Identify if the given sequence is an arithmetic sequence or not. Explain your

answer.

a.) 2, 8, 14, 20, …

b.) 9, 13, 17, 20, 23, …

​

Answer:

The answer is the 3rd one, not equivalent. 8x+4y=4(2x+y)

The mean is approximately 1.67 units of rainfall. The median is 2 units of rainfall.

In statistics, the median is a measure of central tendency that represents the middle value of a set of data. Specifically, it is the value that separates the upper half of the data from the lower half when the data is arranged in order from smallest to largest (or vice versa).

Looking at the line plot, we can see that there are two values marked with a single asterisk and four values marked with two asterisks. Since each asterisk represents a certain amount of rainfall, we can interpret this as follows:

The two values marked with a single asterisk are each 1 unit of rainfall.

The four values marked with two asterisks are each 2 units of rainfall.

Therefore, the data represented in this line plot is as follows:

1, 1, 2, 2, 2, 2

To find the center of this data, we can calculate the mean and median.

The mean is calculated by adding up all the values and dividing by the total number of values. In this case, we have:

(1 + 1 + 2 + 2 + 2 + 2) / 6 = 10 / 6 = 1.67

So the mean is approximately 1.67 units of rainfall.

The median is the middle value when the data is arranged in order. In this case, the data is already in order, so we just need to find the middle value:

The middle value is the average of the two middle numbers:

(2 + 2) / 2 = 2

So the median is 2 units of rainfall.

Based on these calculations, we can conclude that the BEST way to describe the center of the data represented in this line plot is by the median, which is 2 units of rainfall. Therefore, the correct option to complete the statement is:

"The median is 2 inches."

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Step-by-step explanation:

2.5 km = 250000 cm

250000 cm /20000 = 12.5 cm on the map

12.5 cm ^2  x 20 0000 x 20 000   = 5 000 000 000 cm^2 = 500 000 m^2  

Answer:

See below.

Step-by-step explanation:

x+9>17

  -9  -9

x>8

-hope it helps

Answer:

x = 6

Step-by-step explanation:

pythagorean theorem

a^2 = c^2 - b^2

a^2 = 10^2 - 8^2

a^2 = 100 - 64

a^2 = 36

sqrt a^2 = sqrt 36

a = 6

CHECK:

6^2 + 8^2 = 10^2

36 + 64 = 100

yes.

Answer:

The triangle has an area of 192cm^2

Step-by-step explanation:

Given;

the formula to find the area of the triangle,

\(A=\frac{h_{b}b }{2}\)

We can insert the values,

\(A=\frac{24*16}{2} \\\\\\A=\frac{384}{2} \\\\A=192cm^2\)

The area of the triangle is 192cm^2.

the correct answer is negitive one hundred eighty (-180)

Answer:

the solution to the system of inequality is C

Step-by-step explanation:

points on the line: (4, -2) & (-5, 3)

gradient of the line = -5/9

general equation for all straight lines: y = mx + c

substitute one coordinate and the gradient into the equation. 3 = (-5/9)(-5) + c

therefore, c = 2/9

so the general equation is y = (-5/9)x + 2/9

Answer:

13/14

Step-by-step explanation:

Area of a rectangle = l * b

=> 4 1/3 = 3 1/2 + b

=> (4 1/3) / (3 1/2) = b

=> (13/4) / 7/2  = b

=> 13/4 * 2/7

=> 13/2 * 1/7

=> 13/14

Therefore the width = 13/14

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Answer:

\(\boxed {\boxed {\sf 136}}\)

Step-by-step explanation:

The quadratic formula helps us find the roots of a quadratic equation. The equation is:

\(\begin{array}{*{20}c} {x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} } \\ \end{array}\)

where \(ax^2+bx+c=0\)

The discriminant is just the part under the square root. This helps tell us if there are two, one, or zero real solutions.

The discriminant is:

\(b^2-4ac\)

We are given the quadratic: \(9x^2-8x-2=0\)

Therefore, a is 9, b is -8, and c is -2.

\(a=9 \\ b= -8 \\c= -2\\\)

\((-8)^2-[4(9)(-2)]\)

Solve the exponent.

\(64-[4(9)(-2)]\)

Multiply 4, 9, and -2.

\(64-(-72) = 64+72 \\=136\)

The discriminant is 136. Since it is a non-zero, positive number, this quadratic has 2 real solutions/zeroes/roots.

The solution to the system of equations (x,y) are (-1, 2).

A system of equations is a group of two or more equations with the same variables.

A solution to a system of equations is the values of the variables that make all of the equations in the system true. A solution to a system is also an intersection point of the graphs of the equations in the system.

To solve this problem, we need to find x and y which will give us two solutions to the problem.

The value of x and y are -1 and 2 respectively.

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The most appropriate choice for combination will be given by-

Models can wear 112 different types of outfit.

What is combination?

Combination determines the number of ways of selecting some number of particular items from a group of given item, here the order of selection do not matter.

If there are n objects and from there, r objects are chosen, number of ways will be given by

                                  \(n \choose r\) = \(\frac{n!}{(n - r)! \times r!}\)

Here,

Number of tops = 7

Number of pants = 2

Number of jackets = 8

From 7 tops the designer can choose 1 top in \(7 \choose 1\) ways

                                                                        = \(\frac{7!}{(7-1)!\times 1 !}\)

                                                                        = \(\frac{7!}{6!}\)

                                                                        = \(7\)

From 2 pants the designer can choose 1 pant in \(2 \choose 1\) ways

                                                                        = \(\frac{2!}{(2-1)!\times 1 !}\)

                                                                        = \(\frac{2!}{1!}\)

                                                                        = \(2\)

From 8 jackets the designer can choose 1 jacket in \(8 \choose 1\) ways

                                                                        = \(\frac{8!}{(8-1)!\times 1 !}\)

                                                                        = \(\frac{8!}{7!}\)

                                                                        = \(8\)

Total number of different outfits models can wear = \(7 \times 2 \times 8\)

                                                                             = 112

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Answer and Step-by-step explanation:

Since it is a degree 3 polynomial, then it should have 3 solutions. But only one is given -7i which is an imaginary number. Since -7i is part of the solutions, then definitely, +7i is also part of the solutions. Since we are not given the last root, I would choose a suitable number in order to explain the process. Let us choose 1. Therefore, our roots are now:

±7i and 1.

In order to find the polynomial, we have:

x = +7i or –7i or 1, this means:

f(x) = (x – 7i)(x + 7i)(x – 1)

f(x) = [x² +7ix – 7ix – (7i)²](x – 1) = [x² – 49(–1)](x – 1) = (x² + 49)(x – 1) = x³ – x² + 49x – 49

Answer:

12

Step-by-step explanation:

Pythagoras Theorem is clearly used in this question.

To Calculate the Hypotenuse:

C = \(\sqrt{a^2+b^2}\)

The Adjacent angle has already given as 9, so you can factor that into the question.

In Order to calculate the Opposite angle you need to use the following formula.

\(b = \sqrt{c^2-a^2}\)

With the integers we already have for both Hypotenuse and Adjacent factored in this will be your equation:

\(b = \sqrt{15^2-9^2} = 12\)

Therefore you answer is 12, Hope this helps, feel free to make as brainilest.

Answer:

56 5/12 inches tall

Step-by-step explanation:

add karina and Janes inches together than add Cesar and then theres the height

Sand will be placed under the base of a circular pool with a diameter of 14 feet. 1 bag of sand covers about 5 square feet. the number of bags of sand required is 30bags.

The area of the pool is

 A = πr²

 A = 3.14×(7 ft)² = 153.8 ft²

The number of bags of sand required is ...

 (153.8 ft²)/(5 ft²/bag) ≈ 30.76bags

bags of sand are needed.

The diameter is defined as twice the length of the radius of the circle. The radius is measured from the centre of the circle to one endpoint on the boundary of the circle, while the diameter is the distance  measured from one end of the circle to a point on the other end of the circle that passes through the centre. This is indicated by the letter D. The circumference of  a circle has an infinite number of points, which means that the circle has an infinite number of diameters and each diameter of the circle is the same length.

Ø is the symbol  used in the design to indicate the diameter. This symbol is often used in technical data and drawings.

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Since the point negative 4.5 (-4.5) is labeled on this number line representing temperature change, the absolute value of the point labeled in the image means that: B. the temperature equals 4.5 degrees.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

In conclusion, the absolute value of a number is always positive and it can be used for describing the distance of a number from zero (0) on the number line, without taking its direction into consideration.

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Step-by-step explanation:

To determine whether the quadratic function has a minimum or maximum, we need to look at the sign of the coefficient of the squared term. If the coefficient is positive, then the function has a minimum. If the coefficient is negative, then the function has a maximum. In this case, the coefficient of the squared term is positive (since it's a product of two positive factors), so the function has a minimum.

To find the minimum value of the function, we can use the formula:

x = -b / (2a)

where a is the coefficient of the squared term, b is the coefficient of the linear term, and x is the x-coordinate of the minimum (or maximum) point.

In this case, the quadratic function can be written in standard form as:

f(x) = 3x^2 + 42x + 72

where a = 3 and b = 42. Substituting these values into the formula, we get:

x = -42 / (2*3) = -7

So the minimum point occurs at x = -7. To find the corresponding minimum value of the function, we can substitute x = -7 into the original expression:

f(-7) = 3(-7+4)(-7+6) = 3*(-3)*(-1) = 9

Therefore, the quadratic function has a minimum value of 9, which occurs at x = -7.

There are 10,626 ways of arranging the required offices from a body of 24 students.

Combination deals with the way in which a arrangement can be made from a particular lot. In  this case, we want to select  a president, minister of Arts, minister of PE department, and minister of Science from a body of 24 students.

Hence;

24C4 = 24!/4! (24 - 4)! = 24!/4!20!

So;

24 * 23 * 22 * 21 * 20!/20! * 4 * 3 * 2*1

= 24 * 23 * 22 * 21 / 4 * 3 * 2*1

= 10,626 ways

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Answer:

x = 16

Step-by-step explanation:

Opposite sides are equal in a parallelogram

AD = BC

5x - 12 = 3x + 20

5x - 3x = 20 + 12

2x = 32

x = 32/2

x = 16

Answer:

1,908is the       answer you need

Part 1

The equation is \(y=a(x+8)(x-72)\).

Using the point \((62, -490)\) to solve for \(a\),

\(-490=a(62+8)(62-72) \implies a=\frac{7}{10}\\\\\therefore \boxed{y=\frac{7}{10}(x+8)(x-72)}\)

Part 2

When \(x=-8\), \(y=0\).

When \(x=2\), \(y=-490\).

So, the average rate of change is \(\frac{-490-0}{2-(-8)}=\boxed{-49}\)

The coordinates points and quadrants on the grid shown above are listed below.

In Mathematics, a quadrant simply refers to the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate.

Based on the cartesian coordinate (grid) above, the coordinates points and quadrants should be identified as follows;

In conclusion, you should take note of the points on the x-axis and y-axis of the cartesian coordinate (grid).

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The equation is: (2x + 8) / 4 - 3 = x - 7

The solution is x = 12

Let x be the number you thought of at the beginning. Following the steps:

Multiply by 2: 2x

Add 8: 2x + 8

Divide by 4: (2x + 8) / 4

Subtract 3: (2x + 8) / 4 - 3

The final answer is seven less than the number you thought of at the beginning: (2x + 8) / 4 - 3 = x - 7

The equation is: (2x + 8) / 4 - 3 = x - 7

2. (2x + 8) / 4 - 3 = x - 7

(1/2)x + 2 - 3 = x - 7

(1/2)x - 1 = x - 7

Now add 1 to both sides:

(1/2)x = x - 6

Subtract (1/2)x from both sides:

-1/2x = -6

Now multiply both sides by -2:

x = 12

3. Properties used to solve the puzzle

Addition Property of Equality

Multiplication Property of Equality

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Answer: < or >

Step-by-step explanation: