The statement that correctly describes the horizontal asymptote of g(x) is:
Limit of g (x) as x approaches plus-or-minus infinity = 6, so g(x) has an asymptote at y = 6.
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the limit of f(x) as x goes to infinity, as long as this value is different of infinity.In this problem, the function is:
[tex]g(x) = \frac{42x^3 - 15}{7x^3 - 4x^2 - 3}[/tex]
The horizontal asymptote is given as follows:
[tex]y = \lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} \frac{42x^3 - 15}{7x^3 - 4x^2 - 3} = \lim_{x \rightarrow \infty} \frac{42x^3}{7x^3} = \lim_{x \rightarrow \infty} 6 = 6[/tex]
Hence the correct statement is:
Limit of g (x) as x approaches plus-or-minus infinity = 6, so g(x) has an asymptote at y = 6.
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Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint.
Slope and a point that is not an intercept is the information about the graph of the relationship is given.
The rate of painting is 8 m²/h.
28 square meters of the room are still left to paint after three hours. Let y represent the area in square meters that needs painting after x hours. We require a corresponding (x,y) pair in order to describe a point on a graph. In our situation, we require data on the rate of change in the correlation between the area still needing painting and the time after business hours. Hiro can paint eight square meters per hour. Thus, the equation Y = 8x, or the associated slope, is 8. (1)
By entering the number Y = 28 square meters into the previous formula 28 = 8X
=> X = 7/2
It is not an intercept but the point (7/2, 28).
Alternatively put, the location that is not the intersection with the slope
Your question is incomplete but most probably your full question was
Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint. Let y represent the area (in square meters) left to paint after x hours.
Which of the following information about the graph of the relationship is given?
a)Slope and x-intercept
b) Slope and y-intercept
c)X-intercept and y-intercept
d) Y-intercept and a point that is not an intercept
e)Two points that are not intercepts
f)Slope and a point that is not an intercept
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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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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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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! :)
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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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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5. Some chickens and pigs are in a field. How many of each animal are
there if there are 32 heads and 80 legs in total?
Becuase a pig and a chicken each have one head each and we know there are 80 heads, we know that: C + P = 80. When you combine these equations, we find that there are 32 Pigs and 48 Chickens.
What is equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables. A mathematical equation is a formula that uses the equals sign to express the equality of two expressions. A mathematical statement called an equation demonstrates the equality of two mathematical expressions.To learn more about algebraic refer to:
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Which have 7 sides is called?
A heptagon is a seven-sided polygon. It is also sometimes called a septagon, though this usage mixes a Latin prefix sept- (derived from septua-, meaning "seven")
Polygon Formula
The important polygon formulas are: The sum of interior angles of a polygon with “n” sides =180°(n-2) Number of diagonals of a “n-sided” polygon = [n(n-3)]/2. The measure of interior angles of a regular n-sided polygon = [(n-2)180°]/n.
with the Greek suffix -gon (from gonia, meaning "angle"), and is therefore not recommended
This polygon has 7 sides
heptagon is a seven sided polygon
decagon is a ten sided polygon
dodecagon is a 12 sided polygon
hexagon is a six sided polygon
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How do you find the predicted Y value?
The formula for calculating the anticipated value of y, known as the "fitted value," is y I = b 0 + b 1 x i.
What is Y value?Determine the graph's slope and a point first. Write a linear equation in slope-intercept form (y = mx + b) once this is finished.
Rewrite the equation using the supplied point (x, y) and slope (m), inserting the correct values for x, y, and m.
To find the y-intercept using this information, calculate the equation for b.
Find the two points in a graph or table that are displayed.
Take note of each point's coordinates (x, y) first. Find the rise and run to determine the slope using this information.
Y-coordinate difference divided by the.
Hence, The formula for calculating the anticipated value of y, known as the "fitted value," is y I = b 0 + b 1 x i.
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Gary wants to build a shed shaped like a rectangular prism in his backyard. He goes to the store and looks at several different options. The table shows the dimensions and volumes of four different sheds.
Use the formula V = l × w × h to complete the table.
Length (ft) Width (ft) Height (ft) Volume (ft3)Shed 1 15 9 2,160
Shed 2 10 10 1,300
Shed 3 12 9 864
Shed 4 15 12 12
Answer: Shed 1: 291,600 units^3. Shed 2: 130,000 units^3. Shed 3: 93,312 units^3. Shed 4: 2,160 units^3
Step-by-step explanation:
15 times 9 times 2,160 = 291,600
10 times 10 times 1300 = 130,000
12 times 9 times 864 = 93,312
15 times 12 times 12 =2,160
The slope of the line represented by y = 5x is___
The slope of the line represented by y = 3 is ___
The slope of the line represented by x = 4 is___
Answer:
5, 0, Undefined.
Step-by-step explanation:
Answer:
1) 5
2) 0
3) Undefined
The SlopeSlope is a measure of steepness of a line. In Algebra 1, It is how much the y-value changes when the x-value increases by 1.
y-intercept is the y-value of the line when it intersects with the y-axis, or the y-value of the line when the x-value of the line is 0.
Slope-Intercept FormThis form is the most common form for expressing linear equations for graphing and is used when the slope and y-intercept is known.
Form
y = mx + b
Lets break it down. y and x stay as a variable when graphing is it only substituted for a constant when solving for x-intercept, etc.
m is the slope.
b is the y-intercept.
Q)Q1
y = mx + b
y = 5x
Because 5 is the m value, the slope is 5.
Q2
y = mx + b
y = 3
Think about it. What cancels out any real value? Multiplying it by 0. If there is no coefficient behind the x, it means the slope is 0.
y = 0x + 3 = y = 3
Because 0 is the m value, the slope is 0.
When y is equal to a constant after solving, it is a horizontal line with the y-intercept of the constant it is equal to (in this case 3).
Q3
y = mx + b
x = 5
The slope is undefined.
When x is equal to a constant after solving, it is a straight vertical line with the x-intercept of the constant it is equal to (in this case 5). The slope is always undefined.
Which of the following rational functions is graphed below?
Answer:A
Step-by-step explanation:
What is the area of a triangle with the base of 7 cm and the height of 12 cm?
The area of a triangle with the base of 7 cm and the height of 12 cm is 42 square cm.
In the given question we have to find the area of a triangle with the base of 7 cm and the height of 12 cm.
The entire area bounded by a triangle's three sides is referred to as the triangle's area. In essence, it equals half of the base times height, or A = 1/2bh. So, in order to calculate the area of a triangular polygon, we need to know its base (b) and height (h).
Area of Triangle = 1/2 ×b×h
Area of Triangle = 1/2 ×7×12
Area of Triangle = 7×6
Area of Triangle = 42 square cm
Hence, the area of a triangle with the base of 7 cm and the height of 12 cm is 42 square cm.
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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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314
X
1|2
Drag the expressions to the table to show whethe
than or equal to
Less than 1/
DRAG AND
DROP ITEMS
HERE
17
12
X
54
X
1|2
Equal to 1/2
DRAG AND
DROP ITEMS
HERE
12
CLEAR
More than
DRAG AND
DROP ITEMS
HERE
CHECK
The calculations 4(2/9) is 8/9 1, 2(2/5) is 4/5 1, and 8(2/5) is 16/5 > 1, 6×(1/5) is 6/5 > 1, 5×(1/4) is 5/4 > 1.
An example of a fraction?If q is less than 0, a fraction is expressed as p/q. A proper fraction is one that follows the rules, and an improper fraction is another. The numerator in proper fractions is less than the denominator, whereas in improper fractions, the opposite is true.
We are aware that when multiplying fractions, we can eliminate terms from the numerator and denominator of other fractions to make the problem simpler, and we can also multiply numerators and denominators together.
∴ 4×(1/4) = 1.
4×(2/9) = 8/9 < 1.
2×(2/5) = 4/5 < 1.
8×(2/5) = 16/5 > 1.
6×(1/5) = 6/5 > 1.
5×(1/4) = 5/4 > 1.
The calculations 4(2/9) = 8/9 1, 2(2/5) = 4/5 1, and 8(2/5) = 16/5 > 1, 6×(1/5) = 6/5 > 1, 5×(1/4) = 5/4 > 1.
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Fraction 4(2/9) is 8/9 < 1> 1, 6×(1/5) is 6/5 > 1, 5×(1/4) is 5/4 > 1.
What is fraction?If q is less than 0, the fraction is expressed as p/q. Fractions that follow the rules are good fractions and fractions that follow the rules are bad. For proper fractions, the numerator is less than the denominator, and vice versa for improper fractions. When multiplying fractions, you can remove terms from the numerator and denominator of other fractions to simplify the problem. We can multiply the numerator and denominator to each other. ∴ 4×(1/4) = 1.4×(2/9) = 8/9 <1> 1.6×(1/5) = 6/5 > 1.5×(1/4) = 5/4 > 1. Calculation 4(2/9) = 8/9 1, 2(2/5) = 4/5 1 and 8(2/5) = 16/5 > 1, 6×(1/5) = 6/ 5 > 1.5*(1/4) = 5/4 > 1.To learn more about fraction from the given link:
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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:
Can you help me with this?:(
The formula for the given T-chart is f(x)=x-6. T-shaped graphic organiser used to divide information into two categories. A T chart can be used to contrast two ideas, list benefits and drawbacks, separate facts from opinions, and more.
What sort of T chart is that?T Charts are frequently used to compare facts and opinions, problems and solutions, and pros and cons.
What is a timeline with an example?A timeline is a diagram that shows the progression of the use of a group of resources. A timeline is frequently a sensible visualisation option if you're managing a software project and want to show who is doing what and when, or if you're planning a conference and need to schedule meeting rooms.
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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 are 10 examples of substitutes?
The 10 examples of substitutes good and services are :
Butter and margarinePhysical books and e-booksSandals and flip-flopsTuna and salmonSteel-toe boots and composite-toe bootsMinivans and sport utility vehiclesEarrings and necklacesEyeglasses and contact lensesRed Delicious apples and Gala applesCappuccinos and lattesSimilar products that a client may employ for the same purpose are substitute goods. If the product they prefer is offered, your customers might buy it, but they might also look at alternatives if the price, the product's availability, or its quality changes. The demand for an item is frequently affected by these changes as well.
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Write the number in scientific notation. 0.0805 8.05 × 10 8.05 × 10–2 0.805 × 10–1 80.5 × 100–3
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
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
Which of the following are in proportion?
a)21, 35, 24, 40 b) 75, 21, 18, 6
The solution is Option A.
The proportion is given by 21 : 35 : : 24 : 40
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
Now , the equation will be
a)
The four set of numbers are = { 21 , 35 , 24 , 40 }
Now , the ratio of 21/35 = 3/5
The ratio of 24 / 40 = 3/5
Therefore, the proportion is expressed as
A = 3 : 5
And , the proportion equation is
21 : 35 : : 24 : 40
Hence , the proportion is 21 : 35 : : 24 : 40
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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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Help pls
A three-column table is given.
Part A C D
Part 14 28 63
Whole B 40 90
What is the value of B in the table?
20
25
28
30
In the three column table the value of B is 20, and option I is the correct answer.
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total. According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.
From the information given, it's important to calculate the constant of proportionality. In this case, for C, we have 28 part and 40 whole, the constant will be:
Constant = Whole / Part
= 40/28
= 1.428
Therefore, the value of B will be:
Whole = Part × Constant
Whole = 14 × 1.428
B = 20
Hence in the three column table the value of B is 20, and option I is the correct answer.
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Answer:B=20
Step-by-step explanation:
i did the math
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.
Use the point in the graph to find the equation of the line in point-slope form
A
y-3=5(x-1)
B
y+3=5(x+1)
C
y+3=5(x-1)
D
y-3=5(x+1)
Answer:
c
Step-by-step explanation:
welcome
2. Draw a number line diagram and write an expression to represent this situation: "On Tuesday at lunchtime, it was 29°C. By sunset, the temperature had dropped to 16°C.
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
how many pints are in 3 3/4 gal