Therefore, The sequence diverges, as the limit of the sequence as n approaches infinity is infinity. In summary, the sequence an = 6^n / (1 + 7n) diverges.
To determine whether the given sequence converges or diverges, we will examine the limit of the sequence as n approaches infinity. The sequence is an = 6^n / (1 + 7n).
Step 1: Find the limit as n approaches infinity.
lim (n → ∞) (6^n / (1 + 7n))
Step 2: Divide both the numerator and denominator by the highest power of n (n^1 in this case).
lim (n → ∞) ((6^n / n) / (1/n + 7))
Step 3: Apply the limit to each part.
lim (n → ∞) (6^n / n) = ∞
lim (n → ∞) (1/n) = 0
Step 4: Evaluate the limit.
lim (n → ∞) (6^n / (1 + 7n)) = ∞ / (0 + 7) = ∞
Therefore, The sequence diverges, as the limit of the sequence as n approaches infinity is infinity. In summary, the sequence an = 6^n / (1 + 7n) diverges.
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HELP?
A. Acute
B. Obtuse
C. Right
D. Not a triangle
The math club will sell rolls of wrapping paper and ribbon as a fundraiser. They must spend less than $600 to purchase the fundraiser item. Each roll of wrapping paper cost $2. Each roll of ribbon cost the club $3.
A) Is it possible to buy 250 rolls of wrapping paper and meet the conditions above? Why or Why not
B) Is it possible to buy 250 rolls of ribbon and meet the conditions above? Why or Why not
C)Is it possible to buy a combination of 100 rolls of wrapping paper and 100 rolls of ribbon and meet the conditions above? Why or Why not
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.
Is it possible to buy 250 rolls of wrapping paper?
First, we know that:
A roll of wrapping paper cost $2A roll of ribbon cost $3And 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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What is 1 with an exponent of 0?
Answer:
1
Step-by-step explanation:
Anything (besides 0) to the 0 power is 1.
The scale on map indicates that 3/4 of an inch represents 3
miles. If the distance between two points on its map is 2
inches, how far apart are two locations?
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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Determine if the functions are inverses.
Answer: yes
Step-by-step explanation:
What is the domain of the function f/x )= 4 x?
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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Which expression uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3*(2*8)+7 ?
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
What is the commutative property of addition and the associative property of multiplication?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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Given the following two ordered pairs calculate the rate of the function. (−5, −6) and (−3, 0) Enter your answer in the box. m=
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.
*mark me brainliest
Brooklyn had math and reading homework tonight. Brooklyn can solve each math
problem in 2 minutes and she can read each page in 3 minutes. The number of math
problems Brooklyn solved is twice the number of pages she read and it took her 70
minutes to complete all of her homework. Write a system of equations that could be
used to determine the number of math problems Brooklyn solved and the number of
pages
she read. Define the variables that you use to write the system.
Let
Let
System of Equations:
Brooklyn could calculate how many arithmetic problems she completed and how many pages she read using the equations x = 2y and 2x + 3y = 70.
What is meant by mathematical equations?An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.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.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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What is 2 with an exponent of 7?
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.
2^7 = 2 * 2 * 2 * 2 * 2 * 2 * 2 = 128So, 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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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
According to number line, x > 5 is correct,
What is number line?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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In what quadrant-14 -5i located on the complex plane
Third quadrant the complex plane is where the number -14 - 5i is situated.
-14-5i is located in which quadrant?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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4.8cm diameter in area
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
Somebody help please I don’t understand!!
Dividing the quantities of whole recipe by 4 it can be made for one person.
What does math division mean?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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NEED HELP WITH MATH (Explain how you got the answer)
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.
Which condition would prove JKL and XYZ?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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I really need help on this!
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
Which quadrilateral makes this statement true?
Quadrilateral ABCD =
A 114
125
D
Quadrilateral ABCD
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.
How is a quadrilateral calculated?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.
What is a quadrilateral's shape?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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HELP ASAPPPP 20 POINTS WILL MARK BRAINLIEST IF CORRECT
Answer:
first one is 1.-.5
Step-by-step explanation:
what is 3.3 as an exponent
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
24 tiny homes are being built from 15 pallets of wood. How many pallets will each home use
Answer: 1 3/5
Step-by-step explanation:15 x 1 3/5 = 24
The function f(x) = -0.5x^2 + 32.5x - 375 gives a company's profit (or loss) in thousands of dollars, based on what it charges for it's product, x in dollars. If the product is too cheap, the company will not make enough money. If it is too expensive, it will not sell well. A company "breaks even" when it makes enough money to cover it's costs, but hasn't yet made a profit. To break even or make money, how much should the company charge for it's product.
To break even or make money, the company should charge at least $_______ for it's product but no more than $_______
To break even or make money, the company should charge at least $15 for it's product but no more than $50.
How to find the solution to quadratic functions?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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Let z = 19 i and w = 4 10i. what is the first step in determining zw? replace i2 with –1. multiply z by the conjugate of w. apply the distributive property or foil. combine the corresponding real and imaginary parts.
The correct option: 3. Apply the distributive property or FOIL; to determine the value of zw.
What exactly is a complex number?Complex numbers are defined as a combination of real and fictitious numbers. Z = a + ib, where a and bi are real and imaginary numbers, is how a complex number is expressed.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 ).
applying distributive law,z. w = 19 * (4 10i) i * (4 10i).
removing the parenthesis,z. w = 19 * 4 + 19*10i + i * 4 + i * 10i.
Similar to that, further actions are.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?
Replace i2 with –1.Multiply z by the conjugate of w.Apply the distributive property or FOIL.Combine the corresponding real and imaginary parts.Are reflected triangles congruent?
Answer:
Step-by-step explanation:
HELP
How do you solve percentages?
A bag and a ign pen cot 153. 75 peo. The bag cot 28. 85 peo more than the ign pen. How much doe each cot?
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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What is the y-intercept of 10?
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:
How many solutions does each system of equations have?
Part A: {3x−y=13y+3=9x
Part B: {y+4x=7−2y−4=8x
Part C: {4y=3x+48y−6x=8
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.
What are equations?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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How do you use a table to solve a function?
So on solving the provided question we can say that - the function is f(x) = x= +2, -2
what is function?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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The expression 4 square root of 3 times 3 square root of 3^5 is equivalent to
The given expression is equivalent to 486√3
What are expressions?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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Order the fractions from least to greatest.
3
−
4
, 3
−
8
, 1
−
2
, 1
−
4
The ordering of the fraction from least to greatest will be 1/4, 3/8, 1/2, and 3/4.
How to calculate the fraction?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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