Can the expression m2 + 4m + 6 be factored into a product of two binomials?

The given sequence starts with 4, and each subsequent term alternates between adding 2 and subtracting 3, based on whether the previous term is even or odd.

The recursive definition for the given sequence 4, 2, 5, 1, 6, ... can be defined as follows:

1. The first term of the sequence is 4.

2. Each subsequent term is obtained by alternating between adding 2 and subtracting 3 from the previous term.

In other words, if the previous term is even, the next term is obtained by adding 2, and if the previous term is odd, the next term is obtained by subtracting 3.

Term 1: 4 (given)

Term 2: 4 + 2 = 6 (even, added 2)

Term 3: 6 - 3 = 3 (odd, subtracted 3)

Term 4: 3 + 2 = 5 (odd, added 2)

Term 5: 5 - 3 = 2 (even, subtracted 3)

Term 6: 2 + 2 = 4 (even, added 2)

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Note that the most appropriate measure of center in this case is the median, as it is less affected by extreme values. The value of the median is 6.4.

The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution in statistics and probability theory. It is sometimes referred to as "the middle" value in a data collection.

The median is the value in the center of a set of data. First, arrange and sort the data in ascending order from smallest to largest.

Divide the number of observations by two to obtain the midway value. If there are an odd number of observations, round that number up to the next whole number, and the value in that location is the median.

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Answer

she can buy 22 pens

Step-by-step explanation:

.55n+2.85p>24

2.85(4)=11.4

24-11.4=12.6/.55=22

Answer:

27 pens

Step-by-step explanation:

4×228=912

for 4 notebooks she spend $9.12

2400-912=1488

$14.88 left

1488÷055=27.05

Answer:

f(12) = 11

Step-by-step explanation:

Step 1: Define

f(x) = 2/3x + 3

f(12) is x = 12

Step 2: Substitute and Evaluate

f(12) = 2/3(12) + 3

f(12) = 8 + 3

f(12) = 11

Answer:

152.32

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Answer:

I = 1

Step-by-step explanation:

If the w has to be multiplied by one in order to be the same on the other side of the equation.

Answer:

Hello! I hope I’m correct!

Step-by-step explanation:

I think the answer should be: l = 1

First we should flip the equation.

And than divide both sides by w.

Therefore the answer would be:

i = 1

Hope this helps!

If you have any questions about this problem, feel free to ask them!

By: BrainlyAnime ^-^

The range of the function y = 4x + 1 is {y | 1 ≤ y ≤ 41}.

What is the range of data?

The range of data is defined as a measure of the difference between the maximum value of data and the minimum value of data.

The function is given as y = 4x + 1.

The range of the function y = 4x + 1 is the set of all possible output values that the function can produce.

Given that the domain of the function is 0 ≤ x ≤ 10.

The range of this function is the set of all y-values that can be obtained by plugging in x-values between 0 and 10 into the function.

Plugging in x = 0, the value for y = 4(0) + 1 = 1.

Plugging in x = 10, the value for y = 4(10) + 1 = 41.

The range of the function y = 4x + 1 is the set of all y-values between 1 and 41, inclusive.

Therefore, the range of the function is {y | 1 ≤ y ≤ 41}.

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Answer:

The image is not clear but get the idea

Answer: x=4+2i , x=4-2i hope this helps tho :>

Step-by-step explanation

The solutions to the equation x 2 −8x+20=0 are x= 10,-2.

The equation  x 2 −8x+20=0  can be written as (x-10) (x+2) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x-10=0

x+2=0

so, the solution to the equation x 2 −8x+20=0 are x=10 and x=-2.

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Answer:

3

Step-by-step explanation:

slope is rise over run

also, change in y/change in x

slope formula is : (y2-y1)/(x2-x1)

where variables are points in line (x1, y1), (x2, y2)

pick two points where the line passes through a cross

(0,0) and (1,3)

use slope formula

(3-0)/(1-0)

=3/1

=3

slope is 3

The instantaneous acceleration at any time t is given by 10t. The limit definition of a derivative is true because it allows us to find the instantaneous rate of change of a function at a specific point.

To use the limit definition of a derivative to calculate instantaneous acceleration, we need to find the derivative of the velocity function with respect to time. The derivative of velocity gives us acceleration.

The limit definition of a derivative is given by:

f'(x) = lim (h→0) [f(x+h) - f(x)] / h

To calculate instantaneous acceleration, we substitute the velocity function, v(t), into the limit definition. Let's say v(t) = 5t^2.

Using the limit definition, we have:

a(t) = lim (h→0) [v(t+h) - v(t)] / h

Substituting v(t) = 5t^2, we get:

a(t) = lim (h→0) [5(t+h)^2 - 5t^2] / h

Expanding and simplifying:

a(t) = lim (h→0) [10th + 5h^2] / h

Now, we can cancel out the h term:

a(t) = lim (h→0) 10t + 5h

Taking the limit as h approaches 0, we get:

a(t) = 10t

Therefore, the instantaneous acceleration at any time t is given by 10t.

The limit definition of a derivative is true because it allows us to find the instantaneous rate of change of a function at a specific point. By taking the limit as the change in input approaches zero, we are able to approximate the exact rate of change at that point. This concept is fundamental to calculus and is used in various applications such as physics, engineering, and economics.

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Answer:

1

Step-by-step explanation:

16-9=5t+2t

7=7t

1=t

Answer:

t = 1

Step-by-step explanation:

16 - 2t = 5t + 9

=> 16 - 2t - 9 = 5t

=> 16 - 9 = 5t + 2t

=> 7 = 7t

=> 7/7 = t

=> 1/1 = t

=> 1 = t

If repetitions of colors are allowed, there are 59,049 possible selections of collars for the 5 cats.

If Dave can choose from 9 different colors for each of his 5 cats, then he has 9 choices for the first cat, 9 for the second cat, and so on. To find the total number of possible selections, we can multiply the number of choices for each cat together:

9 x 9 x 9 x 9 x 9 = 59,049

In this case, there are 9 ways to choose the collar color for the first cat. Since Dave can choose from the same 9 colors for each of the 5 cats, so he has 9 choices for each cat. Therefore, by the principle of counting, the total number of ways to choose collars for all 5 cats is:

Therefore, if repetitions of colors are allowed, there are 59,049 possible selections of collars for the 5 cats.

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Answer: Conditional frequencies enables users to get more specific information when analyzing a dataset.

Step-by-step explanation: Frequency refers to the count of occurrence of a particular variable.

Relative frequency is obtained by taking the ratio of the counts a particular variable and the total counts and of all available variables in the experiment or data.

Conditional Frequency allows us to input additional constraints to our frequency counts, especially in a two-way table. Enabling us to get more specific information by using conditional statements.

The pair of vertically opposite angles are ∠1 and ∠3 and ∠4 and ∠2.

Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines and are opposite to each other.

Vertically opposite angles share the same vertex  point.

In other words, vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines

Vertically opposite angles are congruent to each other.

Therefore, the pair of vertical angles are as follows:

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When employees have different responsibilities, those relationships can be modeled with multiple associations between the employee class and the linked class.

In object-oriented programming, a class is a blueprint for creating objects that have similar properties and behaviors. One of the key concepts in class design is associations, which represent relationships between classes. Associations are used to define how objects of one class are connected to objects of another class.

When employees have different responsibilities, it means that there are multiple ways in which they can be associated with other classes. For example, a software company may have a class of employees who are responsible for developing software, and another class of employees who are responsible for testing the software. Each of these classes has a different set of responsibilities and requires different skills and knowledge.

To model these relationships, we can create multiple associations between the employee class and the linked class. For example, we could create one association between the employee class and the software development class, and another association between the employee class and the software testing class. Each of these associations would have different attributes, such as the employee's role, responsibilities, and qualifications.

By modeling these relationships with multiple associations, we can create more accurate and flexible class designs that reflect the real-world relationships between employees and their responsibilities. This approach also allows us to easily modify or extend the class design as the requirements change, without having to make major changes to the existing code. Overall, multiple associations provide a powerful tool for designing robust and adaptable class structures.

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Answer:

39 ft^2

Step-by-step explanation:

To find surface area you add up the all the areas of the shapes.

Triangle:

5x3=15

15/2= 7.5

Since there are 4 triangles its 7.5x4 which is 30.

Square:

3x3=9

7.5+7.5+7.5+7.5+9 or 30+9= 39

39 ft squared.

Answer:

Step-by-step explanation:

I think it’s translation because your just sliding the figure

Answer:

im pretty sure its 1/2 pitcher.

Step-by-step explanation:

Answer:

-5/12≈ -0.417−0.417

Step-by-step explanation:

Step 1 of 2: Subtract.

Subtract

1 over 3

1

3

− 3 over 4

3

4

= negative 5 over 12−  

5

12

Step 1 of 2: Subtract, sub-step a: Find common denominator.

Find common denominator

1 over 3

1

3

− 3 over 4

3

4

= ( 1 × 4 ) over ( 3 × 4 )

1 × 4

3 × 4

− ( 3 × 3 ) over ( 4 × 3 )

3 × 3

4 × 3

= 4 over 12

4

12

− 9 over 12

9

12

12 is the least common multiple of denominators 3 and 4. Use it to convert to equivalent fractions with this common denominator.

Step 1 of 2: Subtract, sub-step b: Subtract.

Subtract

4 over 12

4

12

− 9 over 12

9

12

= ( 4 − 9 ) over 12

4 − 9

12

= negative 5 over 12−  

5

12

Given:

Each time Sally waters her tomato plants she uses 5 liters of water.

Sally waters her tomato plants 3 times a week.

To find:

How much water, in liters, does Sally use in a week?

Solution:

We have,

Water used in each time = 5 liters

Number of times Sally waters her tomato plants = 3 times

Now,

Water used in 1 time = 5 liters

Water used in 3 time = 3×5 liters

                                   = 15 liters

Therefore, the Sally use 15 liters of water in a week.

Answer:

76

Step-by-step explanation:

Answer:

three time plus four equals sixteen

Step-by-step explanation:

I think this is what you meant

Answer:

\(x = \frac{y + 6}{3} \)

Step-by-step explanation:

\(1. \: y = 5x - 6 - 2x \\ 2. \: y = 3x - 6 \\ 3. \: y + 6 = 3x \\ 4. \: \frac{y + 6}{3} = x\)

Answer:

-3x=(6-y)

Step-by-step explanation:

2x+y=5x-6

-5x -5x

-3x+y=6

-y. -y

-3x=(6-y)

Answer:

Step-by-step explanation:

1.Collect pairs of data where a relationship is suspected.

2.Draw a graph with the independent variable on the horizontal axis and the dependent variable on the vertical axis. ...

3.Look at the pattern of points to see if a relationship is obvious. ...

4.Divide points on the graph into four quadrants.

The standard form of the equation of line will be;

⇒ 11x + 3y = 9

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The equation of line is,

y = -11/3 x + 3

Since, The standard form of the equation of line will be;

Ax + By = C

Where, A, B and C are integers.

Now, We convert the equation of line in standard form as;

The equation of line is,

y = -11/3 x + 3

Multiply by 3 in both sides,

3 × y = 3 (-11/3 x + 3)

3y = 3 × -11/3 x + 3 × 3

3y = - 11x + 9

3y = - 11x + 9

Add 11x both side;

11x + 3y = - 11x + 9 + 11x

11x + 3y = 9

Thus,

The standard form of the equation of line will be;

⇒ 11x + 3y = 9

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Answer: The car travels 97.5 miles in 1.5 hour.

Step-by-step explanation:

Given: A car is traveling down a highway at a constant speed, described by the equation , described by the equation \(d=65t\), where represents the distance, in miles, that the car travels at this speed in t hours.

To find : Number of miles car travel in 1.5 hour.

Simply put t= 1.5 in the given expression , we get

65(1.5)= 97.5

That means , the car travels 97.5 miles in 1.5 hour.

The distance bewteen the points (-3,5) and (3,1) in a simple radical form is 2√13.

The distance formula used in finding the distance between two points is expressed as;

d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

From the graph;

Point A: (-3,5)

x₁ = -3

y₁ = 5

Point B: (3,1)

x₂ = 3

y₂ = 1

Plug the given values into the distance formula and simplify.

\(d = \sqrt{( x_2 - x_1)^2 + (y_2 -y_1 )^2} \\\\d = \sqrt{( 3-(-3))^2 + (1 -5)^2} \\\\d = \sqrt{( 3+ 3)^2 + (1 -5)^2} \\\\d = \sqrt{( 6)^2 + (-4)^2} \\\\d = \sqrt{36 + 16} \\\\d = \sqrt{52}\\\\d = 2\sqrt{13}\)

Therefore, the distance between the points is 2√13.

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