Answer:
1.25a
Step-by-step explanation:
Original value = a
An increase of 25% can be found by a x 25/100 = 0.25a
The resulting increased value = Original value + Increase in value
= a + 0.25a
= 1.25a
Sometimes it is a more direct approach to use the final value as original value(1 + increase%/100) in which case it would be a(1+25/100) = a(1 + 0.25) = a(1.25) = 1.25a
Function Transformations
Given the point (-2,−1) is on the graph of f(x), find a point (written as an ordered
pair) that must be on each of the transformations of f(x) written below:
Ordered pair on the graph
y=f(x-4)-4
Ordered pair on the graph
y=f(x-4) +4
Ordered pair on the graph
y = f(x+4)-4
Ordered pair on the graph
y = f(x+4) +4
(-6,-5), (-2,3), (2,-5), (6,3) are the ordered pairs given on the graph.
What do you mean by transformation?In mathematics, a transformation is a process that changes the position, size, or orientation of a geometric shape or figure. The term is used in various branches of mathematics, including geometry, algebra, and calculus.
In geometry, transformations include translations, rotations, reflections, and dilations. A translation involves moving a shape a certain distance in a certain direction, while a rotation involves rotating a shape around a fixed point. A reflection involves flipping a shape over a line, and a dilation involves stretching or shrinking a shape by a given scale factor.
In algebra, transformations can involve changing the form of an equation, such as solving for a variable, transforming an equation into a different coordinate system, or solving a system of equations.
In calculus, transformations can involve changing the form of a function, such as finding its derivative or integral, or transforming a function from one coordinate system to another.
To find the ordered pairs that are on the transformations of the function, we can apply the transformations to the original point (-2, -1) to obtain the points on each transformation.
y = f(x-4) - 4: If we apply the x-4 transformation to the x-coordinate of the original point, we get -2-4 = -6. So, the point is (-6, f(-6) - 4).
y = f(x-4) + 4: The x-coordinate of the point is -6, so the point is (-6, f(-6) + 4).
y = f(x+4) - 4: If we apply the x+4 transformation to the x-coordinate of the original point, we get -2+4 = 2. So, the point is (2, f(2) - 4).
y = f(x+4) + 4: The x-coordinate of the point is 2, so the point is (2, f(2) + 4).
So, the ordered pairs that must be on each of the transformations of f(x) are:
y = f(x-4) - 4: (-6, f(-6) - 4)
y = f(x-4) + 4: (-6, f(-6) + 4)
y = f(x+4) - 4: (2, f(2) - 4)
y = f(x+4) + 4: (2, f(2) + 4)
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Convert 1.05 • 10^-8 to standard form.
Answer:
0.0000000105
Step-by-step explanation:
Simply move the decimal 8 places to the left, since it is a negative exponent.
Select the values that are solutions to the inequality x2 + 3x – 4 > 0. –6 –2 0 5
The values that are solutions to inequality are -6 and 5.
Options A and D are the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
x² + 3x - 4 > 0
Now,
Substituting x = -6, -2, 0, 5
(-6)² + 3(-6) - 4 > 0
36 - 18 - 4 > 0
36 - 22 > 0
14 > 0
True.
x² + 3x - 4 > 0
(-2)² + 3 x (-2) - 4 > 0
4 - 6 - 4 > 0
-6 > 0
This is not true.
x² + 3x - 4 > 0
0 + 3 x 0 - 4 > 0
0 + 0 - 4 > 0
-4 > 0
This is not true.
x² + 3x - 4 > 0
5² + 3 x 5 - 4 > 0
25 + 15 - 4 > 0
40 - 4 > 0
36 > 0
This is true.
Thus,
-6 and 5 are the solutions to inequality.
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answer question a and b please
The graph for the functions is attached.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.
Given
A: graph of y = f(x)
since the graph is in form of a parabola so the function is a quadratic function,
f(x) = ax² + bx + c
the vertex of the graph is at (2, 0)
here in the given curve, the value of the y-axis is 0,
and y = f(x) - 3
in the equation y = f(x) - 3
the shape of the curve will be the same but only change in the vertex of the curve, the new vertex for the curve is (2, -3)
for x = 0 y = -3.
B: given y =g(x)
the graph shows the negative cubic function,
g(x) = -x³
and y = g(x + 4)
= -(x + 4)²
the graph will shift towards 4 units left.
Hence the graph is attached for both equations.
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the letters in the word miami are rearranged at random so that every possible anagram is equally likely. what is the probability that it still spells miami?
The letters in the word MIAMI are rearranged at random so that every possible anagram is equally likely. The probability that it still spells MIAMI is 1/5.
Let us count the total number of ways MIAMI can be arranged regardless of condition.
There are 2 M’s 2 I’s 1 A in word.
Total ways of arrangement will be = 5!/2!2!
Total ways of arrangement will be = (5 × 4 × 3 × 2!)/2! × 2 × 1
Total ways of arrangement will be = 5 × 2 × 3
Total ways of arrangement will be = 30 ways
Now, ways in which all similar words are together, thus we have to consider 2M's as one unit, similarly 2 I's as a unit, so number of ways will be 3!.
Thus, the probability will be = 3!/30
The probability will be = (3 × 2 × 1)/30
The probability will be = 6/30
The probability will be = 1/5
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the president of state university wants to forecast student enrollments for this academic year based on the following historical data: year enrollments 5 years ago 15,000 4 years ago 16,000 3 years ago 18,000 2 years ago 20,000 last year 21,000 what is the forecast for this year using exponential smoothing with alpha
The forecast for this year (F(6)) is 18,625. Therefore, the correct answer is 18,625.
Exponential smoothing is a time series forecasting method that uses a weighted average of past observations to make predictions. In this case, the weight assigned to each observation is determined by a smoothing parameter, alpha, which is a value between 0 and 1.
The formula for exponential smoothing with alpha = 0.5 is given by:
F(t) = alpha * Y(t) + (1 - alpha) * F(t-1)
where F(t) is the forecast for time t, Y(t) is the actual observation at time t, and F(t-1) is the forecast for the previous time period.
Starting with the forecast for two years ago, we can use this formula to make a forecast for each year until this academic year.
F(2) = 0.5 * 20,000 + (1 - 0.5) * 16,000 = 18,000
F(3) = 0.5 * 18,000 + (1 - 0.5) * 18,000 = 18,000
F(4) = 0.5 * 16,000 + (1 - 0.5) * 18,000 = 17,000
F(5) = 0.5 * 15,000 + (1 - 0.5) * 17,000 = 16,250
F(6) = 0.5 * 21,000 + (1 - 0.5) * 16,250 = 18,625
So the forecast for this year (F(6)) is 18,625. Therefore, the correct answer is 18,625.
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Complete question:
The president of State University wants to forecast student enrollment for this academic year based on the following historical data: Year Enrollments 5 years ago 15,000 4 years ago 16,000 3 years ago 18,000 2 years ago 20,000 Last year 21,000 What is the forecast for this year using exponential smoothing with alpha = 0.5, if the forecast for two years ago was 16,000?
18,750
19,500
21,000
22,650
None of the above
A recipe for biscuits calls for 1/4 teaspoon baking powder per 1 2/3 cups of flour. What is the unit rate for baking powder and flour?
The ratio of baking powder to flour is 1/192 teaspoon of baking powder for every teaspoon of flour.
The amount of baking powder per unit of flour is the unit rate for baking powder and flour. The amount of flour in this situation equals 1 2/3 cups. We must change the baking powder measurement to the same unit as the flour measurement in order to calculate the unit rate.
For every 1 2/3 cups of flour, 1/4 teaspoon of baking powder should be used as follows:
1/4 teaspoon / (1 2/3 cups)
By changing the numerator and denominator of the fraction on the right side to a standard unit, such as teaspoons, we may make it simpler. 1 2/3 cups equal 48 teaspoons, so:
1/4 teaspoon / (1 2/3 cups) = 1/4 teaspoon / (48 teaspoons)
The ratio of baking powder to teaspoons is as follows:
1/4 teaspoon / (48 teaspoons) = 1/192 teaspoon per teaspoon
So The ratio of baking powder to flour is 1/192 teaspoon of baking powder for every teaspoon of flour.
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At a height of n metres above sea level, the atmospheric pressure is Pn
millibars.
At a height of (n + 1000) metres above sea level, the atmospheric pressure is
P(n + 1000) millibars
where P(n + 1000) = 0.88Pn
At sea level, the atmospheric pressure is 1013 millibars.
Calculate the atmospheric pressure at a height of 3000 metres above sea level.
Give your answer correct to 3 significant figures.
Pressure at 3000 meters above sea level will be 690.33 millibars.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Given, At a height of n meters above sea level, the atmospheric pressure is Pn millibars. At a height of (n + 1000) meters above sea level, the atmospheric pressure is P(n + 1000) millibars.
where,
P(n + 1000) = 0.88Pn
at n = 0
P(1000) = 0.88 P(n = 0)
Since,
P(n = 0) is 1013 milibar
thus,
P(1000) = 0.88 * 1013
At n = 1000
P(1000 + 1000) = 0.88 P(n = 1000)
P( 2000) = 0.88 * 0.88 *1013
at n = 2000
P(2000 + 1000) = 0.88 P(n = 2000)
P( 3000) = 0.88 *0.88* 0.88 *1013
Thus,
P(3000) = 690.33
Therefore, Pressure at 3000 meters above sea level could be 690.33 millibars.
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Three pieces of software cost $20.75, $10.59, and $18.25. What is the total cost of the software.
Answer:
$49.59
Step-by-step explanation:
$20.75+$10.59+$18.25=$49.59
If one bestfriend went to the store with $5 and the other bestfriend went with $20 how many they had in total?
The amount of money they had in total is $25
How to calculate the amount of money that the best friends had in total?One bestfriend went to the store with $5
The other best friend went to the store with $20
The amount of money they had in total can be calculated as follows
= 20 + 5
= 25
Hence the amount of money the best friends had in total is $25
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Answer: 25$
Step-by-step explanation: 20 plus 5 equals 25.
648 divided by 19 in long division
The sum of two numbers is 33 and the difference is 9. What are the numbers?
Answer:
21 & 12
Step-by-step explanation:
let the sum of x and y be 33.. so,
x + y = 33
x - y = 9
x = 9 + y
x + y = 33
9 + y + y = 33
9 + 2y = 33
2y = 24
y = 24/2
y = 12
similarly,
x + y = 33
x + 12 = 33
x = 21
hence, sum: 21 + 12 = 33
difference : 21 - 12 = 9
if gas costs $3.25 per gallon, and it takes 21 seconds to pump one gallon of gas, how long will it take to pump $23.36 worth of gas (in seconds)?
We need to know how many gallons of gas $23.36 will buy, so we divide the amount by the cost per gallon: $23.36 ÷ $3.25 per gallon = 7.20 gallons.
Once we know how many gallons of gas we are buying, we can then find out how long it will take to pump that amount of gas. To do that, we multiply the number of gallons by the time per gallon: 7.20 gallons × 21 seconds/gallon = 151.2 seconds.
So, the answer to the question is 151.2 seconds, which is the total time it will take to pump $23.36 worth of gas at $3.25 per gallon and 21 seconds per gallon.
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Evaluate the expression when c=36 and d=24
The value of the expression after evaluating it according to the values of c and d is 42.
What is an expression?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.
Since, no expression is given, let us assume that the expression is
c + d / 4
Now we have to evaluate the value of the expression according to the values of c and d,
For that, we will simply put the given values in the expression and solved it accordingly,
Put c = 36 and d = 24 in the expression we assumed,
c + d / 4 = 36 + 24/4
= 36 + 6 = 42
Hence, the value of the expression after evaluating it according to the values of c and d is 42.
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8. Express the area of the figure as a monomial.
p2q4 and p2q4
The area of the figure as a monomial with the sides [tex]p^{2} q^{4}[/tex] and [tex]p^{2} q^{4}[/tex] is [tex]p^{4} q^{8}[/tex].
As per the given data we to express the area of the figure as a monomial.
Figure attached at the end of solution.
What is monomial?A polynomial with only one term is called a monomial. An algebraic expression known as a monomial has only one term but might have more than one variable and a higher degree.
As the sides are equal we use the area of the square formula.
Area of the square formula:
The formula for the area of a square is side × side
Simple multiplication is the answer to the equation.
Area of the given figure:
= [tex]p^{2} q^{4} \times p^{2} q^{4}[/tex]
= [tex]p^{4} q^{8}[/tex]
[tex]p^{4} q^{8}[/tex] is a monomial as it is expressed as a single term.
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In the diagram below of triangle ABC, D is the midpoint of AC and E is the
midpoint of BC. If m/CB A = 16 + 6x, and m/CED = 48 - 2x, what is the
measure of ZC BA?
Answer: 40 degrees
Step-by-step explanation:
m/CBA = m/CED
16 + 6x = 48 - 2x; add 2x on both sides and subtract 16 on both
8x = 32; divide 8 on both sides to isolate the x
x = 4
m/CBA = 16+6(4) = 40
What Is a Kilometer in Math?
A kilometer (km) is a unit of length in the metric system, which is based on the meter as the basic unit of length.
It is equal to one thousand meters, or one million centimeters, and is used in many contexts around the world when referring to the measurement of distances between two points.
Kilometers are commonly used in the context of travel, as they are often used to measure the distance between two cities or countries, or to measure the length of a journey or route. In addition, kilometers are often used to measure the depth of bodies of water, and to measure the size of land features such as mountains and valleys.
In mathematics, the kilometer is used to measure the magnitude of certain quantities, such as the speed of an object or the acceleration of a body. It is also used to measure the size of certain objects, such as the radius of a circle or the length of a line.
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A kilometer is a unit of length in the metric system. In mathematics, a kilometer is a unit of length used to measure distance.
It is part of the metric system, which is the most widely used system of measurement in the world. A kilometer is defined as 1000 meters. This makes it a convenient unit of measurement for large distances, such as those between cities, or for measuring the length of roads and highways.
In mathematical calculations involving distances, kilometers can be used to express the length of a segment or the distance between two points. They can also be converted to other units of length, such as meters, centimeters, or miles, by using appropriate conversion factors.
In conclusion, a kilometer is a unit of length in the metric system that is used to measure large distances in mathematics and in everyday life.
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Solve for z zz. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. − 4 z + 31 ≥ 17 z + 23 −4z+31≥17z+23
[tex]-4z+31\geqslant 17z+23\implies 31\geqslant 13z+23\implies 8\geqslant 13z\implies \cfrac{8}{13}\geqslant z[/tex]
A string with a linear density of 2 kg/m and a tension of 100 N is fixed at both ends. Determine the frequency of the first harmonic of the string.
Step-by-step explanation:
The frequency of the first harmonic of a string fixed at both ends can be determined using the formula:
f = (1 / 2L) * √(T / μ)
where f is the frequency, L is the length of the string, T is the tension, and μ is the linear mass density. Plugging in the given values:
f = (1 / 2 * L) * √(100 N / 2 kg/m)
= (1 / 2 * L) * √(50 N/m)
So, the frequency of the first harmonic depends on the length of the string, which is not specified in the problem.
Answer:
Step-by-step explanation:
The frequency of the first harmonic of a string fixed at both ends can be calculated using the formula:
f = (1 / 2L) * (T / μ)^(1/2)
where:
f = frequency
L = length of the string
T = tension
μ = linear density of the string
Plugging in the values:
f = (1 / 2 * L) * (100 N / 2 kg/m)^(1/2)
f = (1 / 2L) * (10 N/kg)^(1/2)
We don't have the length of the string, L, so we can't calculate the frequency.
Drag each expression to show whether the expression is equivalent to 24x−48 24 x - 48 , 36x+12 36 x + 12 , or neither.
the expression 24x - 48 is equivalent to 36x + 12
The label 24x - 48 applies to the expression because it is the same as itself. The value obtained by multiplying 24 by x and then taking 48 out is represented by this expression.
The label "36x + 12" applies to the expression because it is the same as itself. The value generated by multiplying 36 by x and then adding 12 is represented by this expression.
Since the formulations in both situations have distinct coefficients for x and various constant terms, they are not comparable to one another. Since both expressions are equal to one another, the term "neither" does not apply to them.
Therefore, the expression 24x - 48 is equivalent to 36x + 12
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Books in the clearance section at Reading Central Bookmart cost $5.00 for paperbacks and $9.00 for hardbacks. Which inequality best describes the number of paperback books, p, and the number of hardback books, h, that can be purchased for $45.00 or less?
A.
5p + 9h < 45
B.
5p + 9h < 45
C.
9p + 5h > 45
D.
9p + 5h < 45
The inequality best describes the number of paperback books 'p' and the number of hardback books 'h' that can be purchased for $45.00 or less
is 5p + 9h ≤ 45.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, Two types of books paperbacks are represented by 'p', and hardbacks are represented by 'h'.
Also, we can only buy two types of books for $45 or less.
Therefore, The inequality representing the context is,
5p + 9h ≤ 45. (As the cost van be $45 or less not only less)
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Two model cars, A and B, are in a race.
They start together on the starting line.
Assume each car travels at a constant speed.
Car A takes 30 seconds to complete each lap of the track.
Car B takes a whole number of seconds to complete each lap of the track.
The two cars next cross the starting line together 150 seconds after the start of the race.
Find the four possible times that car B could take to complete one lap.
Step 1: Calculate the number of laps the cars have completed. To calculate the number of laps the cars have completed, divide the total time (150 seconds) by the time it takes car A to complete one lap (30 seconds), which gives us a total of 5 laps.
Step 2: Calculate the possible times for car B. To calculate the possible times for car B, we need to find out how many times car B must complete a lap in order to keep up with car A. Since car A takes 30 seconds to complete one lap and the cars have completed 5 laps in 150 seconds, car B must take the same amount of time as car A, i.e. 30 seconds, in order to keep up with car A. Therefore, the possible times for car B are 30, 60, 90, and 120 seconds.
Therefore, the four possible times that car B could take to complete one lap are 30, 60, 90, and 120 seconds.
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2b x b
is this answer only 2b ^ 2 or is there any other answer without using exponentiation
The answer to the expression 2b x b is simply 2b^2. Exponentiation is a mathematical operation that raises a number to a power, and in this case, b is raised to the power of 2.
Alternatively, if exponentiation is not allowed, the answer to the expression is simply 2b * b, which can be simplified to 2b^2 as well.
So, the answer to the expression 2b x b is 2b^2, regardless of whether or not exponentiation is used.
The expression 2b x b represents the product of two scalars, 2 and b, multiplied by a scalar b.
The expression could represent a variety of quantities in mathematics and science, including the area of a rectangle, the volume of a cube, or the kinetic energy of an object, among others.
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Denise has $250 in her checking account. Each time she buys a bottle of water, she spends $2. If Denise buys
x bottles of water, how much money will remain in her account?(1 نقطة)
The remaining amount of money in Denise's account is $250 - (2x).
Therefore, if Denise buys x bottles of water, she will have $250 - (2x) remaining in her account.
Denise has $250 in her checking account.
Each time she buys a bottle of water, she spends $2.
If Denise buys x bottles of water, the total amount of money spent is 2x.
To calculate the remaining amount in Denise's account, we need to subtract the total amount of money spent (2x) from the original amount of money in her account (250).
Therefore, the formula to calculate the remaining amount is $250 - (2x).
Substituting the value of x in the formula, we get the remaining amount of money in Denise's account.
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For every bottle of water Denise buys her balance decreases by $2. So If Denise buys x bottles of water, her balance decreases by $2 * x.
Let's call the amount of money remaining in Denise's account after buying x bottles of water M.
The equation to find M is:
M = 250 - 2x
This equation says that the money remaining in Denise's account is equal to her initial $250 balance minus the amount she spent on buying x bottles of water, which is $2 per bottle.
In other words, for every bottle of water Denise buys, her balance decreases by $2. So, if she buys x bottles of water, her balance decreases by $2 * x.
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Mark Ran 875 miles this year in the track club. Mark Ryan in 52 track meets and ran the same number of miles in each. How many miles did mark run in each track meet? Brainly
Answer:
16.826
Step-by-step explanation:
I think you divide 875 by 52 which is 16.826 correct me if im wrong.
Answer:
16.8 miles in each track meet
Step-by-step explanation:
You divide 875 by 52 to see how many miles Mark ran in each track meet
875/52 = 16.8
Select all possible cross-sections of a sphere
Circle: a cross-section that goes through the center of the sphere and creates a circular shape.
Point: a cross-section that goes through the center of the sphere and creates a single point.
Please solve both questions 6 and 7
Answer:
6. 4x + 28 + x + 19 + 3x + 13
x = 15
7. x + 123 + 113 + 97 + 90 = 540
x = 117
Step-by-step explanation:
6. 4x + 28 + x + 19 + 3x + 13 = 180
8x + 60 = 180
8x = 120
x = 15
7. x + 123 + 113 + 97 + 90 = 540
x + 423 = 540
x = 117
n a two-variable diagram, there is a straight line which is parallel to the vertical axis. the slope of this line is a. zero. b. infinite. c. indicative of a direct relationship between two variables. d. indicative of an inverse relationship between two variables.
The slope of a straight line that is parallel to the vertical axis is zero.
A slope of zero indicates that the line is flat and has no incline or decline. In a two-variable diagram, this means that there is no relationship between the two variables, as a change in one variable does not affect the value of the other. A line with a slope of zero is a horizontal line, and its equation is of the form y = b, where b is a constant value.
In contrast, a line with an infinite slope (or vertical line) would indicate a perfect correlation between the two variables, such that a change in one variable would result in an infinite change in the other. A line with a finite positive or negative slope would indicate a direct or inverse relationship between the two variables, respectively.
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In right triangle ABC, AC = 4 and BC = 5. A new triangle DEC is formed by connecting the midpoints of AC and BC. What is the area of triangle DEC
Answer:
5
Step-by-step explanation:
The midpoint of AC is (2,0), and the midpoint of BC is (0,2.5). The third vertex of triangle DEC is E, the midpoint of AB, which can be found using the midpoint formula:
E = ( (A_x + B_x) / 2, (A_y + B_y) / 2 )
= ( (0 + 2) / 2, (0 + 5) / 2 )
= (1, 2.5)
So the vertices of triangle DEC are (0, 2.5), (2, 0), and (1, 2.5). The area of triangle DEC is half the area of triangle ABC, which is (4 * 5) / 2 = 10. So the area of triangle DEC is 10 / 2 = 5.
Explain the difference between the graphs of inverse variation functions When k > O and when k < 0.
Answer:
Step-by-step explanation:
Inverse variation functions have the form y = k / x, where k is a constant.
When k > 0, the graph of the inverse variation function is a hyperbola that opens upwards or downwards, depending on the sign of k. When k > 0, the hyperbola opens upwards and the two branches of the hyperbola move away from the x-axis as x increases. This means that as x increases, the value of y decreases. When x approaches 0 from the right, y approaches positive infinity, and when x approaches 0 from the left, y approaches negative infinity.
On the other hand, when k < 0, the graph of the inverse variation function is a hyperbola that opens upwards or downwards, depending on the sign of k. When k < 0, the hyperbola opens downwards and the two branches of the hyperbola move toward the x-axis as x increases. This means that as x increases, the value of y increases. When x approaches 0 from the right or left, y approaches negative infinity.
In both cases, the inverse variation function is undefined for x = 0, as division by zero is undefined.