Determine whether the sequence converges or diverges. If it converges, find the limit.an=6^n/(1+7n)

Answer:

first one is 1.-.5

Step-by-step explanation:

So on solving the provided question we can say that -  the function is  f(x) = x= +2, -2

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

the function is -

f(x) = x^2 - 2

f(x) = x= +2, -2

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A map uses scaled drawings. The distance between the two considered cities on that specified map is 6.25 inches

How are scale drawings formed?

For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.

Then it means

1ft : s/k in.

All feet measurements will then we multiplied by s/k to get the drawing's corresponding lengths.

For this case, it is specified that the map uses scaling such that:

3/4 of an inch on map = 3 miles in reality.

Dividing both the quantities by 3, we get:

1 mile in reality = 3/4  / 3  inches on map = 1/4 inches on map

Multiplying both the quantities by 25, we get:

25 miles in reality = 25/4 = 6.25  in map

Since 25 miles is the distance between those two considered cities.

Therefore, the distance between those two cities on map would be of 6.25 inches.

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A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

The area of the quadrilateral is computed as follows if the diagonal and the length of the perpendiculars from the vertices are known: Area of quadrilateral = (12) diagonal length + sum of the length of the perpendiculars drawn from the remaining two vertices.

A quadrilateral is a two-dimensional shape with four sides. Quadrilaterals include the following 2D shapes: square, rectangle, rhombus, trapezium, parallelogram, and kite.

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We will find the costs for each possible buy, and see if it is smaller or larger than $600.

A) They can.

B) They can't.

C) They can.

First, we know that:

And we know that the math club must spend less than $600.

The cost of 250 rolls of wrapping paper will be:

cost = 250*$2 = $500

This is smaller than $600, so they can buy the 250 rolls of wrapping paper.

B) 250 rolls of ribbon will cost:

cost = 250*$3 = $750

This is more than the amount that they have to spend, then they can't buy 250 rolls of ribbon.

C) Here we have the case of 100 of each, the total cost will be:

cost = 100*$2 + 100*$3

cost = $200 + $300 = $500

This is less than their budget, so they can buy this.

More generally, if x = number of rolls of wrapping paper and y = number of rolls of ribbon, we can write the inequality:

x*$2 + y*$3 ≤ $600

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A triangle is said to be congruent with another triangle if its three sides are all congruent. If JK XY, KL YZ, and JL XZ are true, then JKL XYZ is true.

Two triangles are said to be congruent if their three sides are identical to those of another triangle. If JKXY, KLYZ, and JLXZ are true, then JKLXYZ.

Do this Move the orange pointer to M. The two angles JKM and LKM in the preceding diagram create a linear pair. The two non-common legs of the straight line segment JKL are supplementary because they are adjacent and because they always add up to 180 degrees.

It is impossible for the two triangles to be created here since the sum of the two angles is already 18 1 181 circ 181, hence neither J K L triangle (JKL) nor X Y Z triangle (XYZ) can be formed.

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Each system of equations given below has a unique solution 3x−y=13y+3=9x, y+4x=7−2y−4=8x, 4y=3x+48y−6x=8.

A mathematical equation can be defined in a variety of ways. The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal." Mathematical variables are used in even the most fundamental and straightforward algebraic equations.

Given that;

The system of equations is,

⇒ 3x - y = 13

⇒ y + 3 = 9x

Now,

Since, The system of equation is,

⇒ 3x - y = 13

⇒ y + 3 = 9x

It can be written as,

⇒ 3x - y = 13

⇒ 9x - y = 3

Clearly, We have;

⇒ 3/9 = - 1 / - 1

⇒ 1/3 ≠ 1

Thus, It has a Unique solution.

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The ordering of the fraction from least to greatest will be 1/4, 3/8, 1/2, and 3/4.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

The value of 3/4 will be:

= 3/4 × 100

= 75%

The value of 3/8 will be:

= 3/8 × 100

= 37.5%

The value of 1/2 will be:

= 1/2 × 100

= 50%

The value of 1/4 will be:

= 1/4 × 100

= 25%

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The domain of the function f/x = 4x is all real numbers.

The domain of a function is the  et of all values that can be plugged into the equation and produce a valid output. Since any real number, positive, negative, or zero, can be plugged into the equation and produce a valid output, the domain of the function f/x = 4x is all real numbers.

The domain of a function is the set of values that can be plugged into the equation and produce a valid output. In the case of the function f/x = 4x, the domain is all real numbers; that is, any value, positive or negative, can be plugged into the equation and produce a valid output. This means that the domain of the function f/x = 4x includes all real numbers, from the smallest negative number to the largest positive number, as well as zero.

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The correct option: 3. Apply the distributive property or FOIL; to determine the value of zw.

Let z = 19 + i and w = 4 + 10i.

Making a decision is the first step.

The steps to find the product of complex numbers z and w are as follows.

z. w = ( 19 + i )( 4 + 10i ).

z. w = 19 * (4 10i) i * (4 10i).

z. w = 19 * 4 + 19*10i + i * 4 + i * 10i.

z. w = 76 +  190i  + 4i + 10i².

because i² = -1.

z. w = 76 + 194i - 10.

z. w = 66 + 194i.

Thus, in order to find zw in the first step, use the distributive property or FOIL.

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The correct question is-

Let z = 19 + i and w = 4 + 10i.

What is the first step in determining zw?

Answer: 3^2

Step-by-step explanation: i would say that is my answer because , there are 2 threes and in exponential form i think it would be unless its a decimal in between the two threes and not a times

The given expression is equivalent to 486√3

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, √4 of 3√3 of 3⁵

√4 of 3√3 of 3⁵ = 2×3√3×243

= 486√3

Hence, the given expression is equivalent to 486√3

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Answer:

Step-by-step explanation:

Answer: 1 3/5

Step-by-step explanation:15 x 1 3/5 = 24

Brooklyn could calculate how many arithmetic problems she completed and how many pages she read using the equations x = 2y and 2x + 3y = 70.

let

number of math problems Brooklyn solved = x

number of pages she read = y

Time to solve each math = 2 minutes

Time to read each page = 3 minutes

Brooklyn read twice as many pages as there were arithmetic problems to be done.

x = 2y

2x + 3y = 70

Substitute x = 2y into

2x + 3y = 70

2(2y) + 3y = 70

4y + 3y = 70

7y = 70

divide both sides by 7

y = 70/7

y = 10

Recall,

x = 2y

x = 2(10)

x = 20

Therefore, Brooklyn completed 20 math problems and read 10 pages, which equals 20 math problems and 10 pages, respectively.

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Answer:

18.0864 cm^2

Step-by-step explanation:

The formula for the area of the circle is

A = 3.14 · r^2

Radius = D / 2

Radius = 4.8 / 2 = 2.4 cm

Now let's solve for the area of this circle

A = 3.14 · 2.4^2

A = 3.14 · 5.76

A = 18.0864 cm^2

So, the area of this circle is 18.0864 cm^2

Third quadrant the complex plane is where the number -14 - 5i is situated.

Based on the common knowledge, the complex number's real and imaginary components are considered as the x- and y- coordinates of an ordered pair in a 2-D plane.

first quadrant a+bi =(a,b)

second quadrant -a+bi= (-a,b)

third quadrant -a-bi=(-a,-b)

fourth quadrant a,-b=(a,-b)

According to the question,-14-5i is located in third quadrant(-14,-5)

As a result, the complex plane's third quadrant is where the number -14 - 5i is situated.

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3*(28) + 7 can be rewritten as 316 + 7, which can be further simplified by using the associative property of multiplication and the commutative property of addition as (3*16) + 7 = 48 + 7 = 55

The commutative property of addition states that the order of the numbers being added does not matter, for example, a+b = b+a.

The associative property of multiplication states that the grouping of the numbers being multiplied does not matter, for example, (ab)c = a(bc).

Therefore, the expression that uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3*(2*8)+7 is (3*16) + 7 = 48 + 7 = 55.

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Answer:

given points are(-5,-6)and(-3,0),

m=0-(-6)/-3-(-5)

=6/2

=3

Hence,For every +1 unit increase in X axis results in +3 units increase in y axis.

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Answer:

1

Step-by-step explanation:

Anything (besides 0) to the 0 power is 1.

As per the unitary method, the cost of bag is $93.3 and the cost of pen is $64.45

The term unitary method in math is known as the process of solving the  the value of a single unit, and based on this value we can find the value of the required number of units.

Here we have given that the cost of pen and bag is $153.75.

Here we also know that the bag cost $28.85 more than the pen.

Let us consider that x be the cost of pen and here we know that the cost of bag is $28.85 more than the pen then it can be written as,

=> x + 28.85

Therefore, the equation is written as,

=> x + (x + 28.85) = 153.75

Now, we simplify the equation, then we get,

=> 2x + 28.85 = 153.75

Here we need to find the value of x, so, we have to move the other terms on the other side, then we get

=> 2x = 153.75 - 28.85

=> 2x = 124.9

Therefore, the value of x is 64.45.

Therefore, the cost of bag is calculated as,

=> x + 28.85

=> 64.45 + 28.85

=> 93.3

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To break even or make money, the company should charge at least $15 for it's product but no more than $50.

We are given the function that shows the company's profit or loss as;

f(x) = -0.5x² + 32.5x - 375

This function represents a company's profit (or loss) in thousands of dollars.

x represents what it charges for it's product, x in dollars.

Thus, for it to break even, we have to equate f(x) to zero and solve for x to know the maximum and minimum values of x.

Using quadratic formula, we have;

x = [-b ± √(b² - 4ac)]/2a

x = [-32.5 ± √(32.5² - 4(-0.5 * -375))]/2(-0.5)

x = 15 or 50

Thus, the break even charge has a minimum of $15 and a maximum of $50

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2 with an exponent of 7 is 128. It means 2 multiplied by itself 7 times.

When a number is raised to a certain power, it means that the number is multiplied by itself that many times. For example, 2 with an exponent of 7 means 2 multiplied by itself 7 times.

So, 2 with an exponent of 7 is 128.

It's important to note that the exponent is also known as the power, so 2^7 is also read as 2 to the power of 7.

Exponents are a way of shorthand for repeated multiplication. Understanding this concept is important for solving mathematical problems, especially in algebra and calculus.

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Answer: yes

Step-by-step explanation:

Dividing the quantities of whole recipe by 4 it can be made for one person.

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

Any number must have a divisor that is less than the dividend when we divide it. Every time, deduct the product from the dividend number before moving on to the next number in the sequence. Always write the product below the dividend number and the quotient above the line.

Dividing the quantities of whole recipe by 4 -

9/16 cups of pastry dough

5/8 cups vegetables, chopped

1/16 of a cup of butter

salt and pepper to taste

3/8 cups of chicken

*serves one

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Answer:The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Add 10 10 to both sides of the equation. Using the slope-intercept form, the y-intercept is 10 .

Step-by-step explanation:

According to number line, x > 5 is correct,

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when plotting a point.

Here,

Given :

∵ The inequality is -3(2x - 5) < 5(2 - x)

At first simplify each side

∵ -3(2x - 5) = -3(2x) + -3(-5)

Remember (-)(-) = (+)

∴ -3(2x - 5) = - 6x + 15

∵ 5(2 - x) = 5(2) + 5(-x)

Remember (+)(-) = (-)

∴ 5(2 - x) = 10 - 5x

∴ - 6x + 15 < 10 - 5x

Subtract 15 from both sides

∴ - 6x < -5 - 5x

Add 5x to both sides

∴ - x < - 5

∵ The coefficient of x is -1

∴ Divide both sides by -1

∴ x > 5

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Problem 4

I recommend to draw a number line. Place the baseball park at 0 on the number line.

Then place Luke's house at -3. The distance from -3 to 0 is 3 units, to represent the 3 miles.

Place Logan's house at 2 on the number line.

To go from -3 to 2, move 5 units to the right. This is the longest distance possible because each person's house is on opposite sides of the baseball park.

To get the shortest distance possible, we'll place each person's house to the right of 0. This time each person's house is on the same side.

We'll move Luke from -3 to +3. Keep Logan at 2. The distance from 2 to 3 is 1 unit. This is the shortest distance possible.

Answers:

Shortest distance = 1 mile

Longest distance = 5 miles

===============================================

Problem 5

d = distance between Luke's house and Logan's house

Refer to the result of problem 4, where we found d = 1 the smallest possible value of d. And also d = 5 the largest possible value.

In other words: d is between 1 and 5, including each endpoint.

The compound inequality to set up is [tex]1 \le d \le 5[/tex]

The graph involves closed filled in circles at 1 and 5 on the number line. Shade the region between these endpoints. Closed endpoints visually tell the reader "include this endpoint".

Answers:

Inequality:  [tex]\boldsymbol{1 \le d \le 5}[/tex]

Graph: Closed filled in circles at 1 and 5; shading in between

===============================================

Problem 6

The largest distance we previously found was 5 miles.

Luke traveled 0.5 miles so far, meaning he has at most 5-0.5 = 4.5 miles left to go.

Answer:  

4.5 miles

Answer:

Q4  
Shortest distance = 1 mile
Longest distance = 5 miles

Q5
1 ≤ d ≤ 5

Q6
4.5 miles

Step-by-step explanation:

A diagram does help for these questions

Q4

If both Luke and Logan's houses are on the same straight line in the same direction then the difference between their individual distances from the field will be the shortest distance.

See the first diagram

Shortest distance = 3 - 2 = 1 mile

However, if they lived in exactly opposite directions on a straight line then the distance would be the longest and would be 2 + 3 = 5 miles

--------------------------------------------------------------------------------

Q5

The compound inequality would be 1 ≤ d ≤ 5 where d represents all possible distances from the two homes.

(We can also write this as [1, 5] which is called interval notation)

See second figure for how this would be represented on a number line

------------------------------------------------------------------------------

Q6

Since we have determined the greatest distance between the two houses as 5 miles, and Luke has already biked 0.5 mile he has 5 - 0.5 = 4.5 miles left to bike