The end behavior of the graph of f(x) = x^5 + 8x^4 + 16x^3 is that it increases without bound as x approaches positive and negative infinity.
The end behavior of the graph of f(x) = x^5 + 8x^4 + 16x^3 can be determined by examining the degree and leading coefficient of the polynomial. The degree of the polynomial is 5, which indicates that the graph increases without bound as x approaches positive and negative infinity. The leading coefficient of the polynomial is 1, which indicates that the graph increases as x approaches positive and negative infinity.
To illustrate this, let's consider the value of f(x) for increasingly large values of x. For x = 10, f(x) = 10^5 + 8(10^4) + 16(10^3) = 1,000,000 + 80,000 + 160,000 = 1,240,000. As x continues to increase, the value of f(x) continues to increase without bound as the terms of the polynomial become increasingly larger.
Similarly, for x = -10, f(x) = (-10)^5 + 8((-10)^4) + 16((-10)^3) = -1,000,000 + 80,000 - 160,000 = -980,000. As x continues to decrease, the value of f(x) continues to decrease without bound as the terms of the polynomial become increasingly larger.
Thus, the end behavior of the graph of f(x) = x^5 + 8x^4 + 16x^3 is that it increases without bound as x approaches positive and negative infinity.
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What is a constant of dilation?
A constant of dilation is a number used to change the size of a figure while preserving its shape. It is also known as a scale factor.
The constant of dilation is used in a dilation transformation, a type of transformation that changes the size of a figure without changing its shape or orientation.
The constant of dilation is typically represented by the letter "k" and is a number greater than 0. If the constant of dilation is greater than 1, the dilation will increase the size of the figure. If the constant of dilation is less than 1, the dilation will reduce the size of the figure. And if the constant of dilation is equal to 1, the dilation will not change the size of the figure.
It's important to note that the constant of dilation is a factor that applies to all the points of the figure, and it's the same for all the points of a figure during a dilation transformation.
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Write the rational number as a decimal: 4 1/6
Answer: 4.17
Step-by-step explanation:
.
Translate the sentence into an equation.
Six more than the quotient of a number 2 and 4 equals .
Use the variable y for the unknown number.
Answer:
y / 4 + 6 = 2
Step-by-step explanation:
The most Lastri can afford to pay per year in mortgage payments is $13,900, and her credit score is 498. According to the following table for a $150,000 mortgage, by how many points would she need to improve this credit score in order to take a mortgage for $150,000?
According to the table for a $150,000 mortgage, Lastri's credit score needs to improve by 62 points for her to take a mortgage for $150,000.
What is the credit score?The credit score refers to an individual's or entity's creditworthiness rating.
The credit score predicts a person's credit behavior and ability to repay credit.
Financial institutions and lenders use the credit score to determine the amount of credit to offer a borrower, the attached credit risks, and the accompanying interest rate, including monthly payments.
Annual mortgage payments Lastri can afford = $13,900
Monthly payment = $1,158 ($13,900 ÷ 12)
Current credit score = 498
Minimum credit score for a monthly payment of $1,158 = 560
Additional credit score improvement = 62 (560 -498)
Thus, for Lastri to qualify for a $150,000 mortgage, her FICO credit score must improve by 62 points.
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Question Completion:Table
FICO Interest Monthly
Score Rate Payment
720 - 850 5.59% $860
700 - 719 5.71% $872
675 - 699 6.25% $924
620 - 674 7.40% $1,039
560 - 619 8.53% $1,157
500 - 559 9.29% $1,238
dani had $200 in her savings account. When she turned 18, the bank began charging her a $5.00/month fee. Write a function in terms of a for the balance of her savings account if she doesn't notice the monthly fee.
Complete the following. Use standard slope-intercept form.
We can write a function in terms of 'a' for the balance of Dani's savings account if she doesn't notice the monthly fee as:
f(a) = 200 - 5a
where 'a' represents the number of months that have passed since Dani turned 18 and the bank began charging her the monthly fee.
So, f(0) = 200 represents the initial balance in Dani's savings account when she turned 18.
f(1) = 200 - 5(1) = 195 represents the balance in Dani's savings account after 1 month.
f(2) = 200 - 5(2) = 190 represents the balance in Dani's savings account after 2 months and so on.
Therefore, the function f(a) = 200 - 5a represents the balance of Dani's savings account after 'a' number of months if she doesn't notice the monthly fee.
Let me know if this helps! :)
write an expression for “the quoitient of 9 and c
The expression that the quotient of the number 9 and the letter 'c' will be 9 / c.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The quotient of the number 9 and the letter 'c' is written as,
⇒ 9 / c
The expression that the quotient of the number 9 and the letter 'c' will be 9 / c.
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Tell whether the lengths 3, 14, and 10 form the sides of an acute, right, obtuse, or not a triangle.
A. acute
B. right
C. not a triangle
D. obtuse
The lengths 3, 14, and 10 form a obtuse triangle
How to Determine if Three Side Lengths Are a Triangle?It's simpler than it seems to determine whether a triangle has three side lengths. The Triangle Inequality Theorem, which asserts that the sum of a triangle's two side lengths is always greater than the third side, will suffice. You will have a triangle if this holds true for each of the three possibilities of increased side lengths.
Theorem of Triangle Inequality. This theorem merely states that the third side of a triangle cannot be smaller than the total of the first two sides. You will have a valid triangle if this holds true for each of the three possible combinations. To confirm that the triangle is feasible, you will need to go through each of these combinations one at a time. Theorem a+b > c, a+c > b, and b+c > a can alternatively be thought of as an inequality. The triangle has sides of lengths a, b, and c.
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The accompanying table shows the value of a car over time that was purchased for 16100 dollars, where x is years and y is the value of the car in dollars. Write an exponential regression equation for this set of data, rounding all coefficients to the nearest thousandth. Using this equation, determine the value of the car, to the nearest cent, after 16 years.
The value of car to the nearest cent, after 16 years will be $882.
Define the term exponential regression?It is a concept that describes processes that increase at a twice as fast rate. It is employed when the growth starts slowly but quickly accelerates without bounds or when the decay begins strongly but subsequently decelerates to zero.The preceding table displays the increase in value of a car that cost $16,100 over time, where x represents the number of years and y represents the car's cash value.
The formula for the exponential regression will be as follows:
y = A₀e∧(kx)
Where k is a constant and A₀ is the exponential regression coefficient.
So value of y would be $16,100 if x = 0. Next, we have
16,100 = A₀ e∧(k*0)
A₀ = 16,100
The equation will then be:
y = 16,100e∧(kx)
Hence value of y would be $13,431 if x = 1. Next, we have:
13,431 = 16,100e∧(k*1)
e∧(k) = 0.834
Considering all sides, we then have:
ln e∧(k) = ln 0.834
k = -0.181
The equation will then be:
y = 16,100e∧(-0.181*x)
For 16 years,
y = 16,100e∧(-0.181*16)
y = 16100*0.054
After that, a car's value will be:
y = 882
Thus, the value of the car to the nearest cent, after 16 years will be $882.
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Diego says the expression 14−0.6t14−0.6t14−0.6t helps him understand this situation. In this situation, what does this expression represent, and what does the variable ttt stand for?
The expression 14 - 0.6t represents the number of gallons left for t number of days.
The variable t means the number of days.
What does the expression mean?In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this case, each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less. The expression is 14 - 0.6t.
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Complete question
Diego’s family car holds 14 gallons of fuel. Each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less.
Diego says the expression 14 - 0.6t helps him to understand this situation. What does this expression represent, and what does the variable t stand for
how many pints are in 3 3/4 gal
A particle rotates in a clockwise
motion according to the equation
x = 3 cos (0.2t - 0.813)
where t is in seconds
What is its frequency?
The frequency of the motion is given as follows:
0.0318 Hz.
How to obtain the frequency of the motion?A standard cosine function is defined as follows:
g(x) = acos(b(x+c))+d.
The coefficients have these following roles:
a: amplitude.b: The period is of 2π/B.c: phase shift.d: vertical shift.Hence we must look first at coefficient b to obtain the period of the function.
The coefficient b is given as follows:
b = 0.2.
Hence the period of the function is of:
p = 2π/0.2
p = 10π.
The frequency is one divided by the period, hence:
f = 1/10π
f = 0.0318 Hz.
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Simone practices her violin for hour each day. How much time does she spend practicing her violin each week? (A week has 7 days.)
Answer:
simone spends 7 hours a week
Step-by-step explanation:
Simone practices 1 hour every day
a week has 7 days, so
we multiply 7 x 1 = 7 hours per week
7= days of the week
1= hours simone practices every day
What is the image point of ( 6 , 5 ) after the transformation D 5 ∘ 0 ∘T 0,0 ?
The image point of P(x,y) = ( 6 , 5 ) after applying a horizontal reflection is P'(x,y) = (1, 5).
How to determine the image after transformation?In geometry, a rigid transformation is a transformation applied onto a geometric object such that Euclidean distance in every point of it is conserved. Translations are examples of rigid transformations and are defined by this formula:
P'(x,y) = P(x,y) + T(x,y) (1)
Where:
P(x,y) - Original point
T(x,y) - Translation vector
P'(x,y) - Image point
If we know that P(x,y) = (6, 5) and T(x,y) = (5, 0), then the image point is:
P'(x,y) = (6, 5) + (5, 0)
P'(x,y) = (1, -6)
The image point of P(x,y) = (6, 5) after applying a horizontal reflection is P'(x,y) = (1, 5).
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Correct form of the question
What is the image point of (x, y) = (6, 5) after the transformation of translating horizontally the point 5 units to the y-axis?
Please help fast guys
write the slope intercept form of the equation of a line with a slope of -5/8 that passes through the point (-14, 6)
Answer:
Step-by-step explanation:
Slope intercept for y=mx+b
point it passes (-14, 6) wherein b (0, b) is b=6
slope m = -5/8
substitute: y = mx+b
y= (-5/8)x+6
X
Incorrect
1 try left. Try once more
A certain state legislature has senators and representatives. The combined nu
the numbers is 150. There are more representatives than senators.
How many senators and how many representatives are in this state's legislatu
Number of senators: 130
Number of representatives: 150
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Need help with this question?
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(150 + x) + 130 >= 150 is the inequality equation for the state legislature, which consists of senators and members.
what is inequality ?Mathematics uses the term inequality to describe a link between two expressions or values that is not equal. Thus, imbalance is the cause of inequality. The relationship between two non-equal values in mathematics is established by an inequality. Egality and inequality are not synonymous. Whenever two values are not equal, use the not equal sign (). Various inequalities are used to compare values, whether they are small or large. You can eliminate a lot of simple inequalities by modifying both sides until only the variables are left. Inequality is brought on by a number of things, though: On both sides, subtract or multiply negative values. Alternate between left and right.
given
Number of senators: 130
Number of representatives: 150
more representatives than senators
(150 + x) + 130 >= 150 is the inequality equation for the state legislature, which consists of senators and members.
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-3x-3y=3 solve by substitution
Answer: x = 2, y = -3
Step-by-step explanation: From the question,
-3x -3y = 3 ---------- this becomes the first equation
Make y the subject
-3y = 3 + 3x
y = (3 + 3x)/ -3 ----------this becomes our second equation
Substitute the value of y into the first equation
-3x -3(3 + 3x) = 3
-3x -9 + 9x = 3
Collect like terms
-3x + 9x = 3 + 9
6x = 12
Divide both sides by 6
6x/ 6 = 12/ 6
x = 2
Substitute x = 2 into the second equation to find y
y = (3 + 3(2) )/ -3
y = ( 3 + 6) / -3
y = 9/ -3
y = -3
What is the full table of 4?
After responding to the question, we can therefore say that the numbers in the four-way tables are 4,8,12,16,20,24,28,32,36, and 40.
Describe a table.A mathematical table is a collection of numbers that shows the outcome of a calculation using multiple inputs. data with numbers and descriptions that is arranged in rows and columns. The table and 10 pattern are easy to remember. The following is the order of the numbers:2,4,6,8,10,12,14,16,18,20. Value maps are used to show how different data pieces are related to one another. You can incorporate the values table into your science lecture. Scientists and researchers use tables of values to store data and seek for patterns in that data. Then, this pattern is used in forecasting.
Here,
Thus,
table of four are as follows:
4,8,12,16,20,24,28,32,36 and 40.
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Foundations of Algebra B
ous Activity
Week
Juan's Fundraising Progress
Total Sold in
Fruit Baskets
($)
Total Sold
in Pencils
($)
O
Juan is selling fruit baskets and pencils for his
fundraisers. He started his fundraising early and has 12
weeks to reach his goal of selling $300.00 worth of
goods to pay for his trip's cost.
If Juan uses the table shown to represent all of his
data, what interval for the weeks would you use in
column 1 so that all 12 weeks are represented?
Week labels:
English
1, 2, 3, 4
2, 4, 6, 8
3, 6, 9, 12
1, 3, 6, 10
Juan have to sell 4 fruit baskets to make enough money.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Juan's Fundraising Progress Juan sold fruit baskets for $16.50 each and pencils for $1.50 each. His goal is to sell $300 worth of goods to pay for his trip's cost.
His goal is to sell $300, the pencil sold a total of $81, so the fruit basket will sell a total of 300-81=219
Las three week: 219-165 =$54
Fruit baskets for $16.50 per each
54/16.50 =3.27
So, he have to sell 4 fruit baskets to make enough money
Hence, Juan have to sell 4 fruit baskets to make enough money.
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"Your question is incomplete, probably the complete question/missing part is:"
Juan's Fundraising Progress Juan sold fruit baskets for $16.50 each and pencils for $1.50 each. His goal is to sell $300 worth of goods to pay for his trip's cost. How many fruit baskets will Juan need to sell the last three weeks to achieve his goal?
What is the area of 8cm and 5cm triangle?
The area of an 8 cm by 5 cm triangle is 20 cm^2.
The area of a triangle is calculated using the formula A = 1/2 * b * h, where b is the length of the base and h is the height. In this case, the base is 8 cm and the height is 5 cm, so the area of the triangle can be calculated as follows:
A = 1/2 * 8 * 5
A = 20 cm^2
Therefore, the area of an 8 cm by 5 cm triangle is 20 cm^2.
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A gymast practices 6 days each week. She practices he same number of hours each day. If she practices a total of 120 in a 4- week period , how many hours each day does she practice.
The gymnast trains 5 hours per day making a total of 120 hours in a 4 week period
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
Let x represent the number of hours practiced per day. A gymnast practices 6 days each week, hence:
Number of hours practiced per week = 6x
If she practices a total of 120 hours in a 4- week period. Therefore:
6x hours per week * 4 weeks = 120 hour
24x = 120
x = 5
The gymnast trains 5 hours per day.
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Who found the formula for area?
Hippocrates of Chios was the first to show that the area of a disk
Who discovered area formula?
In the 5th century BCE, Hippocrates of Chios was the first to show that the area of a disk (the region enclosed by a circle) is proportional to the square of its diameter, as part of his quadrature of the lune of Hippocrates, but did not identify the constant of proportionality.
A large part of the field of operations research is the use of statistical equations to solve problems in business or military operations.
Music, linguistics, and philosophy all use mathematical models (for example, intensively in analytic philosophy).
A model is, for example, the method for the area of a circle, πr2.
Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'. This quantity has importance in almost all circle-related formulas. The area and circumference of a circle are also measured in terms of radius.
Α= pi r^2
Divide each side by pi
A / pi = r^2
Take the square root of each side
sqrt( A / pi ) = sqrt(r^2)
sqrt( A / pi ) =r
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Please help! Trig!!!!!!!l. Look at the image! And answer the question! Thank u!
On solving the provided question, we can say that - there are 67 numbers less than 100 are divisible by 3, by divisibility test.
what is divisibility test?The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.
= n(A ∪ B)
= n(A) + n(B) - n(A ∩ B)
= 33 + 50 - 16
= 67
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On solving the provided question, we can say that by trigonometry, t = [tex]4\pi /3[/tex]; x = cos([tex]4\pi /3)[/tex] = [tex]-\sqrt{2}/4[/tex] and y = sin([tex]4\pi /3)[/tex] = [tex]-3\sqrt{2}/11[/tex]
what is trigonometry?The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.
here,
by trigonometry,
t = [tex]4\pi /3[/tex]
x = cos([tex]4\pi /3)[/tex] = [tex]-\sqrt{2}/4[/tex]
y = sin([tex]4\pi /3)[/tex] = [tex]-3\sqrt{2}/11[/tex]
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each paper clip is 3/4 of an inch long and cost $0.02. exactly enough paper clips are laid end to end to have a total length of 36 inches what is the total length of 36 inches what is the total cost of these paper clips
What is the additive inverse of 3 /- 7?
The additive inverse of 3/-7 is -3/7. This means that when 3/-7 is added to its additive inverse, the result is 0.
The additive inverse of any number is the number with the same absolute value but with the opposite sign. Therefore, the additive inverse of 3/-7 is -3/7. When two numbers are added together, the signs of the numbers can affect the result. For example, when two negative numbers are added, the result is a negative number. When two positive numbers are added, the result is a positive number. When one number is positive and one number is negative, the result depends on the relative size of the two numbers. For example, if the positive number is larger than the negative number, the result is a positive number. However, if the negative number is larger than the positive number, the result is a negative number. In the case of 3/-7, the negative number is larger than the positive number, so the result of adding 3/-7 to its additive inverse is 0.
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Line e has a slope of -4/9. Line f is parallel to line e. What is the slope of line f? Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
-4/9
Step-by-step explanation:
Line f has the same slope as line e. Parallel lines have the same slope.
Line e has the slope -4/9.
Line f has the slope -4/9.
The vertical distance of a falling ball is directly proportional min to the square of the time of the fall. The ball falls 80 m 4 seconds.
(a) Find the vertical distance fallen in 6 seconds.
(b) If the ball is dropped from a height of 240 m, find the time it takes to hit the ground.
Answer:
180 m , ≈ 6.9 seconds
Step-by-step explanation:
let vertical distance be represented by d and time t
given d is directly proportional to t² , then the equation relating them is
d = kt² ← k is the constant of proportion
to find k use the condition , the ball falls 80 m in 4 seconds , then
80 = k × 4² = 16k ( divide both sides by 16 )
5 = k
d = 5t² ← equation of proportion
(a)
when t = 6
d = 5 × 6² = 5 × 36 = 180 m
(b)
when d = 240
240 = 5t² ( divide both sides by 5 )
48 = t² ( take square root of both sides )
[tex]\sqrt{48}[/tex] = t , that is
t ≈ 6.9 seconds ( to the nearest tenth )
25. Higher Order Thinking How are the ratios 24 laps 1 hour different? 192 laps 8 hours alike? How are they different?
These ratios are different because they express the number of laps for two different numbers of hours.
How do these ratios compare?To better understand how these ratios compare, let's simplify the second ratio:
192 laps/ 8 hours = 24, which means the ratio would be 24 laps per hour
This means that the ratios express the same number of laps per hour.
What makes the ratios different?Basically, the two ratios tell us the number of laps but using different hours. In this way, the first ratio expresses the number of laps in only one hour, while the second ratio amplifies this ratio to eight hours.
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Which of the following rational functions is graphed below?
Answer:A
Step-by-step explanation:
estimate 5.26 × 4.9
I NEED IT ASAP
Answer:
25.774
Step-by-step explanation:
5 x 4.9 = 24.5
0.26 x 4.9 = 1.274
24.5 + 1.274 = 25.774