Answers
The domain of this function can be expressed as (-∞,0) U (0,∞).
The interval on which the function is decreasing is
(-∞,0) U (0,∞).
The interval on which the function is increasing is none.
The interval on which the function is constant is (0,0).
What is domain?The domain of a function is the set of all acceptable inputs for the function. In other words, it is the set of all values for which the function is defined.
The domain of the given function is all real numbers, excluding 0.
This can be seen by observing that the denominator in the fraction is the absolute value of t, which is always positive.
Therefore, the domain of the function is all real numbers except 0, which can be expressed as (-∞,0) U (0,∞).
The function is decreasing over all intervals in its domain since the negative sign preceding the fraction indicates that the value of the function is always negative.
Therefore, the interval on which the function is decreasing is
(-∞,0) U (0,∞).
The function is constant over the interval (0,0) since the absolute value of 0 is 0 and thus, the denominator in the fraction is equal to 0.
Therefore, the interval on which the function is constant is (0,0).
Finally, the function is not increasing over any interval in its domain since the negative sign preceding the fraction indicates that the value of the function is always negative.
Therefore, the interval on which the function is increasing is none.
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Related Questions
Shawnee bought a shirt on sale that was 20% off of the original price. The original price was $5 more than the sale price. What was the original price? Use a model and check your work using the 80/20 rule.
Answers
If the sale price is 20% off the original price, then the original price would be:
x + 0.2x = 1.2x
We also know that the original price was $5 more than the sale price, so:
1.2x = x + 5
Solving for x, we get:
0.2x = 5
x = 25
Therefore, the sale price of the shirt was $25.
To check our work using the 80/20 rule, we can find 20% of the original price:
20% of x = 0.2 * (x + 5) = 0.2x + 1
We can see that 20% of the original price is $5 more than the sale price of $25.
0.2x + 1 = 25 + 5
0.2x = 29
x = 145
Therefore, the original price of the shirt was $145.
To check this answer, we can find the sale price by taking 80% of the original price:
80% of 145 = 0.8 * 145 = 116
We can see that the sale price of $25 is indeed $5 less than the original price of $116.
So our answer checks out!
Select the expression that represents this real-world situation.
Josie has 12 yards of fabric. She is making identical dresses for d dolls. What is the length of fabric used for each doll?
12 + d
12 − d
12 x d
12 ÷ d
Answers
To find the length of fabric used for each doll, we need to divide the total length of fabric (12 yards) by the number of dolls (d). This gives us:
Length of fabric for each doll = 12 ÷ d
For example, if Josie is making 4 identical dresses, then the length of fabric used for each doll would be:
Length of fabric for each doll = 12 ÷ 4 = 3 yards
if 1 million passengers pass through the st. louis airport with checked baggage each month, a successful six sigma program for baggage handling would result in how many passengers with misplaced luggage? group of answer choices 3.4 34 6.0 2700 6 times the monthly standard deviation of passengers
Answers
Answer: 3.4 The number of passengers with misplaced luggage if 1 million passengers pass through the St. Louis airport with checked baggage each month would be 3.4 passengers.
A six sigma program is a quality improvement methodology that uses data and statistical analysis to identify and eliminate defects in a process. Six Sigma methodologies are used to improve efficiency and minimize defects in many business processes, including baggage handling in airports.
Sigma is a term used to refer to standard deviation, which is a measure of the spread of data in a process. A six sigma program aims to reduce the standard deviation in a process to a level where there are fewer than 3.4 defects per million opportunities.
Therefore, if one million passengers pass through the St. Louis airport each month, a successful six sigma program for baggage handling would result in 3.4 passengers with misplaced luggage.
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which of the following is most important in gathering data for use in statistical analysis? a. both efficiency and effectiveness are important when gathering data. b. the data should always be discarded immediately after gathering. c. the data should be gathered in an effective manner. d. the data should be gathered in an efficient manner.
Answers
The statement that is most important in gathering data for use in statistical analysis is option (a) Both efficiency and effectiveness are important when gathering data
Option a. Both efficiency and effectiveness are important when gathering data is the most appropriate answer.
Efficiency refers to the ability to gather data quickly and with minimal resources, while effectiveness refers to the ability to gather accurate and relevant data that is suitable for the intended analysis. Both of these factors are crucial in gathering data for statistical analysis.
Option b. The data should always be discarded immediately after gathering is incorrect because data is usually retained for further analysis and is not discarded immediately after gathering.
Option c. The data should be gathered in an effective manner is partially correct, but it does not address the importance of efficiency in the data gathering process.
Option d. The data should be gathered in an efficient manner is also partially correct, but it does not address the importance of effectiveness in the data gathering process.
Therefore, the correct option is (a) both efficiency and effectiveness are important when gathering data
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Graph the image of V(
–
6,3) after a rotation 90° clockwise around the origin.
Answers
The graph of point V(-6,3) after a rotation 90° clockwise rotation around the origin is given below:
What is graph?
In mathematics, a graph is a visual representation of a set of objects, which are called vertices or nodes, connected by links or edges. A graph can be used to represent relationships or connections between objects in a clear and concise way.
To graph the image of point V(-6, 3) after a 90° clockwise rotation around the origin, we can use the following steps:
Draw the coordinate axes and plot the point V(-6, 3).Draw a perpendicular line from point V to the x-axis. This line represents the distance between the point and the x-axis.To rotate the point 90° clockwise around the origin, we need to swap the x and y coordinates and change the sign of the new x-coordinate. So, the new coordinates will be (3, 6).Plot the new point V' (3, 6) on the graph.Connect the points V and V' with a straight line to show the transformation.The graph of point V(-6, 3) and its image after a 90° clockwise rotation around the origin is shown below:
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A small restaurant has a grease recycling tank in the shape of a cylinder. How much grease measured in cubic centimeters can the restaurant store if the tank has a diameter of 197.2 cm and a height of 223.7 cm? Use 3.14 for `pi`.
Answers
The restaurant can store approximately [tex]6.864 * 10^6[/tex] cubic centimeters of grease in the recycling tank in the shape of a cylinder.
The formula for the volume of a cylinder is V = π[tex]r^2[/tex]h, where V is the volume, r is the radius of the circular base, and h is the height of the cylinder.
To use this formula, we need to know the values of r and h for the grease recycling tank. The problem tells us that the diameter of the tank is 197.2 cm, which means the radius is half of the diameter:
r = d/2 = 197.2 cm / 2 = 98.6 cm.
The problem also tells us that the height of the tank is 223.7 cm.
Now we can plug in the values of r and h into the formula for the volume of a cylinder:
V = π[tex]r^2[/tex]h
V = π[tex](98.6 cm)^2(223.7 cm)[/tex]
V = [tex]3.14 * (98.6 cm)^2 * (223.7 cm)[/tex]
V ≈ [tex]6.864 * 10^6 cm^3[/tex]
Therefore, the volume of the grease recycling tank is approximately [tex]6.864 * 10^6[/tex] cubic centimeters, which means that the restaurant can store that amount of grease in the tank.
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I need help with number 26 asap! Thank you so much!!
Answers
Therefore, the only solution to the equation cot² x cos x = cot²x on the interval [0, 2m) is x = 0.
What is equation?An equation is a mathematical statement that shows the equality between two expressions. The expressions on either side of the equals sign are called the left-hand side and the right-hand side of the equation. An equation can be written in many different forms, but the most common form is: Left-hand side = Right-hand side
In the given question,
We start by bringing all the terms to one side of the equation, which gives:cot² x (cos x - 1) = 0
Now, we need to solve for x such that this equation holds on the interval [0, 2m).
First, we consider the case where cot² x = 0. This occurs when cot x = 0, or x = π/2, 3π/2, 5π/2, etc. However, none of these solutions are in the given interval [0, 2m), so we can ignore this case.
Next, we consider the case where cos x - 1 = 0. This occurs when cos x = 1, or x = 2nπ, where n is an integer. The only solution that is in the given interval [0, 2m) is x = 0.
Therefore, the only solution to the equation cot² x cos x = cot² x on the interval [0, 2m) is x = 0.
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1. Two linear equations are shown in the graph below. Enter the coordinates of these two linear
equations;
Answers
Answer:
y=-0.5x+2; y=3x-5
Step-by-step explanation:
First linear equation:
y=ax+b
A(0,2) B(4,0)
2=a*0+b
0=4*a+b
b=2
4a+b=0
4a+2=0
4a=-2
a=-0.5
y=-0.5x+2
Second linear equation:
y=cx+d
C(0,-5) D(2,1)
-5=c*0+d
1=c*2+d
d=-5
2c+d=1
2c-5=1
2c=6
c=3
y=3x-5
. A pile of bottle caps is located at (4, -10). find the length of the most direct path between Ann and the bottle caps?
Answers
Thus, the most direct path between the bottle caps and Ann is found as:
d = 10.63 units.
Define about the distance formula:The algebraic phrase known as the distance formula, which provides the distances between two places in terms of respective coordinates (in coordinate system).
The distance formulas with points in rectangular coordinates in two- through three-dimensional Euclidean space are based here on Pythagorean theorem.
The formula used to calculate the distance between both the points (x1, y1) and ((x2, y2)
d = √[(x2 - x1)² + (y2 - y1)²]
Coordinates of pile of bottle caps -:(x1, y1) = (4, -10).
Coordinates of ANN - (x2, y2) = (-4, 3).
Using the distance formula:
d = √[(x2 - x1)² + (y2 - y1)²]
d = √[(-4 - 4)² + (-3 + 10)²]
d = √[(64) + 49]
d = 10.63 units
Thus, the most direct path between the bottle caps and Ann is found as:
d = 10.63 units.
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complete question
A pile of bottle caps is located at (4, -10). find the length of the most direct path between Ann and the bottle caps?
The graph for the question is given.
The most important condition for making an inference about a population mean from a significance test is that the data contain no outliers. the data come from a random sample. the sample size is at least 30. the sample size is less than 10% of the population size. the population distribution is exactly Normal.
Answers
The most important condition for making an inference about a population mean from a significance test is that option (b) the data come from a random sample
A random sample is essential to ensure that the sample is representative of the population and that the statistical inference is valid. Other conditions, such as the absence of outliers, sample size, or population distribution, may also affect the validity of the inference, but they are not as crucial as the random sampling condition.
In practice, it is recommended to check for outliers, assess the sample size and the population distribution, and ensure other assumptions of the statistical test are met, such as the normality of the sampling distribution or the equal variance assumption, depending on the test used. However, the random sampling condition remains the most fundamental requirement.
Therefore, the correct option is (b) the data come from a random sample
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It takes 4 people 8 days to paint a wall. How long will it take for 8 people to finish the same wall?
Answers
Answer: 4 days
Step-by-step explanation:
If it takes 4 people 8 days to paint a wall. We can only assume that doubling the number of people would be 2 times as fast. So divide 8/2=4.
Help I’ve tried so hard
Answers
Step-by-step explanation:
The points are 15 units apart
the FIRST expression shows this
You buy a circular rug with a diameter of 7 feet how much floor space for the rug cover
Answers
Step-by-step explanation:
All you need to do here is use the area of a circle equation!
So a=pi(r)^2
A=pi(7)^2
A=pi49
Area would be 49pi or about 153.938 feet^2. Hope this helps!
Answer:
The rug will cover
Step-by-step explanation:
5. discuss the effects on sample size, requirements of changing the desired confidence level, and the acceptable sampling error.
Answers
Changing any of these factors will impact the others. Increasing the sample size generally results in more accurate estimates, while increasing the desired confidence level or decreasing the acceptable sampling error requires a larger sample size.
What is sample size?Sample size refers to the number of individuals or observations included in a study or experiment. It is a crucial component of research design because it determines how much data can be collected and analyzed, as well as the precision and accuracy of the results.
What is sampling error?Sampling error is the difference between the results obtained from a sample and the results that would have been obtained if the entire population had been surveyed. It is a measure of the variability between the sample estimate and the true population parameter.
In the given question,
The sample size, desired confidence level, and acceptable sampling error are all interrelated factors in statistical sampling. Changing any of these factors will have an impact on the others.
First, let's define each factor:
Sample size: The number of individuals or items included in a sample.Confidence level: The degree of certainty that the true population parameter falls within the calculated confidence interval.Sampling error: The degree of error or variation between the sample statistic and the true population parameter.Now, let's discuss the effects of changing each factor:
Sample size: Increasing the sample size generally results in a more accurate estimate of the population parameter. This is because a larger sample size reduces the effect of random variability and increases the precision of the estimate.
Confidence level: Increasing the desired confidence level requires a larger sample size to achieve the same level of precision. This is because a higher level of confidence requires a wider confidence interval, which in turn requires more data points.
Sampling error: Decreasing the acceptable sampling error requires a larger sample size to achieve the same level of precision. This is because a smaller sampling error requires a narrower confidence interval, which in turn requires more data points.
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what is 63.92/9.4 in long division explanation
Answers
In long division, 63.92/9.4 results with quotient of 6.8.
What is long division explanation?Long division is a method of dividing two numbers by repeatedly subtracting the divisor from the dividend and keeping track of the resulting quotient and remainder. This method is often used when dividing two numbers with several digits. The process of long division involves several steps that are repeated until there is no remainder left or until a desired level of precision is achieved.
In long division, the dividend is the number being divided, and the divisor is the number by which the dividend is being divided. The quotient is the result of the division, and the remainder is the amount left over after the division is complete.
006.800
94 | 639.200
−0
63
−0
639
−564
752
−752
0
Thus, In long division, 63.92/9.4 results with quotient of 6.8.
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I need help with number 26 asap! Thank you so much!!
Answers
Ms. Mazzei has a farm on 12 acres of land. She wants to create animal pens that are each 3/11 of an acre. How many pens can Ms. Mazzei have in the 12 acres?
Answers
Ms. Mazzei can have 44 animal pens in her 12 acres of land.
Describe Algebra?Algebra is a branch of mathematics that deals with the manipulation and properties of mathematical expressions, including variables and symbols representing numbers, as well as the rules governing their relationships and operations.
Algebraic equations typically involve variables, which are represented by letters or symbols, and are used to express relationships between different quantities or unknowns. These equations can be manipulated using algebraic operations such as addition, subtraction, multiplication, division, and exponentiation to solve for the value of the variables.
The study of algebra includes a wide range of topics, including linear algebra, abstract algebra, number theory, and algebraic geometry. It is a fundamental part of mathematics and plays a crucial role in many areas of modern science and technology.
To find the number of animal pens Ms. Mazzei can have in 12 acres of land, we need to divide the total area by the area of each pen:
Number of pens = Total area / Area of each pen
Total area = 12 acres
Area of each pen = 3/11 acres
Number of pens = 12 / (3/11)
Number of pens = 44
Therefore, Ms. Mazzei can have 44 animal pens in her 12 acres of land.
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Question 2(Multiple Choice Worth 2 points)
(Comparing Data MC)
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer.
Bus 18, with an IQR of 16
Bus 47, with an IQR of 24
Bus 18, with a range of 16
Bus 47, with a range of 24
Answers
The correct answer is: Bus 18, with an IQR of 9
How to solveTo determine the most consistent bus, we need to calculate the measure of variability, which gives us an idea of the spread of the data.
In this case, we'll use the Interquartile Range (IQR) as the measure of variability.
The IQR is the range between the first quartile (Q1, the 25th percentile) and the third quartile (Q3, the 75th percentile) of the data.
A smaller IQR indicates more consistency in travel times.
Bus 47 Travel Times: 4, 6, 10, 10, 12, 12, 14, 16, 16, 16, 18, 18, 22, 22, 28
Q1 (25th percentile): 10
Q3 (75th percentile): 22
IQR: 22 - 10 = 12
Bus 18 Travel Times: 6, 6, 8, 9, 10, 10, 12, 12, 14, 14, 16, 16, 18, 20, 22
Q1 (25th percentile): 9
Q3 (75th percentile): 18
IQR: 18 - 9 = 9
Comparing the IQRs, we can see that Bus 18 has a smaller IQR (9) compared to Bus 47 (12).
This means that Bus 18 has more consistent travel times than Bus 47.
So, the correct answer is:
Bus 18, with an IQR of 9
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a circle is divided into 5 equal parts what is the measure of the angle that turns through 2 parts
Answers
The measure of the angle that turns through 2 parts of a circle divided into 5 equal parts is 144 degrees.
What is the circumference of a circle?
The circumference of a circle is the distance around its outer edge or boundary. It is the total length of the circular arc, which is the curved part of the circle.
The formula for the circumference of a circle is C = 2πr
If a circle is divided into 5 equal parts, each part corresponds to an angle of 360/5 = 72 degrees.
To find the measure of the angle that turns through 2 parts, we need to multiply 2 by 72 degrees:
2 parts x 72 degrees/part = 144 degrees
Hence, the measure of the angle that turns through 2 parts of a circle divided into 5 equal parts is 144 degrees.
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Simplify the expression. .
2. 3h( 6 – k)
Step by step please
Answers
Explanation
By using distribution multiply the term outside the parentheses by each term inside the parentheses.
3h x 6 and 3h x (-k)
18h - 3hk
This is a new version of the question. Make sure you start new workings.
Select all of the shapes below that are nets of a pentagonal-based pyramid.
Back to task
A
D
Watch video
B
Answ
Answers
The shapes that are nets of a pentagonal-based pyramid are shapes A and D.
What are properties of a pentagonal-based pyramid?A net of a pentagonal-based pyramid is a 2-dimensional pattern that can be folded into a 3-dimensional pentagonal-based pyramid. The net of a pentagonal-based pyramid has the following properties:
It consists of a regular pentagon as the base of the pyramid and five triangles that form the sides of the pyramid.The five triangles are congruent isosceles triangles.The apex of the pyramid is located at the center of the regular pentagon.Each triangle has one vertex at the apex of the pyramid and two vertices on the edges of the regular pentagon.The sum of the angles of each triangle is 180 degrees, and the sum of the angles of the regular pentagon is 540 degrees.The perimeter of the base of the pyramid is equal to five times the length of one side of the regular pentagon.The height of the pyramid is the perpendicular distance from the apex to the base, which can be found using the Pythagorean theorem.Learn more on pentagonal-based pyramid here: https://brainly.com/question/28226952
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if a person is making the median salary for a construction worker, they are making more than what percentage of teachers? they are making more than % of teachers.
Answers
It's difficult to provide a precise answer to this question without knowing the specific median salary for a construction worker and the median salary for teachers in the same geographic area or region.
However, according to data from the Bureau of Labor Statistics (BLS) in the United States, the median annual salary for construction workers as of May 2020 was $38,970, while the median annual salary for elementary, middle, and high school teachers was $61,660. This means that a person making the median salary for a construction worker would be making less than approximately 37% of teachers.
It's important to note that this is a general comparison and the specific salaries can vary depending on factors such as location, years of experience, education level, and job responsibilities.
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What does the three lined equal sign mean
Answers
Answer: identical to/same as
Step-by-step explanation:
Answer:
The ≡ sign means identical to, similar but not exactly the same as, equals
Step-by-step explanation:
Hope this helps! =D
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what is the measurement of the third angle of a triangle if the other two angles each measures 45 degrees?
Answers
Answer: The answer is 90!
Step-by-step explanation:
A triangle's sides have to equal 180 degrees. The other two angles measure 45 degrees + 45 degrees, which equals 90. Now all you have to do is subtract 90 from 180. This equals 90, so the answer is 90 degrees.
Whenever you do problems like this in the future, remember these steps:
Angle 1 + Angle 2
180 - Combination of Angles 1 and 2 = Answer
The reason that you subtract from 180 degrees is because a straight angle is always 180 degrees. If you need more help with problems like these, I recommend watching some tutorials!
I hope this helped you!
The area of a rectangle is found using the formula A=lw
, where l
is the length of the rectangle and w
is the width. Multiply each pair of factors and express the area of each rectangle as a single polynomial in terms of x
.
Question
l=x+14; w=3x+1
Answers
Answer:
The area of the rectangle is given by the formula A = lw. Substituting the given values, we get:
A = (x+14)(3x+1)
Expanding the expression, we get:
A = 3x^2 + x + 42x + 14
A = 3x^2 + 43x + 14
Therefore, the area of the rectangle is given by the polynomial expression 3x^2 + 43x + 14.
Scale factors,
For 19 would it be 5/4 since the polygon is free trying bigger and for 20 would it be 4/5 since it is getting smaller?
All my friends are writing it the other way around but I’m confused because how can it get bigger if it’s less than 1?
Answers
The answers of the following questions are mentioned below respectively.
What is scale factor?Scale factor is the ratio of the lengths of corresponding sides of two similar figures. Two figures are considered similar if they have the same shape, but not necessarily the same size.
19.To find the scale factor of PQRS to JKLM, we can use the fact that the corresponding sides of similar figures are proportional. Thus, we have:
PQ/JK = QR/KL = RS/LM
Substituting the given values, we get:
w/25 = 12/15 = 10/x
Simplifying, we get:
w = 5/3 * 25 = 41.67 (approx)
x = 15/2 = 7.5
y = 25 * 7.5 / 15 = 12.5
Therefore, the scale factor of PQRS to JKLM is PQ/JK = w/25 = 41.67/25 = 1.6667 (approx).
20. To find the scale factor of JKLM to PQRS, we can take the reciprocal of the scale factor of PQRS to JKLM. Thus, we have:
JK/PQ = 1/(PQ/JK) = 1/1.6667 = 0.6 (approx)
Therefore, the scale factor of JKLM to PQRS is JK/PQ = 0.6 (approx).
21. To find the values of ti.. .r. and v, we need more information or equations.
22. To find the perimeter of each polygon, we can add up the lengths of the sides. Thus, we have:
Perimeter of JKLM = KJ + JM + ML + LK = 25 + y + x + 15 = y + x + 40 = 20 + 7.5 + 40 = 67.5
Perimeter of PQRS = PQ + QR + RS + SP = w + 12 + 10 + 16 = w + 38 = 41.67 + 38 = 79.67 (approx)
Therefore, the perimeter of JKLM is 67.5 and the perimeter of PQRS is 79.67 (approx).
23. To find the ratio of the perimeter of PQRS to the perimeter of JKLM, we can divide the perimeter of PQRS by the perimeter of JKLM. Thus, we have:
Ratio of perimeter of PQRS to perimeter of JKLM = Perimeter of PQRS / Perimeter of JKLM = 79.67 / 67.5 = 1.18 (approx)
Therefore, the ratio of the perimeter of PQRS to the perimeter of JKLM is 1.18 (approx).
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19. The scale ratio of PQRS to JKLM is PQ/JK = 1.6667. (approx).
20. JK/PQ is the scale factor of JKLM to PQRS is = 0.6 (approx).
22. The JKLM perimeter is 67.5 and the PQRS perimeter is 79.67 (approx).
23. The PQRS perimeter's ratio to the JKLM perimeter is 1.18. (approx).
What is scale factor?The ratio of the lengths of the respective sides of two similar figures is known as the scale factor. When two figures share the same shape but not necessarily the same height, they are said to be similar.
19. We can use the knowledge that the corresponding sides of comparable figures are proportional to determine the scale factor of PQRS to JKLM.
So, here we are:
[tex]\frac{PQ}{JK}=\frac{QR}{KL}=\frac{RS}{LM}[/tex]
Replace the specified numbers in the aforementioned equation,
[tex]\frac{w}{25}=\frac{12}{25}=\frac{10}{x}[/tex]
Simplifying, we get:
w = 5/3 * 25
= 41.67 (approx)
x = 15/2 = 7.5
y = 25 * 7.5 / 15
= 12.5
As a result, PQ/JK = w/25 is the scale factor for PQRS to JKLM.
= 41.67/25
= 1.6667 (approx).
20. We can take the inverse of the scale factor of PQRS to JKLM to determine the scale factor of JKLM to PQRS. So, here we are:
JK/PQ = 1/(PQ/JK)
= 1/1.6667
= 0.6 (approx)
As a result, JK/PQ is equal to 0.6 when converting JKLM to PQRS. (approx).
21. To find the values of ti.. .r. and v, additional details or formulae are required.
22. We can sum up the side lengths of each polygon to determine its perimeter. So, here we are:
Perimeter of JKLM = KJ + JM + ML + LK
= 25 + y + x + 15
= y + x + 40
= 20 + 7.5 + 40
= 67.5
Perimeter of PQRS = PQ + QR + RS + SP
= w + 12 + 10 + 16
= w + 38
= 41.67 + 38
= 79.67 (approx)
As a result, the JKLM perimeter is 67.5 and the PQRS perimeter is 79.67 (approx).
23. By dividing the perimeters of the two systems, we can determine the percentage of the perimeters of PQRS and JKLM. So, here we are:
Ratio of the PQRS periphery to the JKLM perimeter = Perimeter of PQRS / Perimeter of JKLM = 79.67 / 67.5 = 1.18 (approx)
As a result, the PQRS perimeter's relationship to the JKLM perimeter is 1.18. (approx).
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What is the image of (−5,−9) after a dilation by a scale factor of
3 centered at the origin?
Answers
The image of (-5,-9) after dilation by a scale factor of 3 centered at the origin is (-15,-27).
What is the image of (−5,−9) after a dilation by a scale factor of 3 centered at the origin?To find the image of the point (-5,-9) after dilation by a scale factor of 3 centered at the origin.
We can use the following formula:
(x', y') = (kx, ky)
Where (x', y') are the coordinates of the dilated point, (x, y) are the coordinates of the original point, and k is the scale factor.
In this case, k = 3, and the coordinates of the original point are (-5,-9).
So we have:
x' = 3(-5) = -15
y' = 3(-9) = -27
Therefore, the image after dilation is (-15,-27).
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What is the gradient of the blue line?
Answers
The blue line is the tangent line that passes through the point (0.75, 0.25). The point on the tangent line is (3, 4). The gradient of the curve is approximately 0.6.
Answer:
gradient = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
calculate the gradient m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 2) and (x₂, y₂ ) = (8, 3) ← 2 points on the line
m = [tex]\frac{3-2}{8-4}[/tex] = [tex]\frac{1}{4}[/tex]
write an equation in slope-intercept form of the line that passes through the point (2,15) and (5,21)
Answers
Answer:
y = 2x + 11
Explanation:
N/A
find the slope of a line perpendicular to y=- 1/2x+7
Answers
Answer:
perpendicular slope = 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{1}{2}[/tex] x + 7 ← is in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2