Use the grouping method to factor this polynomial completely. 3x^3+12x^2x+8

The size of the cardboard piece required is 7627.0 in.

The formula for finding the size of a box is

2(L + W) + 8L + 8W = Perimeter of the cardboard piece

Where L = Length, W = Width

We need to find L and W to find the size of the cardboard piece.

7623 = 2(L + W) + 8L + 8W

7623 = 2L + 2W + 8L + 8W

7623 = 10L + 10W

7623/10 = L + W

762.3 = L + W

Let's take L = 500 and W = 262.3 (762.3 - 500 = 262.3)

Now we plug in the values of L and W in the original formula

2(500 + 262.3) + 8(500) + 8(262.3) = 7623

2(762.3) + 4000 + 2102.4 = 7623

1524.6 + 4000 + 2102.4 = 7623

7627.0 = 7623

Therefore, the size of the cardboard piece required is 7627.0 in.

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Using the function f(x) = 500(0.67)^x :

A).f(0) = 500, f(1) = 335, f(2) = 224.45 and f(3) = 150.3815

B). 33% of bugs are eaten each day

C). 67% of the bugs remain each day

D). After day 7 will there remain fewer than 40 bugs in the farm.

The function of a function rule is defined as the process that changes the input value to output.

day 1 will have 165 bugs eaten with a percentage evaluated as;

(165 × 100)/500 = 33%

day 2 will have 110.55 bugs eaten with a percentage evaluated as;

(110.55 × 100)/335 = 33%

day 3 will have 74.0685 bugs eaten with a percentage evaluated as;

(74.0685 × 100)/224.45 = 33%

day 1 will have 335 bugs remaining with a percentage evaluated as;

(335 × 100)/500 = 67%

day 2 will have 224.45 bugs remaining with a percentage evaluated as;

(224.45 × 100)/335 = 67%

day 3 will have 150.3815 bugs remaining with a percentage evaluated as;

(150.3815 × 100)/224.45 = 67%

At day 7;

f(7) = 500(0.67)⁷

f(7) = 30.30.

Therefore, 500, 335, 224.45 and 150.3815 are the respective population the days:0, 1, 2, and 3. for the function f(x) = 500(0.67)^x

33% of bugs are eaten each day

67% of the bugs remain each day and,

After day 7 will there remain fewer than 40 bugs in the farm.

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The equation of the function g(x) will be √ [ (x) -  4 )].

A line that, in analytical geometry, is an asymptote of a curve is one where, as one or both of the x or y coordinates tend to infinity, the distance between the curve and the line approaches zero.

An asymptote of a curve is a line that is tangent to the curve at a point at infinity in projective geometry and related contexts.

Given that the function F(x) is √x and is horizontally stretched by a factor of 4 to form function g(x).

The equation of the stretched function can be written as:-

f(x) = √x

g(x) = √ [ (x) -  4 )]

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Answer:

4,6,8,12

Hope it helps because im not sure if its right

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A bivariate probability distribution is a statistical distribution that describes the joint probability of two random variables. It provides the probability of each combination of values for the two variables. In simple words, it's a way to model the joint probability of two variables and the relationship between them.

A bivariate probability distribution is represented by a probability density function (pdf) or a probability mass function (pmf) depending on whether the variables are continuous or discrete. The function gives the probability of a given pair of values of the two variables. Bivariate probability distributions are useful in understanding the relationship between two variables and can be used to make predictions or draw inferences. It can be visualized using a scatter plot, a contour plot or a 3D plot. It can also be used to calculate the covariance and correlation between the two variables.

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Complete question:

Describe Bivariate Probability Distribution.

The value of the 7th term of the Geometric sequence is 6

A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.

An example of a Geometric sequence is 2, 4, 8, 16, 32, 64, …, where the common ratio is 2.

r is found by dividing the second term by first term.

The nth term of a geometric sequence is S(n) = ar^(n-1).

The common ratio in the sequence = 1458/4374 = 1/3

therefore S(7) = 4374×1/3^( 7-1)

= 4374× (1/3)⁶

= 4374/729

= 6

Therefore the value of the seventh term is 6

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The total cost of the festival tickets for 6 families with 2 adults and 4 children would be $192.

We can start by using the following equation to find the total cost of the child tickets:

Child tickets cost = Number of child tickets x Cost per child ticket

In this case, the number of child tickets is 4 children/family x 6 families = 24 children

The cost per child ticket is $4.

So, the total cost of the child tickets would be:

24 children x $4/child = $96

Similarly, we can find the total cost of the adult tickets:

Adult tickets cost = Number of adult tickets x Cost per adult ticket

In this case, the number of adult tickets is 2 adults/family x 6 families = 12 adults

The cost per adult ticket is $8.

So, the total cost of the adult tickets would be:

12 adults x $8/adult = $96

To find the total cost of the festival tickets, we can add the cost of the child tickets and the cost of the adult tickets:

Total cost = Child tickets cost + Adult tickets cost

$96 + $96 = $192

So, the total cost of the festival tickets for 6 families with 2 adults and 4 children would be $192.

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The scale factor for the dilation from the quadrilateral EFGH to form DABC is the fraction 3/5.

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

Considering the coordinates (1/2, 3/4) and (3/10, 9/4) centered at the original, we will observe the the point 1/2 was increased by 3/5 to become 3/10 at the x–axis, that is;

1/2 × 3/5 = 3/10

Also, the point 3/4 was increased by 3/5 to become 9/20 at the y–axis, that is;

3/4 × 3/5 = 9/20

Therefore, 3/5 is the scale factor of the dilation for the quadrilateral EFGH to DABC.

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To find g(0) we need to substitute x = 0 into the function g(x) = 6x + 2.

g(0) = 6(0) + 2 = 0 + 2 = 2

So, g(0) = 2

Therefore, the value of the function g(x) when x is equal to 0 is 2.

Answer:

18.03

Step-by-step explanation:

Its pretty easy actually,

50x100 When we put 50 correct out of 61 possible into our formula, we get this: (50/61) x 100 = 81.97%

so , 100-81.97 = 18.03

4/5 and 6/10 form a proportion.

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Answer:

  6.9

Step-by-step explanation:

You want half the side length of an equilateral triangle with an altitude of 12.

The altitude shown divides the base into equal parts. If one of those parts is x, then the full side length is 2x. The Pythagorean theorem relates the side lengths of the right triangle:

  (2x)² = x² +12²

  3x² = 144 . . . . . . . . subtract x²

  x² = 48 . . . . . . . . divide by 3

  x = √48 = 4√3 . . . take the square root

  x ≈ 6.9

__

Additional comment

You should be familiar with the fact that a 30°-60°-90° triangle has side lengths in the ratio 1 : √3 : 2. This means the shortest side (x) will have a length of 12/√3 ≈ 6.9, since the middle-length side is shown as having a length of 12.

Answer:

[tex] \sf \: 12th \: term = 37[/tex]

Step-by-step explanation:

Common difference (d) is,

→ d = a2 - a1

→ d = -3 - (-7)

→ d = -3 + 7

→ [ d = 4 ]

Now the 12th term will be,

→ a1 + (d × (n - 1))

→ -7 + (4 × (12 - 1))

→ -7 + (4 × 11)

→ -7 + 44

→ 37 => 12th term

Hence, the answer is 37.

For the value of f (x) = 11, the value of x is

A relation between a set of inputs having one output each is called a function.

We have to given that;

The function is,

⇒ f(x) = -5x + 1

And, f (x) = 11

Now, We have;

⇒ f(x) = -5x + 1

Substitute f (x) = 11, we get;

⇒ 11 = - 5x + 1

⇒ 5x = - 11 + 1

⇒ 5x = - 10

⇒ x = - 2

Thus, The value of x = - 2

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Answer:

27000 m

Step-by-step explanation:

1km = 1000 m

27km = 27 x 1000 = 27000 m

So, the answer is 27000 m

Answer:27 km in meters is 27000 m

Step-by-step explanation:

multiply the length by 1000!

The 100th prime number is 541.

Therefore the answer is 541.

Prime numbers are numbers that are divisible by only 1 and themselves. They are considered to be the "building blocks" of the natural numbers, and are important in number theory and other branches of mathematics.

Prime numbers are fundamental for number theory and have a lot of applications in cryptography, coding theory, and other areas of mathematics.

The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. The primes continue indefinitely, with no repeating pattern or predictable distribution. Finding the nth prime number is not an easy task, it requires knowledge of number theory and a lot of computational power.

In general, the nth prime number grows faster than any polynomial in n. The 100th prime number is larger than the 100th Fibonacci number (which is about 354) and smaller than the 100th triangular number (which is about 5050).

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The solution for given linear inequality will be x>11/2.

What are linear inequalities?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

e.g. y>x+2

Now,

Given linear inequality is

10<2x-1

i.e. x>11/2.

The number line is in image.

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The total words Cecilia types over a 4 minute period is 152 words

An equation is a mathematical expression that contains two or more numbers and variables linked together by mathematical operations such as exponents, multiplication, division, addition, subtraction and so on.

The slope intercept form of a linear equation is:

y = mx + b

where m is the slope and b is the y intercept.

Let y represent the total words that Cecilia types after x minutes.

Cecilia types at a speed of 38 words per minute. Hence:

y = 38x

After 4 minutes:

y = 38(4) = 152 word

The total words Cecilia types over a 4 minute period is 152 words

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Answer:

y=2x+3

Step-by-step explanation:

See attached worksheet.

Guidelines are presented on how to both graphically and mathematically solve for the equation.  

Graphing:  Mark the the two given points and connect them with a ruler to form the line.  These same two points may be used to determine the slope, as is shown.  The slope is 2.  The line intersects the y axis at 3, so the y-intercept is 3.  Using the standard form of an equation, the line is y = 2x + 3, as is outlined in the attachment.

The same line is determined mathematically by using the same technique for calculating slope.  The value of the y-intercept may be found by using one of the two given points in the equation that has the slope of 2:

  y= 2x +b

Enter pont (-1,1), for example, and calculate the value of b. b = 3, (since 1 = 2*(-1)+ b, so b=3).

The equation of this line is y=2x+3

In given word problem the number of cards Alan has is 13 and Number of cards Calvin has is 13.

What is word problem?

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order  to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Here , Let us take Number of card Alan has as A and Number of card bill has as B and Number of cards does Calvin has as C.

Now Alan has 11 less than 2 times the number of cards Bill has then,

=> A = 2B-11 ------------->1

And Calvin has 1 more than 1 times the number of cards Bill has then,

=> C =  B+1 ----------> 2

Here Alan and Calvin has same number of cards then

=> 1 = 2

=> 2B - 11 = B +1

=> 2B-B = 11+1

=> B = 12

Now put B= 12 into 1 then

=> A = 2(12)-11= 24-11 = 13

Now put B= 12 into 2 then

=> C = 12+1 = 13

Hence the number of cards Alan has is 13 and Number of cards Calvin has is 13.

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The polynomial 8X/Y has a coefficient of X of 8.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression. It is often a number, but it can also be any expression. They may also be referred to as parameters if the coefficients are variables in and of themselves.

In the above polynomial 8X/Y, the coefficient of X is 8.

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The slope of the line passing through the points is given by the equation Slope m = 15/11

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be represented as P = P ( 7 , 10 )

Let the second point be represented as Q = Q ( 18 , 25 )

Now , the slope of the line between the points is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 25 - 10 ) / ( 18 - 7 )

On simplifying the equation , we get

Slope m = 15/11

Hence , the slope of the line is m = 15/11

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The equation 7x^4 = 56 can be rewritten as x^4 = 8. To find the real solutions of the equation, we take the fourth root of both sides:

What does a math equation mean?

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

x = ∛8 = 2.

So the real solutions of the equation are x = 2.

Note: since the fourth root of 8 is 2, we can check that the equation holds true. i.e 7*2^4 = 56

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Answer:

To find the final balance of an account earning interest compounded continuously, you can use the formula:

A = Pe^(rt)

where A is the final account balance, P is the initial principal (or starting) amount, r is the interest rate, and t is the time (in years) for which the interest is being calculated.

Substituting in the given values:

A = 550 * e^(0.066 * 10)

Therefore, the final balance would be approximately $1064.14.

Answer:

C)  $1064.14

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

Given:

Substitute the given values into the continuous compounding formula and solve for A:

[tex]\implies A=550e^{0.066 \times 10}[/tex]

[tex]\implies A=550e^{0.66}[/tex]

[tex]\implies A=550(1.93479233...)[/tex]

[tex]\implies A=1064.13578...[/tex]

Therefore, the balance of the account after 10 years would be $1064.14.

Answer:

the highest (hcf) would be 6 , while lowest (lcm) is 5,040

The expression that is equal to the provided expression, x2+7x+8, is 5x/x2+2x-1.

In math, it is possible to multiply, divide, add, or subtract. The following sentence form describes an expression: (Mathematical Operator, Number or Variable, Expression) Numbers, variables, and operations make constitute a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be compared.

given

expression = x²+7x+8/x²+2x-1

x²+8/x²+7x+2x-1

5x + 1/x2 + 2x -1

5x/x²+2x-1

The expression that is equal to the provided expression, x2+7x+8, is 5x/x2+2x-1.

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The coordinates of the point after the transformation is (-7, -4)

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

(x, y) = (-4, 7)

Transformation involves changing the location and/or the size of a shape in a coordinate plane

A point rotating -90° about the origin will have its x-coordinate become its y-coordinate and its y-coordinate become its negative x-coordinate.

Hence, the point (-4, 7) will become (-7, -4) after rotating -90° about the origin.

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Answer:

Step-by-step explanation:

10.00 amps

The curve of the graph would move closer to the y-axis for a > 4

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

f(x) = a(1/2)^x

Such that

a = 4

The graph of the function is added as an attachment

From the given parameters, we can see that the value of a is positive

This implies that an increment in the value of a would make the curve move closer to the y-axis

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