Evaluate the algebraic expression: (5m + 2) when m= 4*

3, 13, 23, 33, 43, 53, 63, and 73 in arithmetic order. The sentence "arithmetic sequence" is accurate.

Solution: Using the method for locating the nth term, we can locate a particular term in an arithmetic series. Step 1: An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d. Therefore, enter the values a = 2 and d = 3 into the formula to determine the nth term.

The difference between every successive term in an arithmetic series is always the same. An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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Answer:

B

Step-by-step explanation:

The association property of multiplication states that if we have three numbers such as:

\(a\cdot b\cdot c\)

Then the order of parentheses will not matter. In other words:

\((a\cdot b)\cdot c=a\cdot (b\cdot c)\)

For instance:

\((3\cdot4)\cdot5=3\cdot(4\cdot5)\)

For the choices, it must have at least three terms. Thus, eliminate A.

It must also have parentheses. Eliminate D.

Choice C represents the distributive property, where you distribute a factor into the expression.

Thus, the correct answer is choice B.

And as previously mentioned, the order of the parentheses does not make the product any different.

\(6*(9*1)=6*(9)=54\\(6*9)*1=(54)*1=54\)

Answer:

The correct answer choice is B.

Step-by-step explanation:

The digits should still be in order, so A is incorrect. 6 * 91 does not even equal 69 * 1!

B shows that be can multiply 6 * 9 * 1 in any order. This means we can place a pair of parentheses around any of these numbers and the answer will still be the same.

C is incorrect. We want an equation that helps give us a better understanding of MULTIPLICATION, not ADDITION. The equation is also false.

Finally, D illustrates the commutative property of multiplication- you can multiply your numbers in any order and it will still have the same value. Put simply, it's incorrect.

Let me know if you need more elaboration!

Answer:

11 cm

Step-by-step explanation:

1m = 100cm

By examining the graph carefully, we can see that the record in 1985 is 2.4 m. In 1970 it was slightly under 2.3 m. For it to be 15cm it would have to be 2.25m. For it to be 9 cm it would the record would have been above 2.3m.

Answer:

2x-3=13

2x=13+3

2x=16

2x/2=16/2

x=8

Answer:

first number is 8

second number is 5

Step-by-step explanation:

None of the other statements necessarily follow from (x-4) being a factor of f(x). So the correct statement is Of(4) = 0

What is a statement?

A statement is a proposition that is either true or false, but not both. It may be a mathematical equation, an inequality, or a proposition that can be tested for its truth value.

What is meant by factor?

A factor refers to a number or algebraic expression that is multiplied by another number or expression to obtain a product. Factors can be either integers or polynomials.

According to the given information

If (x-4) is a factor of f(x), then f(4) = 0. This is because when you divide f(x) by (x-4), the remainder is zero when x=4.

Therefore, the correct statement is: f(4) = 0

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1) The property P that we need to prove by induction is as P(p) = length p = length (rem R p) + numR p. 2) For the base case, we need to prove P([]) = length [] = length (rem R []) + numR []. 3) Inductive hypothesis is P(p) = length p = length (rem R p) + numR p. 4) For the step case, we need to prove P(p) → P(L:p) : length (L:p) = length (rem R (L:p)) + numR (L:p).

1) The property P that we need to prove by induction is as follows:

For all lists of directions p, the property P(p) is defined as:

P(p) = length p = length (rem R p) + numR p

If we can prove this property P by induction, it implies the goal of the exercise, which is to show that length p = length (rem R p) + numR p.

2) Base case goal:

For the base case, we need to prove the following goal:

For an empty list of directions p = [], the property P(p) holds:

P([]) = length [] = length (rem R []) + numR []

Proof:

P([]) simplifies to:

length [] = length (rem R []) + numR []

Using the definition of the length function and rem function, we have:

0 = length [] + numR []

Since the length of an empty list is 0, and there are no occurrences of R in an empty list, numR [] is also 0. Therefore, the base case goal holds.

3) Inductive hypothesis:

Assuming that the property P holds for a list p, we assume the following inductive hypothesis:

P(p) = length p = length (rem R p) + numR p

4) Step case goal:

For the step case, we need to prove the following goal:

Assuming P(p), we need to show that P(L:p) holds:

P(p) → P(L:p) : length (L:p) = length (rem R (L:p)) + numR (L:p)

Proof:

Using the definition of the length function and rem function, we have:

length (L:p) = length (L:(rem R p)) + numR (L:p)

Expanding the length and rem functions, we get:

1 + length p = 1 + length (rem R p) + numR (L:p)

Since L is not equal to R, numR (L:p) remains unchanged:

1 + length p = 1 + length (rem R p) + numR p

By canceling out the common terms on both sides, we get:

length p = length (rem R p) + numR p

This matches the property P(p), so the step case goal holds.

By proving the base case and the step case, we have proven the property P(p) by induction, which implies that length p = length (rem R p) + numR p for all lists of directions p.

Correct Question :

length []=0

length (x:xs)=1+ length xs

​−L1

−L2

Consider the following data types and functions: data Direction =L∣R numR : [Direction] -> Int

numR []=0

numR (L:p)= numR p

numR (R:p)=1+ numR p

Answer the following questions:

1. What precisely should we prove by induction? Specifically, state a property P, including possible quantifiers, so that proving this property by induction implies the (above) goal of this exercise.

2. State (including possible quantifiers) and prove the base case goal.

3. State (including possible quantifiers) the inc्acuctive hypothesis of the proof.

4. State (including possible quantifiers) and prove the step case goal.

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Answer:

Let Solve for x by simplification:

2x+3y=13

   2x+3y =13

Collect constant terms to RHS and Simplify

2x+3y+(-3y)=13+-3y

 2x=-3y+13

   Divide both sides by (2) and Simplify

2x+-3y+13

x=-3y+13 /2

         x = -3/2y+13/2

AND FOR Y BASICALLY IT'S

Y=-5/3 X+28/3

HOPE IT HELPS :D

Answer:

70% Increase is your final answer.

Answer:

5x + 9y -4

Step-by-step explanation:

Answer:

The value of x is 20

Step-by-step explanation:

Because the sum of interior angle of polygons is 360°

The evaluation of the function \(f(x)=e^x\) at a=0 and x=5 by the taylor series will have a value 65.37.

We know the fromula of taylor series is given as:

\(f(x)=f(a)+\dfrac{f'((a)}{1!}(x-a)+\dfrac{f''(a)}{2!}(x-a)^2+\dfrac{f'''(a)}{3!}(x-a)^3.................\)

Now for the function \(f(x)=e^x\) the taylor's series will become.

\(f(x)=e^a+e^ax+\dfrac{e^ax^2}{2!}+\dfrac{e^ax^3}{3!}+\dfrac{e^ax^4}{4!}\)

\(f(x)=1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\dfrac{x^4}{4!}\)

So at x=5 the values will become

\(f(x)=1+5+12.5+20.83+26.04=65.37\)

hence the evaluation of the function \(f(x)=e^x\) at a=0 and x=5 by the taylor series will have a value 65.37.

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To determine the indices for the direction and plane shown in the given cubic unit cell, we need specific information about the direction and plane of interest. Without additional details, it is not possible to provide a step-by-step solution for determining the indices.

The indices for a direction in a crystal lattice are determined based on the vector components along the lattice parameters. The direction is specified by three integers (hkl) that represent the intercepts of the direction on the crystallographic axes. Similarly, the indices for a plane are denoted by three integers (hkl), representing the reciprocals of the intercepts of the plane on the crystallographic axes.

To determine the indices for a specific direction or plane, we need to know the position and orientation of the direction or plane within the cubic unit cell. Without this information, it is not possible to provide a step-by-step solution for finding the indices.

In conclusion, to determine the indices for a direction or plane in a cubic unit cell, specific information about the direction or plane of interest within the unit cell is required. Without this information, it is not possible to provide a detailed step-by-step solution.

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Answer:

2^(3/7)

Step-by-step explanation:

For these types of questions, what is inside the root is the numerator, and what is on top is the denominator.

3 is in the root, so it is the numerator

7 is outside the root, so it is the denominator

Therefore, The answer is 2^(3/7)

Euclidean geometry is more beneficial. Analytical geometry, with its algebraic tools and coordinate system, is often more practical when dealing with complex calculations and numerical analysis.

Analytical geometry, also known as coordinate geometry, combines algebra and geometry by representing geometric figures and relationships using coordinates in a Cartesian coordinate system. This approach offers a more algebraic perspective on geometry, allowing for the use of equations and formulas to analyze geometric properties. It provides a systematic way to solve problems by applying algebraic techniques.

Euclidean geometry, on the other hand, is the traditional branch of geometry that focuses on the study of geometric figures, their properties, and relationships, without the use of coordinates or equations. Euclidean geometry is based on a set of axioms and postulates established by Euclid, emphasizing concepts like points, lines, angles, and shapes.

When it comes to extending beyond two dimensions, the analytical geometry approach is generally easier to work with. Cartesian coordinates readily extend to three dimensions and beyond, allowing for the representation and analysis of objects in higher-dimensional spaces. This is particularly useful in fields such as physics, computer graphics, and engineering, where three-dimensional and multidimensional spaces are commonly encountered.

In situations where precision and exactness are essential, Euclidean geometry is more beneficial. Euclidean principles are applicable in fields like architecture and construction, where the physical properties and measurements of shapes and structures are crucial. Euclidean geometry's emphasis on geometric proofs and deductive reasoning helps establish rigorous mathematical foundations.

Analytical geometry, with its algebraic tools and coordinate system, is often more practical when dealing with complex calculations and numerical analysis. It is frequently employed in fields such as calculus, optimization, and data analysis, where quantitative methods are needed.

Ultimately, the choice between analytical and Euclidean geometry depends on the specific problem, context, and goals at hand. Both approaches have their strengths and applications, and a comprehensive understanding of geometry often involves proficiency in both analytical and Euclidean techniques.

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Step-by-step explanation:

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

The upper end point in a 99% confidence interval for the average income is approximately $15,364.22.

To calculate the upper end point in a 99% confidence interval for the average income, we can use the formula:

Upper end point = sample mean + (Z * (population standard deviation / sqrt(sample size)))

In this case, the sample mean is $15,000, the population standard deviation is $1,000, and the sample size is 50.

First, we need to find the Z-value for a 99% confidence level. The Z-value represents the number of standard deviations away from the mean that corresponds to the desired confidence level. For a 99% confidence level, the Z-value is approximately 2.576.

Now we can calculate the upper end point:

Upper end point = $15,000 + (2.576 * ($1,000 / sqrt(50)))

Calculating the square root of 50:

Upper end point = $15,000 + (2.576 * ($1,000 / 7.071))

Upper end point = $15,000 + (2.576 * $141.42)

Multiplying:

Upper end point = $15,000 + $364.22

Calculating:

Upper end point ≈ $15,364.22

Therefore, the upper end point in a 99% confidence interval for the average income is approximately $15,364.22.

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When the length, breadth, and height are provided as 8 inches, 7.5 inches, and 6 inches, respectively, the rectangular prism's total surface area is 360 inches2.

Surface area is a measure of how much space an object's surface takes up overall. The total area of a three-dimensional shape's surroundings is its surface area. Surface area refers to the total surface area of a three-dimensional shape. You may compute the surface area of a cuboid with six rectangular faces by adding together their individual areas. Alternatively, you can use the following formula to name the box's dimensions: Surface (SA) = 2lh plus 2lw plus 2hw. A three-dimensional shape's surface area is calculated as the total amount of space it occupies (a three-dimensional shape is a shape that has height, width, and depth).

given

rectangle prism has a length of 8 inches and a width of 7.5 inches.

6 inches is the rectangular prism's height.

SA equals two square units of (lh + wh + lw).

A=360 inches2

When the length, breadth, and height are provided as 8 inches, 7.5 inches, and 6 inches, respectively, the rectangular prism's total surface area is 360 inches2.

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Answer:

Step-by-step explanation:

B.12

Answer :

Hey there! I'm happy to help!

To find the area of a triangle you multiply the base by the height.

We see that our base is 5 units long because it stretches from -6 to -1 on the coordinate plane. Our height is 8 because the y value goes from 3 to -5.

To find the area of a triangle, you just multiply the base by the height then divide by 2.

5(8)=40

40/2=20

The area is 20 square units.

Have a wonderful day! :D

Is This What You Triangle Looks Like?

Answer:

Always

Step-by-step explanation:

A whole number will always be an interger.

Answer

(-3, -11), (1, 5)

Explanation

To solve this, we will solve this, we will equate the expressions for y

y = -x² + 2x + 4

4x - y = -1

y = 4x + 1

y = y

4x + 1 = -x² + 2x + 4

x² + 4x - 2x + 1 - 4 = 0

x² + 2x - 3 = 0

x² + 3x - x - 3 = 0

x (x + 3) - 1 (x + 3) = 0

(x + 3) (x - 1) = 0

x + 3 = 0

x = -3

OR

x - 1 = 0

x = 1

y = 4x + 1

If x = -3

y = 4x + 1 = 4(-3) + 1 = -12 + 1 = -11

If x = 1

y = 4x + 1 = 4(1) + 1 = 4 + 1 = 5

(-3, -11) OR (1, 5)

Hope this Helps!!!

3)  since we don't have the information about the interest paid (I), we cannot determine the rate of interest at this time.

(1) To find the total amount Adrian paid in 36 months, we can multiply the monthly installment by the number of installments:

Total payment A = Monthly installment * Number of installments

              = $375 * 36

              = $13,500

Therefore, Adrian paid a total of $13,500 over the course of 36 months.

(2) In the simple interest formula I = Prt, the letters used represent the following variables:

I: Interest (the amount of interest paid)

P: Principal (the initial amount, or in this case, the car worth)

r: Rate of interest (expressed as a decimal)

t: Time (in years)

(3) To find the rate of interest in percentage, we need more information. The simple interest formula can be rearranged to solve for the rate of interest:

r = (I / Pt) * 100

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The conclusion is that the distances bird travel is independent of their size. The Option A is correct.

The table shows the size of each bird in grams and the distance each bird traveled in kilometers. Based on the data, the conclusion that the student can make is that the distances bird travel is independent of their size.

The data shows that the smallest bird weighing only 3.0 grams traveled a much greater distance of 276 kilometers compared to the largest bird weighing 25.0 grams which only traveled a distance of 1 kilometer.  Therefore, it is concluded that the size of a bird does not necessarily determine how far it will travel during migration.

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The given shape in the image is not an equilateral triangle.

The triangle with all three sides equal and all the angles equal is called an equilateral triangle.

In the given figure we can see a triangle this triangle is not an equilateral triangle because the figure is formed between a square grid now if you see closely the base of the triangle can not be equal to the two sides of the triangle.

Because these two sides are the hypotenuse for the remaining right-angle triangle. So the base of the highlighted triangle can not be equal to the other two sides of the triangle.

Therefore given shape in the image is not an equilateral triangle.

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Answer:

$11.93

Step-by-step explanation:

You can write an equation to represent this scenario, where x is the number of minutes spent on the call and y is the total cost of the call.

\(y=0.99x + 5.99\)

Plug in 6 for x:

\(y=0.99(6)+5.99\)

Multiply 6 x 0.99, representing the fact it costs 99 cents per each minute spent on the call:

\(y=5.94+5.99\)

Add the sum of the $5.99 cost to connect the call, plus the charge ($5.94) for spending six minutes:

\(y=11.93\)

Your answer is $11.93!

The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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Answer:

pandas

Step-by-step explanation:

Answer:

\(x = \frac{5}{3}\)

Step-by-step explanation:

Parallelogram

It's a quadrilateral formed by two pairs of parallel sides. The opposite sides have equal lengths.

We are given a parallelogram with opposite sides of 3x+1 and 6x-4. They must be equal, thus:

6x - 4 = 3x + 1

Subtracting 3x:

3x - 4 = 1

Adding 4:

3x = 5

Dividing by 3:

\(\mathbf{x = \frac{5}{3}}\)

Answer:

No only variable on both sides have no solution

Step-by-step explanation:

Then you can get,

for example x=x

or,

y=y

Answer:

Step-by-step explanation:

A. Every equation with variables on both sides has no solution.​ However, it is also possible for an equation with the variable on only one side to also have no solution.

B. If the variable only appears on one side of an​ equation, then the equation can always be solved for the variable. This means that if an equation has no​ solution, then the variable must appear on both sides.

C. Any equation can have one​ solution, infinitely many​ solutions, or no solutions. This does not depend on whether the variable appears on only one side or on both sides.

D. If the variable only appears on one side of an​ equation, then the equation can always be solved for the variable. By​ contrast, an equation with variables on both sides always has no solution or infinitely many solutions.