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The required factor each polynomial by grouping are factored.

A polynomial is an algebraic expression in which the operators "+" and "-" are used to separate terms, and the exponents of the variables are consistently non-negative integers. Polynomials include, for instance, x² + x + 5, y² + 1, and 3x³ - 7x + 2.

1) [tex]x^3+4x^2+2x+8[/tex]

can be factored by grouping as:

[tex]x^3 + 2x + 4x^2 + 8[/tex]

= [tex]x(x^2+2) + 4(x^2+2)[/tex]

= [tex](x+4)(x^2+2)[/tex]

2) [tex]4b^3-6b^2+10b-15[/tex]

can be factored by grouping as:

[tex]2b^2(2b-3)+5(2b-3)[/tex]

=[tex](2b-3)(2b^2+5)[/tex]

3)[tex]2m^3+4m^2+6m+12[/tex]

can be factored by grouping as:

[tex]2m^2(m+2) + 6(m+2)[/tex]

= [tex](2m^2+6)(m+2)[/tex]

= [tex]2(m^2+3)(m+2)[/tex]

4) [tex]7r^3-35r^2+6r-30[/tex]

can be factored by grouping as:

[tex]7r^2(r-5)+6(r-5)[/tex]

=[tex](7r^2+6)(r-5)[/tex]

[tex]10a^3+4a^2+5a+2[/tex]

can be factored by grouping as:

[tex]2a^2(5a+2)+1(5a+2) = (2a^2+1)(5a+2)[/tex]

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Answer:

Step-by-step explanation:

fx

The graph is a linear function with a growth factor of 4

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The graph has the shape of a straight line, so it is linear.

The graph starts at point (0, 0). It passes through point (1, 4).

slope = 4/1 = 4

The slope is 4. Growth factor is the same as slope for a linear function.

Hence, the graph is a linear function with a growth factor of 4

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Answer:

Step-by-step explanation:0.18

With MATLAB 's "t f" function, you may build a transfer function. A transfer function object is created by the "t f" function and can be used to manipulate transfer functions

So, you can create a transfer function with the aid of MATLAB's "t f" function. The "t f" function generates a transfer function object that can be used to manipulate transfer functions in a variety of ways, such as multiplying, adding, and inverting them. The MATLAB "t f" function can produce transfer functions using the following syntax. The numerator and denominator coefficients of the transfer function are "num" and "den", respectively and they are used to compute the system equation:  sys = t f(num, den). The coefficients of "num" and "den" can be visualised as vectors, with "s" serving as the Laplace variable and the coefficients as descending powers of "s." Consider using the transfer function equation below as an example to create

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Total 816 triangles that can be formed using diagonals from a common vertex of a 21-gon.

In mathematics, a diagonal is a line joining two vertices of a polygon or solid whose vertices do not lie on the same edge. Diagonals are generally defined as oblique lines or slanted lines connecting the vertices of a shape. A diagonal is defined as a horizontal shape with sides/edges and corners. 

Solution of the given problem:

Firstly, choose 3 vertices of 21-gon which are not adjacent to each other.

Secondly, connect all three vertices to a common vertex.

Now, there are 18 vertices that are not adjacent to common vertex and there are now 18 diagonals that can be drawn to the common vertex up to these vertices.

To form a triangle using these diagonals, we need to choose 3 of these 18 vertices, this can be calculated using the binomial coefficient formula:

18 choose 3 = 18! / (3! * (18 - 3)!) = (18 * 17 * 16) / (3 * 2 * 1) = 816

Thus, total 816 triangles can be formed.

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Answer: (9,8) A

Step-by-step explanation: how the mandle 10 30  6 150 144

Answer:

x > - 6

Step-by-step explanation:

[tex]\frac{x}{2}[/tex] > - 3 ( multiply both sides by 2 to clear the fraction )

x > - 6

Answer: The square root of 216 is equal to approximately 6.485281.

Step-by-step explanation:

The square root of 216 is equal to the number that, when multiplied by itself, gives 216. The value of the square root of 216 can be found using several methods, including estimation, the long division method, and a calculator. Here, I'll provide a step-by-step explanation using estimation.

Step 1: Estimate the value of the square root.

One way to estimate the value of the square root of 216 is to find two perfect squares that are close to 216, and whose square roots are therefore close to the square root of 216. In this case, the perfect squares closest to 216 are 144 (12^2) and 225 (15^2). Since 216 is closer to 144, the square root of 216 is likely to be closer to 12 than to 15.

Step 2: Refine the estimate.

To refine the estimate of the square root of 216, we can average the two closest perfect squares and their square roots. In this case, the average of 12 and 15 is 13.5, and this is a better estimate of the square root of 216 than either 12 or 15 alone.

Step 3: Improve the estimate using a more precise method.

One method for finding an even more precise estimate of the square root of 216 is to use the Newton-Raphson formula for finding square roots. This formula involves repeatedly applying the following equation:

x_n+1 = (x_n + n/x_n) / 2,

where x_n is the nth estimate of the square root, and n is the number whose square root we are trying to find (in this case, n = 216). We can start with an initial estimate, such as x_0 = 13.5, and iterate the formula until the estimate converges to a desired level of precision.

Step 4: Use a calculator or other tools to find the exact value.

Finally, we can use a calculator or computer program to find the exact value of the square root of 216 to as many decimal places as desired. The exact value of the square root of 216 is equal to approximately 6.485281.

Answer:

Step-by-step explanation:

Permutations and combinations are mathematical concepts that deal with counting the number of different arrangements or selections of objects from a set.

Permutations:

A permutation is an arrangement of objects in a specific order. For example, consider a set of three letters: A, B, and C. There are 3! = 6 possible permutations of these letters, which are ABC, ACB, BAC, BCA, CAB, and CBA. The notation "3!" is the factorial notation, which means 3 × 2 × 1.

Combinations:

A combination is a selection of objects, where the order does not matter. For example, consider a set of three letters: A, B, and C. There are 3 C 2 = 3 possible combinations of two letters from this set, which are AB, AC, and BC. The notation "3 C 2" is the combination notation, which means the number of ways to choose k objects from a set of n objects.

In summary, permutations deal with the arrangement of objects in a specific order, while combinations deal with the selection of objects without regard to the order.

Location A has the warmer average temperature, by about 0.6°F (rounded to one decimal place).

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To compare the temperatures of Location A and Location B, we need to convert the temperature of Location B from Celsius to Fahrenheit. We can use the formula:

°F = (°C × 9/5) + 32

Substituting the given temperature of Location B, we get:

°F = (29.3 × 9/5) + 32 = 84.74°F (rounded to two decimal places)

So, the average temperature of Location A is 85.3°F and the average temperature of Location B is 84.74°F (rounded to two decimal places).

Therefore, Location A has the warmer average temperature, by about 0.6°F (rounded to one decimal place).

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The expression in simplest form that represents the total cost for x students is 11.55x, the correct option is C.

Expression in mathematics can be defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that a student in a math class has to buy the items in the table.

Now,

x(9.65+0.65+1.25)

=9.65x+0.65x+1.25x

=11.55x

Therefore, the expression in simplest form will be 11.55x.

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The cost of each ticket is $34.17

To find the cost of each ticket, we need to divide the total cost of the tickets by the number of tickets.

In this case, the total cost of the tickets is $102.51 for three tickets.

So, to find the cost of one ticket,

We can divide $102.51 by 3:

Using the above as a guide, we have the following:

$102.51 ÷ 3 = $34.17

Hence, each ticket costs $34.17.

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The value of x is given as follows:

x = 30.

Similar triangles are triangles that share these two features presented as follows:

For the two similar triangles, we have that B and N are equivalent angles, hence they are congruent and the value of x is given as follows:

2x + 7 = 67

2x = 60

x = 60/2

x = 30.

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Answer: put tow points, 1  on the x-axis (horizontal) and the other 1 on y-axis (vertical).

x = 7

y = -8

and you make a straight line , connecting them

The linear function through the points (-8,-2) and (-4,6) is given as follows:

y = 2x + 14.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Given two points, the slope is calculated as the change in y divided by the change in x, hence:

m = (6 - (-2))/(-4 - (-8))

m = 8/4

m = 2.

Hence:

y = 2x + b.

When x = -8, y = -2, hence the intercept b is obtained as follows:

-2 = 2(-8) + b

b = 14.

Hence the equation is:

y = 2x + 14.

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The conversion rate for grams to tablespoons is 1 gram is equal to 0.2 tablespoons. This conversion is useful for both converting small amounts of ingredients in recipes and converting larger amounts of ingredients in recipes.50 grams is equal to 10 tablespoons."

This means that 50 grams is equal to 10 tablespoons. To calculate the value of 50 grams in tablespoons, we can use the following formula:50 grams x 0.2 tablespoons = 10 tablespoons.The value of 50 grams in tablespoons is 10 tablespoons.To convert from grams to tablespoons, the basic formula is to multiply the weight in grams by 0.2. This conversion is useful for converting small amounts of ingredients in recipes, as many recipes call for weights in grams rather than tablespoons. For example, if a recipe calls for 20 grams of butter, this would be equal to 4 tablespoons. To convert from tablespoons to grams, the basic formula is to multiply the weight in tablespoons by 5. This conversion is useful for converting larger amounts of ingredients in recipes, as many recipes call for weights in tablespoons rather than grams. For example, if a recipe calls for 8 tablespoons of sugar, this would be equal to 40 grams. To summarize, the value of 50 grams in tablespoons is 10 tablespoons. This conversion is useful for both converting small amounts of ingredients in recipes and converting larger amounts of ingredients in recipes.

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Answer:

$88.55

Step-by-step explanation:

First find how much the 30% off discount will be.

115 x 0.30 = 34.5

Subtract it from original price

$115 - 34.5 = $80.5

Now find the 10% tax

80.5 x 0.10 = 8.05

Add that to the price

$80.5 + 8.05 = 88.55

The dresser's final sale price is $88.55

The factored expression of (a-b) * 2 + 3(b-a)^2 is (-2 + 3(b - a))(b - a)

From the question, we have the following parameters that can be used in our computation:

(a-b)*z+3(b-a)^2

Express properly

So, we have

(a-b) * 2 + 3(b-a)^2

Rewrite as

-2(b - a) + 3(b - a)^2

Factor out b - a from the expression

So, we have

(-2 + 3(b - a))(b - a)

Hence, the factored expression is (-2 + 3(b - a))(b - a)

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The numeric value of the function when x = 0 is found replacing each instance of x by zero in the definition of the function.

If a graph is given, then the numeric value is given as the value of y when the function crosses the y-axis.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

Supposing we have a function definition, then the numeric value at x = 0 is found replacing each instance of x by zero.

On graph, x = 0 is when the graph of the function touches or crosses the y-axis.

The problem is incomplete, hence the general procedure to obtain the numeric value at x = 0 was presented.

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Answer:

option 1 --> sec A = c/a

option 3 --> sin(b) = b/c

option 4 --> Sin(A) = a/c

Step-by-step explanation:

Since cos is adjacent, we know the legs are a and b and the hypotenuse is c

For angle B

For Angle A

Julie will reach her goal 21 days before Mary.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

Mary and Julie both have a goal of raising $1000 for charity.

Mary raises money in every 4 days = $12.

In one day Mary raises money = 12/4

                                                   = $3

Mary needs time to reach her goal = 1000/3

                                                         = 333.33  ≈ 334 days

Julie raises money in every 6 days = $19

In one day Julie raises money = 19/6

                                                  = $3.1666 ≈ $3.2

Julie needs time to reach her goal = 1000/ 3.2

                                                          = 312.5 ≈ 313 days

Difference of the days between both of them to reach their goal

= 334 - 313 = 21 days  

Julie will reach her goal first, 21 days before Mary.

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Answer:

You probably know that it is a good idea to brush your teeth every day. What does this do that helps prevent tooth decay?

Step-by-step explanation

If the given function is f(3/4), then evaluation of function (3/4) = 5/4.

What is expression ?

An expression is a mathematical phrase that can contain numbers, variables, and operators such as addition, subtraction, multiplication, and division. It can also contain functions, exponents, and other mathematical symbols.

Expressions can be used to represent a wide range of mathematical concepts, such as equations, inequalities, and formulas. They can be as simple as a single number or variable, or they can be more complex, involving multiple operations and variables.

What is function ?

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. In other words, a function is a rule or mapping that assigns a unique output to each input.

Functions can be expressed using a variety of mathematical expressions, such as algebraic formulas, graphs, and tables. They are used to model relationships between variables in many areas of mathematics, science, engineering, and other fields.

According t o given condition :

To find f(3/4), we simply substitute 3/4 in place of x in the given function f(x):

f(3/4) = 2(3/4) - 1/4

Simplifying the expression, we get:

f(3/4) = 6/4 - 1/4

f(3/4) = 5/4

Therefore, if the given function is f(3/4), then evaluation of function (3/4) = 5/4.

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The volume of the composite figure is equal to 1395 square inches.

In this problem we need to determine the volume of a composite figure, which is the result of combining the volumes of a right prism and a pyramid, whose volume formulas are listed below:

Pyramid

V = (1 / 3) · w · l · h

Prism

V = w · l · h

Where:

Now we proceed to determine the volume of composite solid:

V = (9 in) · (15 in) · (7 in) + (1 / 3) · (15 in) · (9 in) · (10 in)

V = 1395 in³

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Answer:

x= -177

Step-by-step explanation:

−13(x + 11) + 12x =-26

x=-177

The correct statement that describes how the slope relates to the height of the water in the pool is: The height of the water increases 2 inches per minute, the correct option is A.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

where (x₁, y₁) and (x₂, y₂) are the two points that you are trying to find the slope between.

We are given that;

The time in minutes: 2, 4, 6, 8, 10

Height in inches: 8, 12, 16, 20, 24

Now,

The slope of the line through the points is 2, which means that for every 1 unit of time (in minutes) that passes, the height of the water in the pool increases by 2 units (in inches).

Therefore, by the given slope answer will be height of the water increases 2 inches per minute.

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A student need a raw score of 36.

We can find the raw score (R) of the student by substituting A = 60 into the the formula and then solve for R. That is:

A = 10√R

√R = 60/10

√R = 6

R = 6²

R = 36

Thus, a student need a raw score of 36 to get a passing grade after her score is adjusted.

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The number of shirts that Janice can buy without going over her limit is; 3 shirts

The number of shirts she can buy is denoted as s.

Cost of each shirt = $14

Cost of a pair of jeans = $32

She wants to spend less than $88.

Thus, the inequality that depicts this problem is;

14s + 32 < 88

Subtract 32 from both sides to get;

14s < 56

Divide both sides by 14 to get;

s < 4

Thus, maximum number of shirts will be 3 shirts

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Answer:

a = 149 degrees

Step-by-step explanation:

Angles must add up to 180 degrees so,

180 - 31 = 149.