Now let's check if f(x) = g(h(x)):
gh(x)) = g(x + 1) = (x + 1)² + 1 = x² + 2x + 1 + 1 - 1 = x² + 2x + 1
The formulas for g(x) and h(x), which are g(x) = x² + 1 and h(x) = x + 1, such that their composition yields:
f(x) = g(h(x)) = x² + 2x + 1.
In both cases, we use the composition of functions f(x) = g(h(x)) to relate the functions g(x), h(x), and their inverses. These formulas allow us to find the other function given one of the functions in the composition.
Suppose we have the function f(x) = g(h(x)). Here, we have three functions: f(x), g(x), and h(x). We're given one of these functions and asked to find the formulas for the other two functions so that their composition results in f(x).
To find a formula for one of the functions in the composition f(x) = g(h(x)), we can substitute the other function into it and simplify.
(1) If we want to find a formula for g(x) given f(x) = g(h(x)), we can substitute h(x) for x in g(x), which gives us g(h(x)). This means that g(x) = f(h^{-1}(x)), where h^{-1}(x) is the inverse function of h(x).
(2) If we want to find a formula for h(x) given f(x) = g(h(x)), we can substitute g(x) for f(x) and solve for h(x). This gives us h(x) = g^{-1}(f(x)), where g^{-1}(x) is the inverse function of g(x).
Given: f(x) = x² + 2x + 1
We need to find the formulas for g(x) and h(x) such that f(x) = g(h(x)).
One possible choice for g(x) could be g(x) = x² + 1. Now we need to find the function h(x) such that when we compose g(h(x)), it results in f(x) = x² + 2x + 1.
To do this, we can see that g(x) has x² + 1, and f(x) has x² + 2x + 1. We need to add a term '2x' in the composition. Therefore, we can choose h(x) = x + 1.
Now, let's check if f(x) = g(h(x)):
g(h(x)) = g(x + 1) = (x + 1)² + 1 = x² + 2x + 1 + 1 - 1 = x² + 2x + 1
Thus, we have successfully found the formulas for g(x) and h(x), which are g(x) = x² + 1 and h(x) = x + 1, such that their composition yields f(x) = g(h(x)) = x² + 2x + 1.
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Find X and then find JL
The value of x is calculated as x = 3, while the length of segment JL is calculated as 18 units.
How to Find the Value of x in the Figure Given?Create an equation based on the fact that the diagonals of the shape shown bisects each other to form equal segments such as:
JN = LN
Plug in the values to find x:
15 - 2x = 4x - 3
Combine like terms:
15 + 3 = 4x + 2x
18 = 6x
18/6 = x
x = 3
Length of JL = 15 - 2x + 4x - 3 = 12 + 2x
Plug in the value of x:
Length of JL = 12 + 2(3) = 18 units
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write an equation of the line that passes through each pair of points (5, 7), (-8, -4)
Answer:
y = 11x/13 + 36/13
Step-by-step explanation:
We can write the line using y = mx + b form.
To find the slope, m, we can use the formula (y1 - y2) / (x1 - x2):
(7-(-4)) / (5-(-8)) = (7+4) / (5+8) = 11 / 13.
To find b, we can plug in one of the points. Lets use (5, 7).
y = 11/13 * x + b
7 = 11/13 * 5 + b
7 - 55/13 = b
b = 91/13 - 55/13 = (91-55)/13 = 36/13.
Your equation is:
y = 11x/13 + 36/13.
Answer: y = [tex]\frac{11}{13}[/tex]x + [tex]\frac{36}{13}[/tex]
Step-by-step explanation:
First, we will find the slope.
[tex]m=\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }=\frac{-4-7}{-8-5} =\frac{-11}{-13} =\frac{11}{13}[/tex]
Next, we will substitute this slope and a given point in and solve for our y-intercept (b).
y = [tex]\frac{11}{13}[/tex]x + b
(7) = [tex]\frac{11}{13}[/tex](5) + b
(7) = [tex]\frac{11}{13}[/tex](5) + b
7 = [tex]\frac{55}{13}[/tex] + b
b = 7 - [tex]\frac{55}{13}[/tex]
b = [tex]\frac{36}{13}[/tex]
Final equation:
y = mx + b
y = [tex]\frac{11}{13}[/tex]x + [tex]\frac{36}{13}[/tex]
TEXT ANSWER
Use the multiplication rule to simplify:
b7 . b²
Tip: When writing math questions, the coefficient would go in front of variables: 7b*[tex]b^2[/tex]
Anyways, in this case, since we cannot mutiply 7 by b, the 7 will stay put
But.... we can mutiply b by b
[tex]b^2[/tex][tex]*b[/tex]=b^3
Tip: B's with no exponent has an exponent with one
Questions?
So,7 will stay put and b and b^2 will simply to b^3
[tex]7b^3[/tex]=Answer
Select the statement that best describes the expression 4+3x
A. 4 plus 3plus x
B. The sum of 4 and 3
C. The product of 4 and 3x
D. 4 plus 3 times x
The correct option is D, the statement that best describes the expression 4+3x means "4 plus 3 times x".
An expression is a combination of numbers, symbols, and/or variables that represents a mathematical or logical statement. It can be as simple as a single number or letter, or as complex as a series of operations that involve multiple variables and functions. Expressions can be used to represent equations, inequalities, functions, and other mathematical concepts. They can be evaluated to produce a numerical value or a boolean value (true or false) depending on the values of the variables involved.
Expressions are used to represent calculations or logical conditions. They can be used to assign values to variables, manipulate data, and control the flow of a program. expressions are a fundamental concept in both mathematics and computer science, and play a critical role in solving problems and building complex systems.
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The equation 8x − 2y = 25 represents a linear function. Which equation represents the same function?
A. The number of minutes m to cook c cups of rice
B. The volume V of a cube with side length s
C. The distance walked after m minutes at r feet per minute
D. The cost C for t tickets to a museum
HELP OR DIE
None of the options presented represent the same function as the given equation 8x − 2y = 25.
The equation 8x − 2y = 25 represents a linear function in terms of variables x and y. To determine which equation represents the same function, we need to look for an equation that has a similar form.
A. "The number of minutes m to cook c cups of rice" does not have the same form as the given equation, so it does not represent the same function.
B. "The volume V of a cube with side length s" also does not have the same form as the given equation, so it does not represent the same function.
C. "The distance walked after m minutes at r feet per minute" does not match the given equation, so it does not represent the same function.
D. "The cost C for t tickets to a museum does not have the same form as the given equation, so it does not represent the same function.
Therefore, none of the given options represent the same function as the equation 8x − 2y = 25.
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Convers Corporation (calendar year-end) acquired the following assets during the current tax year: (ignore §179 expense and bonus depreciation for this problem): (Use MACRS Table 1, Table 2 and Table 5. )
Asset Date Placed in Service Original Basis
Machinery October 25 $ 92,000
Computer equipment February 3 32,000
Delivery truck* March 17 45,000
Furniture April 22 172,000
Total $ 341,000
*The delivery truck is not a luxury automobile. In addition to these assets, Convers installed new flooring (qualified improvement property) to its office building on May 12 at a cost of $520,000. A. What is the allowable MACRS depreciation on Convers’s property in the current year assuming Convers does not elect §179 expense and elects out of bonus depreciation? (Round your intermediate calculations and final answer to the nearest whole dollar amount. )
The allowable MACRS depreciation on Convers’s property in the current year assuming Convers does not elect §179 expense and elects out of bonus depreciation is $39,805.
To calculate the allowable MACRS depreciation, we need to determine the depreciation for each asset using the MACRS tables:
Machinery:Placed in service in October, which is in the fourth quarter
Depreciation method: 5-year property
Percentage from Table 1: 20.00%
Basis for depreciation: $92,000
Depreciation for the current year: 20.00% x $92,000 x 0.5 = $9,200
Computer equipment:Placed in service in February, which is in the first quarter
Depreciation method: 5-year property
Percentage from Table 1: 20.00%
Basis for depreciation: $32,000
Depreciation for the current year: 20.00% x $32,000 x 0.75 = $4,800
Delivery truck:Placed in service in March, which is in the first quarter
Depreciation method: 5-year property
Percentage from Table 1: 20.00%
Basis for depreciation: $45,000
Depreciation for the current year: 20.00% x $45,000 x 0.75 = $6,750
Furniture:Placed in service in April, which is in the second quarter
Depreciation method: 7-year property
Percentage from Table 2: 14.29%
Basis for depreciation: $172,000
Depreciation for the current year: 14.29% x $172,000 x 0.5 = $12,285
Flooring:Placed in service in May, which is in the second quarter
Depreciation method: 39-year property
Percentage from Table 5: 2.564%
Basis for depreciation: $520,000
Depreciation for the current year: 2.564% x $520,000 x 0.5 = $6,670
The total allowable MACRS depreciation for Convers Corporation in the current year is the sum of the depreciation for each asset:
$9,200 + $4,800 + $6,750 + $12,285 + $6,670 = $39,805
Therefore, the allowable MACRS depreciation on Convers’s property in the current year is $39,805.
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Marshall is renting a bike for the day. It costs $13 for up to one hour. After one hour, the price increases to $20. After three hours, the price increases again to $50. The maximum time he can rent the bike is 10 hours total
The piecewise function that represents the situation is therefore:
Costs Possible hours
13 0 < x ≤ 1
20 1 < x ≤ 3
50 3 < x ≤ 10
How to find the piecewise function ?We see that up to one hour, the cost to Marshall would be $ 13 so the possible hours at that price is 0 < x ≤ 1 .
Likewise from one hour, the price goes up to $ 20 which means that possible hours become 1 < x ≤ 3 because the price will increase at 3 hours again.
From 3 hours, the price becomes $ 50 and there are a maximum of 10 hours so the hours become 3 < x ≤ 10 .
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a city maintains a database of all traffic tickets that were issued over the past ten years. the tickets are divided into the following two categories. moving violations nonmoving violations the data recorded for each ticket include only the following information. the month and year in which the ticket was issued the category of the ticket which of the following questions cannot be answered using only the information in the database? responses have the total number of traffic tickets per year increased each year over the past ten years? have the total number of traffic tickets per year increased each year over the past ten years? in the past ten years, were nonmoving violations more likely to occur on a weekend than on a weekday? in the past ten years, were nonmoving violations more likely to occur on a weekend than on a weekday? in the past ten years, were there any months when moving violations occurred more often than nonmoving violations? in the past ten years, were there any months when moving violations occurred more often than nonmoving violations? in how many of the past ten years were there more than one million moving violations?
The statement about the chances of occurrence of nonmoving violations more on a weekend than on a weekday in past ten years is cannot be answered using only the information in the database. So, option(b) is provide the right answer.
Database: The database is a large collection of data and it is used to store and retrieve the accordingly. It has an organization of a certain amount of data that needs and it contains. We have a database of all traffic tickets that were issued over the past ten years in a city. The informations including are
the tickets are divided into two categories. 1) moving violations2) nonmoving violations
the month and year in which the ticket was issued the category of the ticket.We have to recongise the statement which is not answering by the above informations in database. First statement is can be answerable, because we have data of year in which tickets are issued. Similarly, statements third and fourth related to data of tickets issued in month and year in past ten years. So, both are answerable statements. Therefore, the second statement
is cannot be answerable here.
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Complete question:
a city maintains a database of all traffic tickets that were issued over the past ten years. the tickets are divided into the following two categories. moving violations nonmoving violations the data recorded for each ticket include only the following information. the month and year in which the ticket was issued the category of the ticket which of the following questions cannot be answered using only the information in the database? responses
a) have the total number of traffic tickets per year increased each year over the past ten years?
b) in the past ten years, were nonmoving violations more likely to occur on a weekend than on a weekday?
c) in the past ten years, were there any months when moving violations occurred more often than nonmoving violations?
d) in how many of the past ten years were there more than one million moving violations?
Center: (2, 8) radius: 3
What is the equation of a circle with the center and radius given?
Solve the given differential equation 3 4ydx - 4xdy + x³dx = 7dx The solution is= (Type an equation.)
The solution of the given differential equation is y = x + Cx⁴ - x²/4, where C is a constant.
We begin by rearranging the terms as follows:
(4y + x³ - 7)dx = (4x)dy
Integrating both sides, we get:
4xy + (1/4)x⁴ - 7x = 2y² + C
where C is the constant of integration.
Next, we can rearrange this equation to solve for y:
y² = 2xy + (1/8)x⁴ - (7/2)x - C/2
y² - 2xy = (1/8)x⁴ - (7/2)x - C/2
We can complete the square to obtain a more useful expression:
(y - x)² = (1/8)x⁴ - (7/2)x - C/2 + x²
y - x = ±sqrt((1/8)x⁴ - (7/2)x - C/2 + x²)
Simplifying this expression, we get:
y = x ±sqrt(Cx⁴ - (1/4)x⁴ + 7x - C)
Taking the positive sign for simplicity, we get the final solution as:
y = x + sqrt(Cx⁴ - (1/4)x⁴ + 7x - C)
where C is the constant of integration.
We can also simplify this solution further by using the identity (a + b)² = a² + 2ab + b² to get:
y = x + Cx⁴ - x²/4
where C is a constant, as desired.
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What is the measure of ∠SQR?
the ∠sqr is 4y= 4*29=116° we can get this answer with supplementary angle fact and sum of angle in triangle is 180 degree
what is supplementary angle ?
In geometry, two angles are called supplementary angles if their sum is equal to 180 degrees. In other words, if angle A and angle B are supplementary, Supplementary angles are commonly found in many geometric shapes, such as triangles and quadrilaterals, as well as in other applications of geometry. When two angles are supplementary, they form a straight line or a straight angle, which is an angle that measures exactly 180 degrees. For example, if one angle of a triangle measures 80 degrees, then the other two angles are supplementary and together measure 100 degrees (180 degrees - 80 degrees).
In the given question,
with the fact of complimentary angles we can write as follows
angle trq+ angle qrs =180
angle qrs=180-145=35 degree
so in triangle we have sum of all angle is 180 degree so we can write as follows
∠r+∠q+∠s=180
35+4y+y=180
5y=180-35
y=145/5
y=29 degree
so the ∠sqr is 4y= 4*29=116°
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Ariel is filling a giant beach ball with air. The radius of the beach ball is 30 cm. What is the volume of air that the beach ball will hold? Either enter an exact answer in terms of Pi.
The volume of air that the beach ball will hold is 36000π cubic cm
What is the volume of air that the beach ball will holdFrom the question, we have the following parameters that can be used in our computation:
The radius of the beach ball is 30 cm.
This means that
r = 30
The volume of air that the beach ball will hold is calculated as
V = 4/3πr³
Substitute the known values in the above equation, so, we have the following representation
V = 4/3π * 30³
Evaluate
V = 36000π
Hence, the volume of air that the beach ball will hold is 36000π cubic cm
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A force of 80 pounds on a rope is used to pull a box up a ramp inclined at 10 degrees from the horizontal. The rope forms an angle of 33 degrees with the horizontal. How much work is done pulling the box 26 feet along the ramp?
The work done on the displacement is 301.95J
What is the work done in pulling the boxTo determine the work done, we need to find the displacement in which the box moved.
cos θ = adjacent / hypothenuse
cos 33 = adjacent / 80
adjacent = 80 * cos 33
adjacent = 67.1 lbs
The force applied is 67.1lbs
The displacement on the ramp;
sin θ = opposite / hypothenuse
sin 10 = opposite / 26
opposite = 26 * sin 10
opposite = 4.5 ft
The work done in moving the object can be calculated as;
work done = force * displacement
work done = 67.1 * 4.5
work done = 301.95 J
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The equation m = 1. 4p represents the mass, m, in grams, of
p polished stones.
We know that the total mass of 5 polished stones would be 7 grams according to this equation
Sure! The equation m = 1.4p represents the mass, m, in grams, of p polished stones.
This means that if you know the number of polished stones, p, you can use this equation to calculate their total mass, m, in grams. For example, if you have 5 polished stones, you can plug in p = 5 and solve for m: m = 1.4 x 5 = 7 grams.
So the total mass of 5 polished stones would be 7 grams according to this equation.
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Based on the equation, the number of grams which the mass increase for every 7 polished stones is: D. 9.8 g.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.Based on the information provided above, a linear equation that models the mass in grams is given by;
y = mx + c
m = 1.4p
By substituting the given parameter (x = 7 polished stones), we have the following:
m = 1.4(7)
m = 9.8 g
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
I need help with this question.
Answer: The answer is (C
Step-by-step explanation:
Question
A restaurant is serving a special lunch combo meal that includes a drink, a main dish, and a dessert. Customers can choose from 5 drinks, 6 main dishes, and 3 desserts.
How many different combo meals are possible?
Select from the drop-down menu to correctly complete the statement.
Customers can create (14, 39, 60, 120) different lunch combo meals.
The number of different combo meals possible in a restaurant that is serving a special dinner combo meal is 90.
We are given that the customers can choose from 5 drinks, 6 main dishes, and 3 desserts. We have to find that how many different combos are possible. It means that we have to do an arrangement for such a situation. Arrangement of things means to group them in a systematic order, in all the possible ways.
We know that the number of possible ways to arrange is n! where n is the number of objects. As we know that the dinner includes 5 drinks, 6 main types of dishes, and 3 types of desserts. The number of different combo meals possible can be found by simply multiplying all the meals. Thus,
n = 5 * 6 * 3
n = 90
Therefore, the number of different combo meals possible in a restaurant that is serving a special dinner combo meal that includes a drink, a main dish, and a dessert is 90.
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the relationship between group size and percent woodland appears to be negative and nonlinear. which of the following statements explains such a relationship? responses as the percent of woodland increases, the number of deer observed in a group decreases at a fairly constant rate. as the percent of woodland increases, the number of deer observed in a group decreases at a fairly constant rate. as the percent of woodland increases, the number of deer observed in a group increases at a fairly constant rate. as the percent of woodland increases, the number of deer observed in a group increases at a fairly constant rate. as the percent of woodland increases, the number of deer observed in a group decreases quickly at first and then more slowly. as the percent of woodland increases, the number of deer observed in a group decreases quickly at first and then more slowly. as the percent of woodland increases, the number of deer observed in a group increases quickly at first and then more slowly. as the percent of woodland increases, the number of deer observed in a group increases quickly at first and then more slowly. as the percent of woodland increases, the number of deer observed in a group remains fairly constant.
The statement that explains the negative and nonlinear relationship between group size and percent woodland is given by the percent of woodland increases, the number of deer observed in a group decreases quickly at first and then more slowly.
This statement suggests that as the amount of woodland id increases, when the number of deer in a group decreases.
However, the rate of decrease is not constant, but rather decreases more slowly as the percent of woodland increases.
This suggests that there may be some threshold or tipping point.
At which the relationship between group size and percent woodland becomes less pronounced.
This kind of relationship is not uncommon in ecological studies.
Where factors like habitat availability, food availability, and predation risk can all influence animal behavior and population dynamics.
Nonlinear relationships like this one can help researchers better understand complex interplay between these factors and behavior of animals they study.
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When the price of a certain product is $40, 25 items can be sold. When the price of the same
product costs $20, 185 items can be sold. On the other hand, when the price of this product
is $40, 200 items will be produced. But when the price of this product is $20, only 100 items
will be produced. Use this information to find supply and demand functions (assume for
simplicity that the functions are linear), and compute the consumer and producer surplus at
the equilibrium price
Based on the information, the equilibrium price is $56.67
How to calculate the equillbriumUsing the first data point, we have:
25 = a - 40b
Using the second data point, we have:
185 = a - 20b
Solving these two equations simultaneously, we get:
a = 325
b = 5/2
So the demand function is:
Qd = 325 - 5/2 P
the supply function is:
Qs = -100 + 5P
325 - 5/2 P = -100 + 5P
425 = 15/2 P
P = $56.67
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Henry earned $850 over the summer working odd jobs. he wants to put his money into a savings account for when he is ready to buy a car. his bank offers a simple interest account at 5%, how much interest will henry have earned after 4 years?
Answer:
We can use the formula for simple interest to calculate the interest earned by Henry:
Simple Interest = (Principal * Rate * Time)
where,
Principal = $850 (initial amount)
Rate = 5% per year (as given)
Time = 4 years (as given)
Substituting the values, we get:
Simple Interest = (850 * 0.05 * 4) = $170
Therefore, Henry will have earned $170 in interest after 4 years of keeping his money in the savings account.
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If (2, 3) is a point on locus whose equation is ax + 2y = 16 and also show that (0, 8) is another point on the locus.
11
Differentiate the function and find the slope of the tangent line at the given value of the independent variable s=8-41², 1=-3 s'(t)=0 The slope of the tangent line is at t= -3.
The slope of the tangent line to the function [tex]s(t) = 8 - 41t^2[/tex] at t = -3 is 246.
Process of finding slope:1. Differentiate the function s(t) with respect to the independent variable t: [tex]s(t) = 8 - 41t^2[/tex].
2. Calculate the derivative s'(t).
3. Evaluate the derivative at the given value of t.
Step 1: Differentiate the function [tex]s(t) = 8 - 41t^2[/tex].
To differentiate this function, we apply the power rule for differentiation.
The derivative of a constant (8) is 0, and the derivative of 41t^2 is -82t
(since we multiply the exponent 2 by the coefficient 41 and then subtract 1 from the exponent).
Step 2: Calculate the derivative s'(t).
s'(t) = 0 - 82t
Step 3: Evaluate the derivative at the given value of t (t = -3).
s'(-3) = -82(-3) = 246
The slope of the tangent line to the function [tex]s(t) = 8 - 41t^2[/tex] at t = -3 is 246.
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Joshua's mail truck travels 14 miles every day he works
and is not used at all on days he does not work. At the
end of his 100th day of work the mail truck shows a
mileage of 76,762. Model Joshua's truck mileage as a
function of the number of days he has worked. When
will he reach 100,000 miles?
Solving the equation, Joshua will reach 100,000 miles after approximately 1,760 days of work.
To model Joshua's truck mileage as a function of the number of days he has worked, we can use the following equation:
Mileage (M) = 14 * Number of days worked (D) + Initial Mileage (I)
First, we need to determine the initial mileage on the mail truck. To do this, we can use the information given for his 100th day of work:
76,762 = 14 * 100 + Initial Mileage
76,762 = 1,400 + Initial Mileage
Initial Mileage (I) = 76,762 - 1,400
Initial Mileage (I) = 75,362
Now we can rewrite the equation as:
Mileage (M) = 14 * Number of days worked (D) + 75,362
To find when Joshua will reach 100,000 miles, we can set M equal to 100,000 and solve for D:
100,000 = 14 * D + 75,362
24,638 = 14 * D
D ≈ 24,638 / 14
D ≈ 1,759.857
Since Joshua cannot work a fraction of a day, he will reach 100,000 miles after approximately 1,760 days of work.
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Stephanie throws a paper airplane off the roof of her school. Her classmates measure the plane’s height, in feet, after each second. The table shows some of her data.
T= 0, 1, 2, 3, 4
h(t)= 200, 208, 212, 212, 208
Find the equation for h(t), and use it to determine how long it will take the plane to hit the ground. Round to the nearest hundredth
The paper airplane will not hit the ground within the given time frame.
To find the equation for h( t), we need to find the rate of change or the pitch of the function. We can do this by chancing the difference in height and time for any two points on the line. Let's choose the first two points,( 0,200) and( 1,208).
pitch = ( change in height)/( change in time)
pitch = ( 208- 200)/( 1- 0) = 8
So, the equation for h( t) can be written in pitch- intercept form as h( t) = 8t b
To find the value of b, we can use any of the given points.
Let's use( 0,200) 200 = 8( 0) b b = 200
So, the equation for h( t) is h( t) = 8t 200
To find how long it'll take the aeroplane to hit the ground, we need to find when h( t) = 0,
since that would mean the height is 0 bases or the ground position. 0 = 8t 200 working for t,
we get t = -25
Since time cannot be negative the paper airplane will not hit the ground within the given time frame.
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In δmno, m = 540 inches, n = 330 inches and o=600 inches. find the measure of ∠o to the nearest 10th of a degree
The measure of ∠O in ΔMNO is approximately 41.5°.
To find the measure of ∠O, we can use the Law of Cosines in ΔMNO, with sides M = 540 inches, N = 330 inches, and O = 600 inches. The Law of Cosines states:
O² = M² + N² - 2MN * cos(∠O)
Rearrange the equation to solve for cos(∠O):
cos(∠O) = (M² + N² - O²) / (2MN)
Substitute the values:
cos(∠O) = (540² + 330² - 600²) / (2 * 540 * 330)
cos(∠O) ≈ -0.7944
Now, find the angle using the inverse cosine function:
∠O ≈ arccos(-0.7944) ≈ 141.5°
Since ∠O is an obtuse angle, we need to find its supplement to the nearest 10th:
180° - 141.5° ≈ 38.5°
Thus, the measure of ∠O is approximately 38.5°.
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ETA 4
Answer the following:
Myla bought an item P2,500. She decided to sell it wil 2% markup. How much will Myla’s selling price be?
Joan sold her old iphone for P5000 at 8% markdown rate. Find the markdown and the original cost of the phone.
A student assistant bought an item for P520 but later decided to sell it at P550. What is the markup?
Mother organize a garage sale and earned P120 on one item at 60% markdown. How much did mother buy the item?
The cost of a t-sirt from the manufacturer is P400. If loan wants a 30% markup based on the selling price, how much will her selling price be?
1. Myla bought an item for P2,500 and decided to sell it with a 2% markup. The selling price will be P2,500 + (2% of P2,500) = P2,500 + P50 = P2,550.
2. Joan sold her old iPhone for P5,000 at an 8% markdown rate. To find the markdown and the original cost, we first calculate the markdown: P5,000 = 92% of original price. So, the original price was P5,000 ÷ 0.92 ≈ P5,434.78. The markdown is P5,434.78 - P5,000 = P434.78.
3. The student assistant bought an item for P520 and sold it for P550. The markup is P550 - P520 = P30.
4. Mother earned P120 on an item at a 60% markdown. Let X be the original price, then X * 60% = P120. X = P120 ÷ 0.60 = P200. So, the mother bought the item for P200.
5. The cost of a t-shirt from the manufacturer is P400. If Loan wants a 30% markup based on the selling price, we'll let X be the selling price, then X - 30% of X = P400. So, 0.7X = P400. X = P400 ÷ 0.7 ≈ P571.43. Loan's selling price will be P571.43.
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Find the coordinates of the points on the curve x(????)=3????^2 +1 ????????????y(????)=????^3 −1, for which the tangent linehas a slope of 1/2
The coordinates of the point on the curve where the tangent line has a slope of 1/2 are (4, 0).
To find the coordinates of the points on the curve x(t) = 3t^2 + 1 and y(t) = t^3 - 1, where the tangent line has a slope of 1/2, follow these steps:
1. Calculate the derivatives of x(t) and y(t) with respect to t:
dx/dt = 6t
dy/dt = 3t^2
2. The slope of the tangent line is given by dy/dx, so calculate dy/dx using the chain rule:
dy/dx = (dy/dt) / (dx/dt) = (3t^2) / (6t) = t/2
3. Set the slope equal to 1/2 and solve for t:
t/2 = 1/2
t = 1
4. Plug the value of t back into the original equations for x(t) and y(t) to find the coordinates of the point:
x(1) = 3(1)^2 + 1 = 4
y(1) = (1)^3 - 1 = 0
The coordinates of the point on the curve where the tangent line has a slope of 1/2 are (4, 0).
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Molly's cafe has regular coffee and decaffeinated coffee. this morning, the cafe served 30 coffees in all, 40% of which were regular. how many regular coffees did the cafe serve?
The cafe served 12 regular coffees.
Out of the 30 coffees served at Molly's cafe this morning, 40% were regular coffee. To determine the number of regular coffees, we can calculate 40% of 30.
To find the value,
Step 1: Convert the percentage to a decimal by dividing it by 100. So, 40% = 40/100 = 0.4.
Step 2: Multiply the total number of coffees served by the decimal. So, 30 * 0.4 = 12.
Hence, the cafe served 12 regular coffees. The remaining 60% (or 18 coffees) would be decaffeinated. It is important to note that percentages represent proportions or fractions of a whole. In this case, 40% indicates that 40 out of 100 parts (or 40/100) are regular coffees. By applying this proportion to the total number of coffees served (30), we can determine the specific quantity. This method can be used in various scenarios involving percentages to find a portion of a whole. Therefore, Molly's cafe served 12 regular coffees and 18 decaffeinated coffees, making a total of 30 coffees.
Your answer: Molly's cafe served 12 regular coffees this morning.
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Determine the common ratio for each of the following geometric series and determine which ones have an infinite sum
The common ratio for the geometric series 1, 1/2, 1/4, 1/8, ... is 1/2 and the sum of series is 2 which is finite.
To determine whether the series has an infinite sum, we can use the formula for the sum of an infinite geometric series, which is:
S = a/(1-r),
where a is the first term and r is the common ratio.
In this case, a = 1 and r = 1/2, so
S = 1/(1 - 1/2) = 2.
Since the value of S is finite and not infinite, we can conclude that the given geometric series has a finite sum of 2.
The common ratio of a geometric series is the ratio between consecutive terms. For example, in the series 1, 2, 4, 8, 16, ..., the common ratio is 2 because each term is obtained by multiplying the previous term by 2.
To determine whether a geometric series has an infinite sum, we can use the formula for the sum of an infinite geometric series, which is S = a/(1-r), where a is the first term and r is the common ratio.
If the value of r is between -1 and 1 (excluding -1), then the series has a finite sum. If the value of r is greater than 1 or less than -1, then the series has an infinite sum.
In the given series 1, 1/2, 1/4, 1/8, ..., the common ratio is 1/2. To find the sum of the series, we can use the formula S = a/(1-r) with a=1 and r=1/2, which gives S=2. Since the value of S is finite and not infinite, we can conclude that the given geometric series has a finite sum of 2.
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complete question:
Determine the common ratio for each of the following geometric series and determine which ones have an infinite sum 1,1/2,1/4,1/8....
Help translations and reflections
Thus, Coordinates of image of points A', B' and C' are- A'(-6, 10), B'(-2, -8), C'(4 , -7)
Explain about the reflection along the y-axis:A figure is transformed into a reflection by a transformational process. In a point, a line, or a plane, figures can be reflected. The image and preimage coincide when reflecting any symbol in a line or a point.
The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).Given coordinates of points A, B and C
A(6, 10), B(2, -8), C(-4 , -7)
After reflection (x, y) ---> (-x, y).
Thus, Coordinates of image of points A', B' and C' are-
A'(-6, 10), B'(-2, -8), C'(4 , -7)
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(a) if f(4) = 6, what is f-|(6)? f-'(6) = (b) Suppose a function can be described by y = f(x). The function and its inverse intersect when y = (c) Consider a linear function f (x) = ax + b where a 70. Is the inverse of this linear function always a linear function? (No answer given) If f(x) = ax + b and a € 0, then f-'(x) =
To find f-1(6), we need to find the value of x that gives f(x) = 6. However, we don't have enough information about the function f to do this. We need to know whether f is a linear function or not.
When the function and its inverse intersect, we have f(x) = f-1(x). Substituting y for both f(x) and f-1(x), we get y = f(y). To find the value of y when this is true, we need to solve for y:
y = f(y)
y = f-1(y)
Substituting y = f(x), we get:
f(x) = f-1(f(x))
f(x) = x
So the function and its inverse intersect when y = x.
If a = 0, then the linear function is f(x) = b, which is a constant function. Constant functions do not have inverses, so the inverse of f(x) = b does not exist.
If a ≠ 0, then the inverse of f(x) = ax + b is given by:
f-'(x) = (x - b) / a
This is also a linear function, so the inverse of a linear function is always a linear function when a ≠ 0.
(a) To find the inverse of a linear function, you need to swap the x and y values. Given that f(4) = 6, the inverse function f^(-1)(6) would yield the value of x when y = 6. Since we know that f(4) = 6, it implies that f^(-1)(6) = 4.
A function and its inverse intersect when the input value (x) is equal to the output value (y). In other words, they intersect when y = x.
(c) Yes, the inverse of a linear function is always a linear function. If f(x) = ax + b, where a ≠ 0, then the inverse function, f^(-1)(x), can be found by swapping x and y values and solving for y. In this case, x = ay + b. Solving for y, we get y = (x - b) / a, which is also a linear function.
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