-(3x+1)+7=4-(3x + 2)
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The perimeter of the triangle is 23x + 17.

Perimeter is simply the sum of all sides of a polygon.

Given the sides of the triangle;

Side one = 10x + 19

Side two = 12x - 2

Side three = x

To find the perimeter, we add the sides

Perimeter = Side one + Side two + side three

Perimeter = 10x + 19 + 12x - 2 + x

Collect and add like terms

Perimeter = 10x + 12x + x - 2 + 19

Perimeter = 23x - 2 + 19

Perimeter = 23x + 17

Therefore, the perimeter is 23x + 17.

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Based on the given data, the distance from center to center of two consecutive holes is approximately 25.83 inches.

To solve this problem, we need to divide the length of the metal strip (excluding the 2 inches on each end) by the number of holes to be drilled, and that will give us the distance from center to center of two consecutive holes.

So the length of the metal strip available for the 12 holes is:

3414 - 2 - 2 = 3410 inches

Dividing this length by the number of holes gives us:

3410 ÷ 12 = 284.166666... inches

To find the distance from center to center of two consecutive holes, we need to divide this value by the number of spaces between the holes, which is 11 (since there are 12 holes, but only 11 spaces between them). So:

284.166666... ÷ 11 = 25.833333...

Rounding this to the nearest hundredth of an inch, we get:

25.83 inches (to the nearest hundredth)

Therefore, the distance from center to center of two consecutive holes is approximately 25.83 inches.

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Answer:

A. A lively accompaniment

Step-by-step explanation:

B. Dissonant - would most likely result in a eerie mood

C. A slow tempo - could result in melancholy or calm emotions

D. A minor key - could also result in melancholy emotions

The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).

What is a polynomial ?

A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) multiplied by coefficients.

where n is a non-negative integer (the degree of the polynomial), x is the variable, and (the coefficients of the polynomial). The highest power of x in the expression is n, and this term is called the leading term. The coefficient of the leading term, a_n, is called the leading coefficient.

To find the other linear factors of the polynomial function f(x) = x³ - 4x² - 3x + 18, we can use long division by dividing the polynomial function by (x + 2).

Here's how the long division would look like:

x³ - 4x² - 3x + 18

       ÷ x + 2

__________________________

x² - 6x - 20

             ÷ x + 2

__________________________

x - 22

       ÷ x + 2

__________________________

-20

here -20 is the remainder.

The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).

So, the other linear factors are x - 22.

Therefore, The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

y = f(x) represents a function with output value as y and x as an input in the function.

Therefore, f(2) represents value of function (y) at x = 2

so the correct choice here would be : " the output (y - value) when x = 2 "

Answer:

2 . of(0)=2/1/2 this is answer number 2

The solution is, option 2 neither linear nor exponential.

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

here, we have,

The given function is

x    : -5       -3      -1       1      3

f(x) :8192   512   32      2    18

when we plot this function in the excel we get to know that it a regression as shown in the figure attached  

because value of  lies between (0,1)

which shows regression

therefore it is neither linear nor exponential.

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The parameters for the home mortgage, and the monthly payment, PMT,  for the mortgage are as follows;

Part 1;

P = $175,000, APR = 7%, n = 12, Y = 30

Part 2;

The monthly payment for the mortgage, PMT ≈ $1,164.28

A mortgage is a loan agreement, with the possession of the collateral presented for the loan such as a house being bought with the loan amount, being relinquished by the debtor, upon default

Part 1

The value of the mortgage  = $175,000

The fixed Annual Percentage Rate, APR = 7%

The duration of the payment = 30 years

Part 2; The monthly payment PMT loan formula can be presented in the following format;

Therefore;

[tex]PMT = \frac{175000\times \frac{0.07}{12} }{1-\left(1+\frac{0.07}{12}\right)^{(-12\times 30)} } \approx 1164.28[/tex]

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The GCF of the polynomials are

1. for 15x²+18 , the GCF is 3

2. for -18y⁴+6y³+24y² ,the GCF is 6y²

The GCF stands for the “greatest common factor”. The GCF is defined as the largest number that is a factor of two or more numbers. For example, the GCF of 24 and 36 is 12, because the largest factor that is shared by 24 and 36 is 12. 24 and 36 have other factors in common, but 12 is the largest.

The GCF is the highest factor that can be used to divide through 2 or more terms

1. For 15x²+18, 3 is a factor of 15 and 18 and it's the greatest factor, therefore the GCF is 3

2. For -18y⁴+6y³+24y², between 18,6 and 24, 6 is the greatest factor Ang between y⁴ ,y³, y², y² is the greatest factor. Therefore the GCF of the expression is 6y².

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The correct solution to the problem is m = 92 and the error made was subtracting 7 from both sides of the equation instead of dividing both sides by 7

Incorrect Work/Solution:

m = the number of messages Nigel sent

644 = 7m

subtract 7 from both sides

644 - 7= 7m - 7

637 = m

Nigel sent an average of 637 messages

each day last week.

Correct solution:

644 = 7m

divide both sides by 7

m = 644/7

m = 92

Therefore, Nigel sent an average of 92 messages

each day last week.

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Step-by-step explanation:

0.25c = 63.25

We would just get c alone by dividing by 0.25 on both sides of the equal sign

c = 253

Answer: C = 253

Step-by-step explanation:

On solving the provided question we can say that The average rate of change between x₁ and x₂ and a function f(x), is 10.

The subject of mathematics includes quantities and their variatiοns, equations and related structures, shapes and their locations, and places where they can be fοund. The term "functiοn" refers to the relationship between a set of inputs, each of which has an assοciated output.

A connectiοn between inputs and οutputs in which each input leads tο a single, distinct result is known as a function. Each functiοn is given a domain and a codοmain, or scope. Usually, f is used to denοte functions (x). input is an x. There are fοur main types of functiοns accessible. based οn the following factors: on functiοns, one-to-one functiοns, many-to-one functions, inside functiοns, and on functions.

The average rate of change between x=x and a function f(x)

F(x₂) - F(x₁)/(x₂) - x₁

so,

f(x) = x²

average rate = f(6) - f(4) / 6-4 = 36-16 / 2 = 20/2 = 10

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The equation which is in the quadratic form is 6x⁴ + 7x² - 3 = 0. So Option B is correct.

An equation is quadratic in form if it can be written in the form of ax + bx + c = 0, where a, b, and c are constants and x is the variable.

Among the given equations, we can see that the first, third, and fourth equations are not quadratic in form, since they contain x raised to powers other than 2.

The second equation, 6x⁴ + 7x² - 3 = 0, can be written in quadratic form by making a substitution.

If we let y = x², then we can write the equation as 6y² + 7y - 3 = 0,

which is a quadratic equation in y. Substituting back x² for y,

we get:

6x⁴ + 7x² - 3 = 0

So the second equation is quadratic in form.

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Answer:

Step-by-step explanation:

answer b, trust

Answer:

416,`735

Step-by-step explanation:

Do inverse operations

The constant of proportionality for the given graph is 6.

The two sequences of numbers are proportional or directly proportional if the ratio between the corresponding elements of two sequences of numbers, typically experimental data, is constant and is known as the coefficient of proportionality or proportionality constant.

From the given graph the point is (5,30) from which the line is passing.

The equation for the constant of proportionality is written as below,

y = kx

Substitute the points in the above equation,

y = kx

30 = k x 5

k = 30 / 5

k = 6

Therefore, the proportionality constant for the displayed graph is 6.

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Answer:

To solve this problem, we can use the formula for exponential growth:

V(t) = V0 * (1 + r)^t

where:

V(t) is the value of the equipment at time t

V0 is the initial value of the equipment ($15,000)

r is the annual growth rate (15.9% or 0.159)

t is the time in years

We want to find the time t when the value of the equipment will be less than $7500. So we can set up the following inequality:

V(t) < 7500

Substituting the formula for V(t), we get:

V0 * (1 + r)^t < 7500

Substituting the given values, we get:

15000 * (1 + 0.159)^t < 7500

Simplifying and solving for t,

we get:(1 + 0.159)^t < 0.5

t * log(1 + 0.159) < log(0.5)

t > log(0.5) / log(1 + 0.159)

Using a calculator, we get:

t > 2.64

So the company's new equipment will be worth less than $7500 after about 2.64 years.

Step-by-step explanation:

Answer: interest= 670

Step-by-step explanation:

(1+r)^t*principal

Answer:

Step-by-step explanation:

I do not know bro. If I was a robot i'd know. I don't. I'm different.

Using the system of equations, we found the number of adult tickets sold as 82 and the number of child tickets sold as 42.

What is the system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Given,

Number of tickets sold = 124

Cost of one adult ticket = $ 12.50

Cost of one child ticket = $ 6.50

Total money received = $ 1298

We can write a system of equations using the above information.

Number of adult tickets sold = x

Number of child tickets sold = y

x + y = 124

12.5x + 6.5y = 1298

Solving the above equations, we can find x and y.

Multiplying the first equation by 6.5

6.5x+ 6.5y = 806

12.5x + 6.5y = 1298

Subtracting the equations,

-6x = -492

x = 82

Substituting the above value in any one of the equation

82 + y = 124

y = 42

Therefore from the system of equations, the number of adult tickets sold is 82 and the number of child tickets sold is 42.

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The slope of the line with the points (6, 3) and (12, 6) is equal to 1/2.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (6, 12).

Points on y-axis = (3, 6).

Substituting the given data points into the slope formula, we have the following;

Slope, m = (6 - 3)/(12 - 6)

Slope, m = 3/6

Slope, m = 1/2.

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The volume of the given complex structure would be = 56 m³

The structure is made up of the big and small cubes.

The volume of the big cube = length × breadth × width = 7 × 3 × 4 = 84 m³

The volume of the small cube cut out = length * breadth * width = 4 × 7 × (4 - 3) = 28 m³

Volume of the complex figure = 84 m³ - 28 m³ = 56 m³

The volume of the complex figure shown in the diagram is 56 m³.

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Answer:

  1 1/6 cups

Step-by-step explanation:

You want to know the amount of bleach to use with 3 1/2 gallons of water to obtain the same strength as 1 2/3 cups of bleach in 5 gallons of water.

The quantities are proportional, so the amount of bleach (b) will need to be ...

  b/(3 1/2 gal) = (1 2/3 cups)/(5 gal)

Multiplying by 3 1/2 gal, we get ...

  b = (3 1/2)(1 2/3)/5 cups = 1 1/6 cups

Mrs. Hanson should use 1 1/6 cups of bleach in 3 1/2 gallons of water.

If a rectangular room is 2 meters longer than it is wide, and its perimeter is 24 meters then the  dimensions of the room: 7 meter x 5 meter

Perimeter is a mathematical term, it indicates total outer boundary of a figure, we define it only for two dimensional figures.

Perimeter = Sum of length of the all the sides

Let x be the width of the room in meters.

Then the length of the room is 2 meters longer, which means it is x+2 meters.

In this case, we know that the perimeter is 24 meters.

So we can set up an equation:

Perimeter = 2Length + 2Width

Substituting the values we know:

24 = 2(x+2) + 2x

Simplifying the equation:

24 = 2x + 4 + 2x

24 = 4x + 4

20 = 4x

x = 5

So the width of the room is 5 meters, and the length is x+2 = 7 meters.

Therefore, the dimensions of the room are 7 meters by 5 meters.

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The solution is,

(a) Output = 37

(b) Input = 9

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

Given

y=5x -3

Solving (a): Output, when input = 8

This means that, we solve for y when x = 8

So, we have:

y=5x -3

 =5*8 -3

 =40 - 3

 = 37

Solving (b): Input, when output = 42

This means that, we solve for x when y = 42

So, we have:

y=5x -3

5x = 42+3

    = 45

Collect like terms

Divide both sides by 5

x = 9

Hence, The solution is,

(a) Output = 37

(b) Input = 9

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Answer:domain is (2, ∞), range is (-∞,∞)

Step-by-step explanation:

domain is (2, ∞) as it aproaches 2 but never reaches and range is (-∞,∞)

The domain and the range of the ordered pairs in interval notations are as follows: 1) Domain = [0,4], Range = [1,5]   ; (2) Domain [-1,-4], Range =[0,-3]

The domain of a function is the collection of all conceivable values that may be used as inputs, or alternatively, it is the whole array of possible values for independent variables.

The range of a function is the set of every possible value for the dependent variable's outcomes, or the whole set of all possible values when the domain is substituted.

In a set of ordered pairs (x,y), the domain (input) refers to all the x-values and the range refers to all the y-values.

From the points on the graph given:

(0,1) (1,2) (2,3) (3,4) (4,5)

Domain: (0, 1, 2, 3, 4)

Range: (1, 2, 3, 4, 5)

(-1,0) (-2,-1) (-3,-2) (-4,-3)

Domain: ( -1, -2, -3, -4)

Range: (0, -1, -2, -3)

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The amount after 13 years with a compound interest of 6.9 % is given by the equation A = $ 5,149.69

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the amount after compound interest be represented as A

Now , the equation will be

The principal amount P = $ 2,100

The rate of interest r = 6.9 %

The number of years b = 13 years

when compounded continuously ,

The compound interest amount A = Pe^rt

Substituting the values in the equation , we get

A = 2,100.00 ( 2.71828 ) ^ ( 0.069 ) ( 13 )

A = 2,100 ( 2.71828 )^( 0.897 )

On further simplification , we get

A = $ 5,149.69

Hence , the amount after 13 years is $ 5,149.69

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Answer: To calculate the total cost of the units in beginning inventory for each year, we need to multiply the number of units by the per-unit cost:

Year 1: Cost of units in beginning inventory = 0 units * $13 + $5 + $5 = $0

Year 2: Cost of units in beginning inventory = 1,000 units * ($13 + $5 + $5) = 1,000 * $23 = $23,000

To calculate the total cost of the units produced during each year, we need to multiply the number of units by the per-unit cost:

Year 1: Cost of units produced = 10,000 units * ($13 + $5 + $5) = 10,000 * $23 = $230,000

Year 2: Cost of units produced = 9,000 units * ($13 + $5 + $5) = 9,000 * $23 = $207,000

To calculate the total cost of the units sold during each year, we need to multiply the number of units sold by the per-unit cost:

Year 1: Cost of units sold = 9,000 units * ($13 + $5 + $5 + $6) = 9,000 * $29 = $261,000

Year 2: Cost of units sold = 8,000 units * ($13 + $5 + $5 + $6) = 8,000 * $29 = $232,000

To calculate the total variable manufacturing costs for each year, we need to sum the costs of the units in beginning inventory, units produced, and units sold:

Year 1: Total variable manufacturing costs = $0 + $230,000 + $261,000 = $491,000

Year 2: Total variable manufacturing costs = $23,000 + $207,000 + $232,000 = $462,000

To calculate the total fixed manufacturing overhead costs for each year, we need to add the fixed manufacturing overhead per year to the total variable manufacturing costs:

Year 1: Total manufacturing costs = $491,000 + $90,000 = $581,000

Year 2: Total manufacturing costs = $462,000 + $90,000 = $552,000

To calculate the total variable selling and administrative expenses for each year, we need to multiply the number of units sold by the variable selling and administrative expense per unit:

Year 1: Total variable selling and administrative expenses = 9,000 units * $6 = $54,000

Year 2: Total variable selling and administrative expenses = 8,000 units * $6 = $48,000

To calculate the total selling and administrative expenses for each year, we need to add the fixed selling and administrative expenses per year to the total variable selling and administrative expenses:

Year 1: Total selling and administrative expenses = $54,000 + $61,000 = $115,000

Year 2: Total selling and administrative expenses = $48,000 + $61,000 = $109,000

Step-by-step explanation: