r = \begin{bmatrix}1 & 0\\ 0 & 0\end{bmatrix}\)

\(\rm Q = \dfrac{1}{\sqrt{39} }\begin{bmatrix}6 & 3\\ 3 & -6\end{bmatrix}\)

Now, matrix A is given by the formula:

\(\rm A=Q[T]_rQ^{-1}\)

Now, substitute the value of known terms in the above equation.

\(\rm A = \dfrac{1}{\sqrt{39} }\begin{bmatrix}6 & 3\\ 3 & -6\end{bmatrix}\begin{bmatrix}1 & 0\\ 0 & 0\end{bmatrix}\dfrac{1}{\sqrt{39} }\begin{bmatrix}6 & 3\\ 3 & -6\end{bmatrix}\)

Simplify the above expression.

\(\rm A = \dfrac{1}{{39} }\begin{bmatrix}6 & 18\\ 18 & 9\end{bmatrix}\)

\(\rm A = \dfrac{3}{{39} }\begin{bmatrix}2 & 6\\ 6 & 3\end{bmatrix}\)

\(\rm A = \dfrac{1}{{13} }\begin{bmatrix}2 & 6\\ 6 & 3\end{bmatrix}\)

Multiply by 1/13 in the matrix.

\(\rm A = \begin{bmatrix}\dfrac{2}{13} & \dfrac{6}{13}\\ \dfrac{6}{13} & \dfrac{3}{13}\end{bmatrix}\)

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Answer:

x_>6 Option 4

Step-by-step explanation:

Answer: x = - 10

Step-by-step explanation:

    We will use the equation given, substitute -1,000 in for y, and solve.

y = x³

(1,000) = x³

\(\sqrt[3]{ (1,000)} = \sqrt[3]{x^3}\)

- 10 = x

x = - 10

Answer:

The common difference in the given sequence is 5.

Step-by-step explanation:

The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15

Answer:

4,896sq

Step-by-step explanation:

just multiply bro

Answer:

104m²

Step-by-step explanation:

\(Area =\frac{b_{12} + b_{2}}{2}*h=\frac{9+17}{2}*8=104m^{2}\)

Given statement solution is :- The y-intercept is (0, -3).

The term "intercept" refers to the location where a line or curve crosses a graph's axis.

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.

To find the x-intercept, we set y = 0 and solve for x.

0 = (1/4)x - 3

Add 3 to both sides:

3 = (1/4)x

Multiply both sides by 4 to isolate x:

12 = x

So the x-intercept is (12, 0).

We set x = 0 and then solve for y to determine the y-intercept.

y = (1/4)(0) - 3

y = -3

So the y-intercept is (0, -3).

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a) The slope of a line perpendicular for the  equation  y=1.9x−4.8 is -1/1.9

b) The slope of a line perpendicular for the  equation  y=−75x+2 is -75.

For the first equation, we can start by realizing that the slope of a line perpendicular to a given line is the negative reciprocal of the slope of a given line. To find the slope of the given line, we can use the point-slope form of a line, y=mx+b, where m is the slope and b is the y-intercept. Now plugging in the given equation, we get 1.9x-4.8=mx+b, which simplifies to m=1.9. taking the negative reciprocal of m=1.9, we get -1/1.0 for the slope of the line perpendicular to the given equation.

For the second equation, we can use the same process as the first. We have y=-75x+2, which can be written as -75x+2 = mx+b. Simplifying, we get m=-75. Taking the negative reciprocal of ma=-75, we get 75/1 for the slope of the line perpendicular to the given equation.

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Answer:

1200

Step-by-step explanation:

it's just 400x3 which is 1200

Answer:-(-1,026/3

Step-by-step explanation:

The function represents a reflection of f(x) = 5(0.8)x across the x-axis is f(x) = -5(0.8)^x

Images that are reflected are mirror images of each other. When a point is reflected across the line y = x, the x-coordinates and y-coordinates change their position. In a similar manner, when a point is reflected across the line y = -x, the coordinates changes position but are negated.

Given the exponential function below

f(x) = 5(0.8)^x

If the function f(x) is reflected over the x-axis, the resulting function will be

-f(x)

This means that we are going to negate the function f(x) as shown;

f(x) = -5(0.8)^x

Hence the function represents a reflection of f(x) = 5(0.8)x across the x-axis is f(x) = -5(0.8)^x

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Answer:

The answer is one solution because the graphs are together in one specific point.

Answer:

Two solutions

Step-by-step explanation:

Answer:

15.75

Step-by-step explanation:

Answer:

Equivalent representations of percent problems

Step-by-step explanation:

Answer

\(\pink\sf{y=-1}\)

Step-by-step explanation

I'm assuming that this exercise is asking us to simplify the equation \(\sf{y=0.5(6)-4}\).

We know that 0.5 (6) means 0.5 multiplied by 6. That is the same as 6 divided by 2, which is 3:

\(\sf{y=3-4}\)

And now we just simplify the last part:

\(\sf{y=-1}\)

∴ answer: y = -1

Answer:

x = 2

Step-by-step explanation:

8 = 6x + -2x

8 = 4x

8 = 4x

4 4

2 = x

Answer:

approximately 28.26 square feet

Step-by-step explanation:

The formula for the area of a circle is A = pi(r)^2. So, the radius is half of the diameter, meaning it's 3 feet. Then we square it to get 9, and multiply by pi, or 3.14. This leads us to the approximated answer of 28.26 square feet.

The area is:

28.27 square feet

Work/explanation:

Since the tabletop is circular, we use the formula for a circle's area, which is: \(\bf{A=\pi r^2}\).

We have the diameter, and to find the radius, we divide the diameter by 2, which gives us 6 ÷ 2 = 3 feet, so the radius of the tabletop is 3 feet.

Now, here's a diagram for you;

\(\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 3\ ft}\end{picture}\)

Plug in the data:

\(\sf{A=\pi\times3^2}\)

\(\sf{A=\pi\times9}\)

\(\sf{A=28.27\:ft^2}\)

Answer:

0

Step-by-step explanation:

-18-(-18)

= -18+18 [(+) + (+)=(+)]

=0 [(-) + (-)=(-)]

the answer is g(x)= (x+6).

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

from the given , we get,

f(x)=x^4

and, f(g(x))= (x+6)^4

hence, the answer is g(x)= (x+6).

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