The function g(x) is created by applying an horizontal translation 4 units left and a reflection over the x-axis. (Correct choices: Third option, fifth option)
How to determine the characteristics of rigid transformations by comparing two functions
In this problem we have two functions related to each other because of the existence of rigid transformations. Rigid transformations are transformations applied to geometric loci such that Euclidean distance is conserved at every point of the geometric locus.
Let be f(x) = - 2 · cos (x - 1) + 3, then we use the concept of horizontal translation 4 units in the + x direction:
f'(x) = - 2 · cos (x - 1 + 4) + 3
f'(x) = - 2 · cos (x + 3) + 3 (1)
Now we apply a reflection over the x-axis:
g(x) = - [- 2 · cos (x + 3) + 3]
g(x) = 2 · cos (x + 3) - 3
Therefore, the function g(x) is created by applying an horizontal translation 4 units left and a reflection over the x-axis. (Correct choices: Third option, fifth option)
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Describe the possible lengths of the third side of the triangle given that the lengths of the other two sides are 5 inches and 12 inches.
( )in. < x < ( )in.
To satisfy the lengths of the two sides of the triangle given in the question, the possible lengths of the third side are any value greater than 7 inches and less than 17 inches but not equal to 5 or 12 inches.
What are triangles?A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.
How are the sides of the triangles related?According to the law of the sides of a triangle, the lengths of any two of the triangle's sides added together are always more than the length of the third side. The triangle inequality theorem is another name for this condition.
If we know the lengths of two sides of a triangle, we can use the "triangle inequality theorem" to determine the possible lengths of the third side. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given that the lengths of two sides of a triangle are 5 inches and 12 inches, the length of the third side must be:
Greater than 0 inches
Less than the sum of the other two sides (5 inches + 12 inches = 17 inches)
Greater than the difference between the other two sides (abs(5 inches - 12 inches) = 7 inches)
So the possible lengths of the third side are any value greater than 7 inches and less than 17 inches but not equal to 5 or 12 inches.
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Help frrr thankkk you
Answer:
14
Step-by-step explanation:
There are many measurements of the human body that are positively correlated. For example, the length of one's forearm (measured from elbow to wrist) is approximately the same length as the foot (measured from heel to toe). They are positively correlated because, as one measurement increases, so does the other measurement.
You will discover through this project whether a human's arm span (measured across the body with the arms extended) is correlated to his height.
You will need to collect data from 11 people, which will give you 12 data points including your own personal data. You will turn in and answer questions regarding only one scatter plot if doing the project alone.
Part One: Measurements
Measure your own height and arm span (from finger-tip to finger-tip) in inches. You will likely need some help from a parent, guardian, or sibling to get accurate measurements. Record your measurements on the "Data Record" document. Use the "Data Record" to help you complete Part Two of this project.
Measure 11 additional people, and record their arm spans and heights in inches.
Part Two: Representation of Data with Plots
Using graphing software of your choice, create a scatter plot of your data. Predict the line of best fit, and sketch it on your graph.
Copy and paste your scatter plot into a word processing document.
Part Three: The Line of Best Fit
Include your scatter plot and the answers to the following questions in your word processing document.
Which variable did you plot on the x-axis, and which variable did you plot on the y-axis? Explain why you assigned the variables in that way.
Write the equation of the line of best fit using the slope-intercept form of the line
Part two
Using graphing software of your choice, create a scatter plot of your data. Predict the line of best fit, and sketch it on your graph.
Copy and paste your scatter plot into a word processing document.
part three
Show all your work, including the points used to determine the slope and how the equation was determined.
What does the slope of the line represent within the context of your graph? What does the y-intercept represent?
Test the residuals of two other points to determine how well the line of best fit models the data.
Use the line of best fit to help you to describe the data correlation.
Using the line of best fit that you found in Part Three, Question 2, approximate how tall is a person whose arm span is 66 inches?
According to your line of best fit, what is the arm span of a 74-inch-tall person?
The diagram relating to the scatterplot for the data is attached.
How to explain the scatterplot?I put the height of people on the x-axis because this is what I am trying to correlate the arm span to. I put the arm span on the y-axis because it is dependent on height.
I used point (60,61) and (70,72) to draw the line of best fit and to get the equation. First, to get the slope I would use the slope formula of m = 72-61/70-60 or 11/10 to get a slope of approximately 1.1. Then I used (60,61) to get the rest of the equation by plugging it in: y-61 = 1.1(x -60). This becomes y-61 = 1.1x - 66. Add 61 to both sides and the final equation is y = 1.1x – 5.
The slope represents the rate of change arm span based on height. The y intercept is the arm span.
Using points (66,68) and points (70,72) I plug each into the equation y=1.1x-5 to figure each out based on the difference from the actual points and get .4 for (66,68) and 0 for point (70,72) so I would say, based on .4 and 0 for these two points that this is a good line of best fit.
Based on this data, for every inch in height, the arm span increases by 1.1 inches.
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2. Which equation has the solution x = -1? A 2x1 = 3x - 2
B 8x + 7 = 9x - 8
C -5x -4 = 4x + 3
D 7x+8 = -6x - 5
The equation that has the solution x = -1 is D. 7x+8 = -6x - 5
To find the solution of an equation, we need to find the value of the variable that makes the equation true. In this case, we need to find the value of x that makes the equation 7x+8 = -6x - 5 true.
We can start isolating the x variable by adding or subtracting the same terms on both sides of the equation.
D. 7x+8 = -6x - 5
13x = -13
x = -1
So the solution of the equation is x = -1
We can check if this is the solution by substituting it back in the equation. If the equation is true, both sides will be equal when x is -1.
7x+8 = -6x - 5
7*-1 + 8 = -6*-1 -5
-7+8 = 6 -5
1 = 1 (true)
Therefore, D. 7x+8 = -6x - 5 has x = -1 as the solution.
graph the function f: f(x)=√x²-4 x+4 and determine its range and discuss its monotony
Range of function is {5, 4, 3, 2, 1, 0,1} and the function is monotonous.
what is function?
A function is a mathematical expression that state the relationship between an independent variable and a dependent variable. The value of independent variable is called domain and the value of dependent variable is called range.
What is the range of the function bellow?
given, a function f(x) = √ (x² - 4x +4)
now for every input value of x we will get an output value for f(x).
we select the domain of function as x = {-3, -2, -1, 0, 1, 2, 3}
when we put the x value in the function, we get f(-3) = √[(-3²) - 4×(-3)+4]
f(-3) = √25 =5
similarly, f( -2) = 4
f(-1) = 3
f(0) = 2
f(1) = 1
f(2) =0
f(3) = 1
the range of function is {5, 4, 3, 2, 1, 0,1}
The range of function indicates that it is neither increasing nor decreasing.
hence the function is a monotonous function.
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please solve this
it would mean so much to me please
Solve the system of equations using substitution. y = −2x + 14x + 2y = −1 a. (0, −3) b. (−3, 0) c. no solution d. infinitely many solutions
The system of equations y = −2x + 14x + 2y = −1 using substitution is [tex](\frac{9}{3} ,12)[/tex].
What is algebraic equation ?
An algebraic equation is a mathematical expression that contains one or more variables, and an equal sign. The goal is to find the value or values of the variables that make the equation true. Algebraic equations can take many forms, such as linear equations, quadratic equations, polynomial equations, and more.
y = −2x + 14
x + 2y = −1
We can use the first equation to solve for y in terms of x:
y = −2x + 14
Now we can substitute this expression for y into the second equation,
x + 2(-2x + 14) = -1
x + (-4x + 28) = -1
-3x = -29
x = 9/3
Now we can substitute this value for x back into the first equation to find y,
y = -2(9/3) + 14 = -6/3 + 14 = -2 + 14 = 12
Hence , The system of equations y = −2x + 14x + 2y = −1 using substitution is [tex](\frac{9}{3} ,12)[/tex].
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What is equality easy answer?
Equality means being equal in all aspects such as status, rights irrespective of caste, colour, race, gender, etc.
Now, According to the question:
What is a equality in math?
Equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object. The equality between A and B is written A = B, and pronounced A equals B.
Example of Equality
Two equations that have the same solution are called equivalent equations e.g. 5 +3 = 2 + 6. And this as we learned in a previous section is shown by the equality sign =. An inverse operation are two operations that undo each other e.g. addition and subtraction or multiplication and division.
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What is the approximate side length of the square?
3.0 units
3.5 units
4.2 units
4.9 units
The approximate side length of the square is 4.2 units. Hence option B is the correct option.
What is a square?
A square is a regular quadrilateral in Euclidean geometry, which means it has four equal sides and four equal angles. It can alternatively be defined as a rectangle having two neighboring sides of identical length.
Given that the length of half of the diagonal is 3 units.
The diagonals of the square cut each other at a right angle.
The length of OB is 3 units and OC is 3 units.
The △BOC is a right triangle at O.
The hypotenuse of △BOC is BC. The legs of △BOC are OB and OC.
According to the Pythagorean theorem,
OB² + OC² = BC²
3² + 3² = BC²
BC² = 9 + 9
BC² = 18
BC = 3√2
BC ≈ 4.2
The approximate side length of the square is 4.2 units.
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What is the coefficient of x² in 5x²y?
5y is the coefficient of x² in the given polynomial 5x²y.
What is coefficient of polynomial?Polynomial coefficients are the integers preceding a word. Terms are often composed of a number and a variable (for example, 2 x 2 2x2 2x2, where 2 is the number and x is the variable). The coefficient is represented by the number portion. Simply put, it is the leading term's coefficient. The polynomial degree is the largest power of the variable that occurs in the polynomial. The leading phrase is the one with the greatest power of the variable: the term with the greatest degree. The leading coefficient is the leading term's coefficient.
Here,
The coefficient of x^2 in the above polynomial 5x^2y is 5y.
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is it easier to describe the solution of a system of linear inequalities in words or to show it using a graph?
It depends on the context and the audience. Both describing the solution of a system of linear inequalities in words and showing it using a graph have their own advantages.
An explanation graph is what?
A graph is a representation of the relationship between two variables that are normally measured along one of a pair of axes at right angles.
Describing the solution of a system of linear inequalities in words is often useful when the system is simple and the inequalities are easy to understand. It can be a more straightforward way to explain the solution, especially when the audience is not familiar with reading graphs.
On the other hand, using a graph to show the solution of a system of linear inequalities can be more efficient and effective when the system is more complex and the inequalities are harder to understand. Graphs can provide a visual representation of the solution, which can make it easier for the audience to understand the solution and see how it relates to the original problem. Additionally, it can be easier to find the exact point of intersection between the inequalities by looking at the graph.
Both methods can be useful depending on the situation, so it's best to consider your audience, the complexity of the system, and the goal of your explanation when deciding which method to use.
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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
The probability of landing on yellow is less than the probability of landing on blue
How to determine which statement about probability is true?Probability is the likelihood of a desired event happening.
Since there are one orange, two purple, two yellow, and three blue and the spinner divided into eight equal colored sections.
Thus, we can write the probabilities as follow:
probability of orange = 1/8
probability of purple = 2/8 = 1/4
probability of yellow = 2/8 = 1/4
probability of blue = 3/8
Therefore, the probability of landing on yellow is less than the probability of landing on blue is the true statement
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wanda wants to buy a pair of shoes that cost $48 If sales tax costs 8.25% what will be the total cost
Answer:51.96 dollars total
Step-by-step explanation:
go to a smart cauculator and add 8.25% to 48
Tasha earned $7.55 per hour and an additional $100 in tips waiting tables on Saturday night. Altogether she earned $160.40. Write an equation for this situation. Use h to represent the number of hours.
The equation that represents the situation is $160.40 = $100 + $7.55h.
What is the equation ?An equation is a statement that consists of numbers or letters and an equal to sign. The amount earned is a function of the tip, hours worked and the pay per hour.
The form of the equation is:
Total amount earned =tip + (amount earned peer hour)
$160.40 = $100 + ($7.55 x h)
$160.40 = $100 + $7.55h
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How do you simplify the base of an exponent?
The base of an exponent can be simplified by multiplying it by itself as many times as the exponent indicates. If you want to simplify the base of an exponent in an expression, it would be done by raising the base to the power of the exponent using the notation aᵇ = aa...*a (b times)
THE BASE OF AN EXPONENTThe base of an exponent is the number that is being multiplied by itself a certain number of times. The exponent is the number indicating how many times the base is being multiplied by itself.
For example, in the expression 2³, the base is 2 and the exponent is 3. This means that 2 is being multiplied by itself 3 times, or 2 * 2 * 2. The simplified form of this expression is 8.
In general, if the base is 'a' and the exponent is 'b' then the simplified form of the expression is 'a' raised to the power 'b' or aᵇ = aa*...*a (b times)
It's also important to note that when the exponent is 1, the expression can't be simplified anymore. For example, 2¹ = 2, where 2 is the base and 1 is the exponent.
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Kevin conducted a survey of a random sample of registered voters in his town to determine their preferred candidate for mayor in the next election. The results of the survey are shown in the table below.
Survey Results
Candidate Likely Voter Preference
A 240
B 210
C 50
There are 18,000 registered voters in Kevin’s town. Based on the data in the table, what is the best estimate of the number of people who will vote for Candidate A if all the registered voters cast a ballot?
Candidate A is likely to receive 8640 voters if all 18000 voters cast their ballot.
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here: The survey results from the sample as
A -240
B-210
C-50
The total number of people surveyed is 500
Now as per the given survey results the voters likely to vote for candidate A is P(A)=240/500
=12/25
Similarly, the probability that the voters vote for Candidate A and B are
P(A)=210/500
=21/50
P(B)=1/10
∴ If 18000 voters vote the voters likely to vote for A are
=12/25 ×18000
=8640 voters
Hence, Candidate A is likely to receive 8640 voters if all 18000 voters cast their ballot.
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16. Coach Murphy has an end of the season celebration for his basketball team. He provided a pizza lunch and
distributed a homemade DVD of the season's highlights to each player. It cost him $5 per player for the pizza
lunch and $2 per player for the DVD. If there were 8 players on the team, use the Distributive Property to find
the total cost for the celebration.
Answer:
$56.00
Step-by-step explanation:
8(5 + 2) Distribute the 8
8(5) + 8(2)
40 + 16
56
Answer as quickly as you can! I will mark Brainliest:
Lincoln spends $55 of his allowance every month and saves the rest.
This month he decides to spend only $45, increasing his savings by 40%.
What is his monthly allowance?
On solving the provided question we can say that by percentage 40% of savings = 40% of 20 = 40/100 X 20 = $8 140% of savings = 140% of 20 = 140/100 X 20 = $28 his monthly allowance is = $8 + $28 = $36
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
Increase in savings $20
by percentage
40% of savings = 40% of 20 = 40/100 X 20 = $8
140% of savings = 140% of 20 = 140/100 X 20 = $28
his monthly allowance is = $8 + $28 = $36
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Sam and harry are family. Sam is currently five times harry's age. Sam's age is also 10 more than three times harry's age. The following system of equations models this scenario: x = 5y x = 10 + 3y what are their current ages? sam is 25 years old, and harry is 5 years old. Sam is 30 years old, and harry is 6 years old. Sam is 35 years old, and harry is 7 years old. Sam is 40 years old, and harry is 8 years old.
Sam is 25 years old, and Harry is 5 years old.
If we multiply the age of Harry (5) five times, it will give us 25:
5×5= 25
and if we multiply Harry's age three times and then add up ten, it will give us 25:
(5×3) +10 = 25
15 + 10 = 25
25 = 25
what is -8r=64 step by step
Can someone please help me with this math problem, ASAP? The problem is in the picture, THANKS!
Answer:
Length = Width = 55
Step-by-step explanation:
Perimeter of rectangle = 2(length + width)
Let x = length; let y = width.
perimeter = 2(x + y)
The perimeter must be 220.
2(x + y) = 220
x + y = 110
y = 110 - x
length = x
width = 110 - x
area = length × width
area = x(110 - x)
area = 110x - x²
A = 110x - x²
Take the first derivative of the area function and set equal to zero. Then solve for x.
A' = 110 - 2x
110 - 2x = 0
2x = 110
x = 55
y = 110 - x = 110 - 55 = 55
Answer: Length = Width = 55
What is the first common multiple of 4 and 10?
Answer:
20
Step-by-step explanation:
4 ans ten both have 20 in common and it jas ro be the first because the next is like 40
Which of the following is a rational number?
A. 66
B.π
C. 36
D. 40
Answer:
36
Step-by-step explanation:
Can someone help me answer this question
House sales at Home Realty increased by 18% this year. Last year Billy sold 50 houses. How many houses were sold this year.
a: 9 houses
b: 59 houses
c: 68 houses
d: 900 houses
Answer:
b: 59 houses
Step-by-step explanation:
50 + 18% of 50 =
= 50 + 0.18 × 50
= 50 + 9
= 59
Answer:
b
Step-by-step explanation:
The area of a square photo frame is 250cm2. Find the perimeter of the photo frame, leaving your answer correct to 1 decimal place.
Therefore ,perimeter of square photo frame = 63.2 centimeter.
What is the perimeter?The total length of boundary of a closed geometric shape is called perimeter. Different geometric shape has different formula for determining perimeter. For a square shaped object perimeter is the four times of its side length.
Here,
Area of a square photo frame = 250 square centimeter.
We know, area of a square photo frame = square of side length
if side length = s
area = s²
it is given that area of a square photo frame = 250 cm²
250 cm² = s²
s = √250 cm
s = 15.81 cm
side length = 15.81 cm
formula for perimeter = 4× side length
perimeter of frame = 4×15.81 = 63.24 cm
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Let U represent the set of people in a certain community who were asked if they subscribe to an information source.Let D ={ x ∈ U | x subscribes to The Daily Informer }andN ={ x ∈ U | x subscribes to News Magazine }(Assume these sets are not disjoint.) Write the set that represents the set of people surveyed who subscribe to exactly one of the two news sources given.a) N ∪ Db) ( N c ∩ D ) ∪ ( N ∩ D c )c) N c ∩ Dd) ( N ∩ D )ce) ( N c ∪ D ) ∩ ( N ∪ D c )
The people who only get news from one of the two sources we surveyed are in the group represented by set (B) ( Nc∩D) ∪ (N∩Dc).
What are sets?A set is like a bunch of different stuff put together; it includes elements or members, which can be anything mathematical, like numbers, symbols, shapes, variables, or even other sets.
So, we have:
N = { x ∈ U | x subscribes to News Magazine }
D = { x ∈ U | x subscribes to The Daily Informer }
As, N∩D ≠ ∅.
It looks like a decent amount of people surveyed only have a subscription to News Magazine and not any other magazines.
= Subscribe to News Magazine and not Daily Informer
= N ∩ D c
Out of the people surveyed, 4 of them only subscribe to the Daily Informer.
= Subscribe to Daily informer and not subscribe to News Magazine
= D ∩ N c
Out of the people surveyed, 4 of them only subscribe to the Daily Informer.
= Subscribe to News Magazine and not subscribe to Daily Informer or subscribe to Daily informer and not subscribe to News Magazine
= ( N ∩ D c ) ∪ ( D ∩ N c )
= ( N c ∩ D ) ∪ ( N ∩ D c )
Therefore, the people who only get news from one of the two sources we surveyed are in the group represented by set (B) ( Nc∩D) ∪ (N∩Dc).
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Complete question:
Let U represent the set of people in a certain community who were asked if they subscribe to an information source. Let D ={ x ∈ U | x subscribes to The Daily Informer } and N ={ x ∈ U | x subscribes to News Magazine } (Assume these sets are not disjoint.) Write the set that represents the set of people surveyed who subscribe to exactly one of the two news sources given.
a. N ∪ D
b. ( N c ∩ D ) ∪ ( N ∩ D c )
c. N c ∩ D
d. ( N ∩ D )c
e. ( N c ∪ D ) ∩ ( N ∪ D c )
Select the correct answer. Which two of the functions shown here have identical graphs and why? A. f and g, because the log of a quotient is the quotient of the logs B. g and j, because the quotient of two logs is the sum of the logs C. f and h, because the log of a quotient is the difference of the logs D. g and h, because the quotient of two logs is the difference of the logs
F and h, because the log of a quotient is the difference of the log. Logs work that way when you subtract one log from another you can rewrite it as a fraction. The correct is option C.
What do logs mean?
Logarithm is a power to which a range of should be raised for you to get a few different wide varieties as an example the bottom ten logarithms of a hundred is two because ten raised to the electricity of is one hundred: log a hundred = 2.
There are three common types of logarithms such as:
Common logarithms: where the base is 10 Binary logarithms: where the base is 2 Natural logarithms: where the base is e ≈ 2.71828Therefore logarithm is the mathematical expression used to answer the question.
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Given E(-6, y), F(6, 5), G(14, 11), and
H(8,-13), find the value of y so that
EF is perpendicular to GH.
the answer is y = 16.
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
here, we have,
E(-6, y), F(6, 5), G(14, 11), and H(8,-13),
& EF is perpendicular to GH.
now, we get,
The slope of GH is ...
G -H = (14, 11) -(8, -13) = (6, 24) = (Δx, Δy)
slope = Δy/Δx = 24/6 = 4
The perpendicular line through F will have a slope of the negative reciprocal of this, or -1/4.
The point-slope form of the equation can be written as ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
The perpendicular line through F is then ...
y -13 = (-1/4)(x -6)
For an x-value of -6, the value of y will be ...
y = (-1/4)(-6 -6) +13 = 12/4 +13 = 16
hence, The value of y so that EF is perpendicular to GH is 16.
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10 POINTS FOR ANY ONE HOW CAN ANSWER THIS
:)
Answer: A=16 B=14 C=34
Step-by-step explanation: