Use triangle XYZ to answer questions 1-3
1) You special right triangles to help fine the length of segment XY. What is the exact base of triangle XYZ?
2) what is the exact area of triangle XYZ? Leave your answer in RADICAL terms. Show your work
3) What is the area of triangle XYZ to the nearest tenth of a square ft?
Answers
For the triangle XYZ, the answers are:1)XY=\(8\sqrt{3}\); 2)Exact Area of triangle XYZ= \(32\sqrt{3} ft\) and 3) Area of triangle XYZ = 55.4 ft.
RIGHT TRIANGLE
A triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: \((hypotenuse)^2=(leg_1)^2+(leg_2)^2\) . And the main trigonometric ratios are:
\(sin(\alpha )=\frac{opposite \;leg}{hypotenuse} \\ \\ cos(\alpha )=\frac{adjacent\;leg}{hypotenuse}\\ \\ tan(\alpha )=\frac{opposite \;leg}{adjacent\;leg}\)
Finding the segment XY.\(cos (30 )=\frac{adjacent\;leg}{hypotenuse} \\ \\ \frac{\sqrt{3} }{2} =\frac{XY}{16} \\ \\ 2XY=16\sqrt{3} \\ \\ XY=8\sqrt{3}\;ft\)
2.Finding the exact area of triangle XYZ
The area of a right triangle is equal to \(\frac{1}{2} * base *height\). In this exercise the base is equal to \(8\sqrt{3}\). For finding the height, you should apply the trigonometric ratio for sin.
\(sin (30 )=\frac{opposite\;leg}{hypotenuse} \\ \\ \frac{{1} }{2} =\frac{XZ}{16} \\ \\ 2XZ=16\\ \\ XZ=8\;ft\)
Therefore, the area will be:
\(\frac{1}{2} * base *height\\ \\ \frac{1}{2} * 8\sqrt{3} *8=32\sqrt{3} ft\)
3.Finding the area of triangle XYZ to the nearest tenth of a square ft
Knowing that \(\sqrt{3}= 1.73205\dots\), the solution will be:
\(\frac{1}{2} * base *height\\ \\ \frac{1}{2} * 8\sqrt{3} *8=32\sqrt{3} =32*1.73205=55.4 ft\)
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Related Questions
the given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.
Answers
The scatterplot with the least squares line provides insights into the relationship between average annual global surface temperature and the years from 2000 to 2015, allowing us to assess trends, strength of correlation, and make predictions within certain limitations.
The scatterplot represents the relationship between the average annual global surface temperature, in degrees Celsius, and the corresponding years from 2000 to 2015. The line drawn on the plot is the least squares line, which is the best fit line that minimizes the overall distance between the observed data points and the line.
The least squares line is determined using a statistical method called linear regression. It calculates the equation of a straight line that represents the trend in the data. This line serves as a mathematical model to estimate the average temperature based on the year.
By analyzing the scatterplot and the least squares line, we can make several observations. Firstly, we can see whether the temperature has been increasing, decreasing, or remaining relatively stable over the given years. If the slope of the line is positive, it indicates a positive correlation, implying that the temperature has been increasing. Conversely, a negative slope suggests a decreasing trend.
Additionally, we can evaluate the strength of the relationship between temperature and time by examining how closely the data points cluster around the line. If the points are closely grouped around the line, it suggests a strong correlation, indicating that the line is a good representation of the data. On the other hand, if the points are more scattered, the correlation may be weaker.
Furthermore, the line can be used to predict the average annual global surface temperature for future years beyond the data range of 2000 to 2015. However, it's important to note that such predictions should be made with caution and considering other factors that may affect global temperatures, such as climate change and natural variability.
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Question
The given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.
Question 4 (1 point)
One way to convert from inches to centimeters is to multiply the number of inches by
2.54. How many centimeters are there in inch?
10.16 cm
1/635 cm
0.635 cm
1/10.16 cm
Answers
Answer:
Step-by-step explanation:
Inches to CM Conversion
1 Inch (in) is equal to 2.54 cm. To convert inches to cm, multiply the inch value by 2.54. For example, to find out how many cm is 12 inches, multiply 12 by 2.54, that makes 30.48 cm is 12 in.
At a collector's fair, Jason sold six sports cards at $56 each and bought eight sports cards at $43 each. What was Jason's net profit and loss?
(Order of Operations and integers)
Answers
Answer:
He lost $8
Step-by-step explanation:
sold 6 x $56 = $336
bought 8 x $43 = $344
344 - 336 = $8
Jackie has two puppies. One weighs 5 9/16 pounds and the other weighs 6 1/4 pounds. Find the difference in their weights.
Answers
weights = pounds
Answer: Jackie has two puppies. One weighs 5 9/16 pounds and the other weighs 6 1/4 pounds. Find the difference in their weights.
Step-by-step explanation:
"DIFFERENCE" means to subtract their weights. We will subtract lesser amount from the greater amount to get our answer.
Also, we need to first make these mixed numbers into improper fractions by using the rule below:
If a number is given in this form:
We can do the operation below to make it improper fraction:
The bigger number is . So we subtract the other from this after changing to improper fraction.
and
Now, we subtract via doing LCM and get our answer: The difference in weight is 11/16 pounds
please help me someone with this problem
Answers
Fill the Blank!!!
The point ( 2, 4 ) ________ on the line y = -2x + 6 because when the value of x and y are substituted in the equation the result is 4 = ____ .
A. Is Not
B.2
C. -2
D. 10
E. Is
F. 4
Answers
The requried, point ( 2, 4 ) in not on the line y = -2x + 6 because when the value of x and y are substituted in the equation the result is 4 = 2. Options A and B both are correct.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
Given line,
y = -2x + 6
Now, put the given point (2, 4) in the line,
4 = -2(2) + 6
4 = -4 + 6
4 = 2
Thus, the requried, point ( 2, 4 ) in not on the line y = -2x + 6 because when the value of x and y are substituted in the equation the result is 4 = 2. Options A and B both are correct.
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Please help me it’s really important to me
Answers
2. e
3. a
4. c
5. d
6. f
7. g
8. h
hope this helps there is really no way of explaining you would have to study you theorems
Ronald is 39 years old, and he owns her car, which he uses to drive to work.
His collision deductible is $500, and he does not have comprehensive
coverage. If his car's safety rating is 12, how much does he pay each month
for car insurance?
O A. $172.55
B. $143.75
C. $150.50
D. $135.35
Answers
Answer: $143.75
Step-by-step explanation:
Answer:
143.75
Step-by-step explanation:
Please answer quick Please
Answers
Answer:
n^3-4n^2+5
Step-by-step explanation:
Find the Laplace domain X(s) equation by implanting the given parameters and find the time domain x(t) using inverse Laplace transform.
Answers
The Laplace domain equation X(s) is found to be X(s) = (s + 2)/(s^2 + 5s + 6). The time domain equation x(t) can be obtained by applying the inverse Laplace transform to X(s), resulting in x(t) = e^(-t) - e^(-2t).
Given the Laplace domain equation X(s), we need to substitute the given parameters and find its expression in terms of s. The equation provided is X(s) = (s + 2)/(s^2 + 5s + 6).
To obtain the time domain equation x(t), we need to apply the inverse Laplace transform to X(s). The inverse Laplace transform of X(s) will give us x(t) in terms of t.
Applying the inverse Laplace transform to X(s) involves finding the inverse transform of each term separately. The inverse Laplace transform of (s + 2) is simply 1, representing the unit step function. The inverse Laplace transform of (s^2 + 5s + 6) is e^(-t) - e^(-2t), which can be obtained through partial fraction decomposition.
Therefore, the time domain equation x(t) is given by x(t) = e^(-t) - e^(-2t), where t represents time.
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Y=x^3, y=-1, x=2 square cross section perpendicular to the y-axis
Answers
The required answer is a square cross-section with a side length of 3.
What is surface area?The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
Here,
The cross-section we are interested in is a square that lies in the plane y=-1. To find this square, we need to find the value of x where the curve y=x³ intersects the plane y=-1.
y=x³ and y=-1 intersect when,
x = (-1)^(1/3)
x = -1, since (-1)³ = -1.
The curve y=x³ intersects the plane y=-1 again when x=2, since 2³=8 and -1<8. Therefore, the square cross-section perpendicular to the y-axis that we are looking for has a side length 2-(-1)=3.
Hence, the answer is a square with a side length of 3.
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what is the probability that a randomly selected customer had at least one order in the previous month or uses express shipping?
Answers
The probability that a randomly selected customer had at least one order in the previous month or uses express shipping is 0.9242.
Describe Probability?Probability is a branch of mathematics that deals with the study of random events or outcomes. It is used to measure the likelihood or chance of an event occurring, ranging from impossible (0 probability) to certain (1 probability).
The basic concept of probability involves determining the ratio of the number of favorable outcomes to the total number of possible outcomes. This ratio is expressed as a fraction, decimal, or percentage.
For example, if you toss a fair coin, there are two possible outcomes: heads or tails. The probability of getting heads is 1/2 or 0.5 or 50%, and the probability of getting tails is also 1/2 or 0.5 or 50%.
P( at least one order in the previous month or uses express shipping)
=P(at least one order in the previous month) + P(uses express shipping) - P(at least one order in the previous month and uses express shipping)
\(\frac{107+63}{211} +\frac{131}{211} -\frac{65+41}{211}\)
= 0.9242
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Nine students were asked how many miles they live from school. Their answers are listed below.1,1,6,5,1,5,1,1,8
Answers
The mode of the data is 1. The range of the data is 7.
What is the mean of a data set?
A data set is a grouping of data. A data set refers to one or more database tables in the case of tabular data, where each column of a table represents a specific variable and each row corresponds to a specific record of the data set in question.
Given data set is 1,1,6,5,1,5,1,1,8.
The element of a set whose frequency is highest is known the mode of the data set.
The frequency of 1 is 5.
The frequency of 5 is 2.
The frequency of 6 is 1.
The frequency of 8 is 1.
The mode of the data is 1.
The difference of the highest value and lowest value of the data set is the range of the data.
The highest value is 8 and the lowest value is 1. The difference between them is 8 - 1 = 7.
The range of the data is 7.
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The range of the given data is 7 and the mode is 1.
What is mode?In statistics, modes are values that occur repeatedly in a particular set. Values or numbers in a data set that occur frequently or more frequently are sometimes called modal or modal values. This is one of three measures of central tendency, along with mean and median. A mode is the value that occurs most frequently in a set of data values. If X is a discrete random variable, the mode is the value x at which the probability mass function takes the maximum value. That is, the values that are most likely to be sampled. The most common number, the number that occurs most frequently. example: The mode of {4 , 2, 4, 3, 2, 2} is 2. This is because it happens 3 times. This happens more often than any other number.To learn more about mode from the given link:
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Explanation:
Range = The highest value - the lowest value
Mode = the value that appeared the most.
Question:
Nine students were asked how many miles they live from school. Their answers are listed below.
1,1,6,5,1,5,1,1,8
Find the range and the mode for the data.
In the testing of hypothesis about the population mean when the population standard deviation is unknown, the critical values are determined using:
A. z-distribution
B. t-distribution
C. F-distribution
D. β-distribution
Answers
The correct answer is B. t-distribution.
In the testing of hypothesis about the population mean when the population standard deviation is unknown, the critical values are determined using the t-distribution.
When the population standard deviation is unknown, we use the t-distribution to account for the uncertainty in estimating the population standard deviation from the sample data.
The t-distribution is similar to the standard normal (z) distribution but has thicker tails, which allows for more variability in the data.
The critical values, also known as the cutoff values, are the boundary values that determine the rejection region for the hypothesis test. These values are obtained from the t-distribution table or using statistical software.
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please someone tell me the answers to these I dont remember how to do distributive property
Answers
Answer:
Step-by-step explanation:
Hope this help
Johnny has $100 in the bank and plans to deposit $15 per day. Sal has $250
in the bank and plans to withdraw $10 from the bank each day. How many days
until they have the same amount in the bank?
Answers
Answer:
6 days
Step-by-step explanation:
First we have to write an expression that represents Johnny's and Sal's banking plans.
Johnny: He has an initial value of $100 and that value will increase by $15 every day. So the expression looks like: 15x + 100, where x is the amount of days it's been.
Sal: An initial value of $250 and the value will decrease by $10 everyday. The expression looks like: -10x + 250, where x is the amount of days it's been.
To find how many days they have until they have the same amount of money in the bank, we can set the expressions equal to each other and solve for x:
15x + 100 = -10x + 250
Add 10x to both sides to isolate the x on one side of the equation:
25x + 100 = 250
Subtract 100 from both sides of the equation to isolate 25x:
25x = 150
Divide both sides by 25 to find the value of x:
x = 6
Since x represents the amount of days it's been, x = 6 means that it will take 6 days for their bank accounts to have the same amount of money in them.
Hope this helps :)
A child rolls a ball on a level floor 3.5m to another child. If the ball makes 15.0 revolutions, what is its diameter?
Answers
The diameter of the ball is approximately 16.67 meters.
To find the diameter of the ball, we can use the relationship between the distance traveled and the number of revolutions.
The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter.
Given that the ball rolls a distance of 3.5 meters and makes 15.0 revolutions, we can calculate the circumference of the path it travels:
C = 3.5 m * 15.0 = 52.5 m
Since each revolution covers the circumference of the ball, we have C = πd. Plugging in the known value for C, we can solve for the diameter (d):
52.5 m = πd
Dividing both sides of the equation by π, we get:
d = 52.5 m / π
Using a calculator, we can evaluate this expression:
d ≈ 16.67 meters
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Math need help asap ty po sa makaka sagot
Answers
please see analysis
Step-by-step explanation:\(\left\{\right.{ \triangle}\ RST\cong { \triangle}\ DE\)F
\((SSS\ Congruence\ Postulate)\)
\(2.\ { \triangle\ CAT\cong { \triangle\ BED\ \left\{\right.Given\left.\ \right\}\)
\(\bar{AT}\cong\bar{ED}\)
\(\overline{AT}=20\)
\(so\ \overline{ED}=20\)
\(DE=3x-7=20\rightarrow\ x=9\)
I hope this helps you:)
A salesman makes both a base salary and also a commission, which is a percentage of what he sells. Each month, if his sales total s dollars, he makes a total of 2000 0. 1s dollars. What does 2000 represent?.
Answers
Linear equation is the equation in which the highest power of the unknown variable is one.
The given equation the constant 2000 represents the base salary or the fixed salary of the salesman.
To find that what does 2000 represent in the given linear equation we need to know about the linear equation.
What is linear equation?Linear equation is the equation in which the highest power of the unknown variable is one.
Given information-
Total sales by salesman each month is \(s\) dollars.
The total money made by the salesman each month by selling goods of \(s\) dollars given by,
\(S=2000+0.1s\)
The above equation given in the problem is the linear equation. In this linear equation the salary of salesman depends on his sales.
The constant amount of $2000 is the fixed amount of the salesman.
The variable \(s\) is the variable on which the salary of the salesman depends. Thus due to this variable the salary of the salesman changes.
Hence in the given equation the constant 2000 represents the base salary or the fixed salary of the salesman.
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The focus group techniques fall under the qualitative research
paradigm. With reference to the above statement examine the
qualitative research paradigm.
Answers
A qualitative research paradigm is a research approach that focuses on understanding and interpreting subjective experiences, meanings, and social phenomena.
It involves collecting and analyzing non-numerical data to gain insights into individuals' perspectives and the social context in which they exist. Focus group techniques are one of the methods used within the qualitative research paradigm to gather data through group discussions.
The qualitative research paradigm aims to explore and understand the complexity and nuances of human experiences, behaviors, and social phenomena. It recognizes the importance of context and seeks to generate rich and in-depth understandings rather than generalizable conclusions. Qualitative research methods involve collecting data through methods such as interviews, observations, and document analysis. The data collected is typically in the form of words, images, or other non-numerical formats. Researchers then analyze the data using various techniques, such as thematic analysis or grounded theory, to identify patterns, themes, and meanings.
Focus group techniques are one of the commonly used methods within the qualitative research paradigm. Focus groups involve bringing together a small group of participants who share common characteristics or experiences to engage in a facilitated discussion on a specific topic of interest. The group interaction allows participants to share their perspectives, experiences, and opinions while also influencing and being influenced by others in the group. This method provides rich qualitative data and allows researchers to explore group dynamics, collective meanings, and shared understandings.
Overall, the qualitative research paradigm and focus group techniques emphasize the importance of understanding subjective experiences, social interactions, and contextual factors to gain insights into human phenomena.
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What is the answer??
Answers
the answer is c, -2.
If it's not correct I'm sorry but I'm 98% sure its correct
Find the value of x (and y, if applicable)
Answers
Answer:
13√(2) = x
Step-by-step explanation:
The given is an isosceles triangle so the two side lenghts are same (13 units)
in right triangles the square lenght of the hypotenus is equal to sum of two side's square lenght
13^2 + 13^2 = x^2
169 + 169 = x^2
338 = x^2
13√(2) = x
In above problem, what does 3 stand for?
Answers
Answer:
there is no problem
Step-by-step explanation:
Missy started with $217 in her bank account. She deposits $25.50 each week and never withdraws any money. What expression can Missy use to determine her account balance after w weeks?
Answers
Answer: yep
Step-by-step explanation:
Answer:
217+25.5w
ye thats it
When the sample accurately represents the population, the results of the study are said to have a high degree of ______. Group of answer choices generalizability validity quality error
Answers
When the sample accurately represents the population, the results of the study are said to have a "high degree of generalizability."
Generalizability refers to the extent to which the findings of a study can be extended to other populations or situations beyond the sample studied.
In other words, if the sample used in a study is representative of the population of interest, then the findings can be applied to the population with a high degree of confidence. For example, if a study is conducted on the effects of a new medication on a sample of patients with a particular medical condition and the sample is representative of the larger population of patients with that condition, then the findings of the study can be generalized to the larger population.This means that the medication can be prescribed to other patients with the same medical condition, based on the findings of the study.Generalizability is an important consideration in research, as it allows for the findings of a study to have practical applications beyond the sample studied. However, it is important to note that the degree of generalizability may vary depending on the characteristics of the sample and the population of interest, and researchers must carefully consider the extent to which their findings can be generalized.Know more about the Generalizability
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Find the surface area of a square pyramid with side length 6 cm and slant height 5
cm.
Answers
The surface area of the square pyramid is 96 sq. mi.
Given:
side length (s) = 6 mi
slant height (l) = 5 mi
*image of a typical square pyramid is shown in the attachment below.
Recall:
Formula for surface area of square pyramid (SA) = \(A+\frac{1}{2}Pl\)
Where,
\(A=\) area of the base = \(s^2=6^2=36\) sq mi
\(P=\) perimeter of the base = \(4(s)=4*6=24\) mi
\(l=\) slant height = 5 mi
Plug in the values
\(SA=36+\frac{1}{2} *24*5\)
\(SA=36+60\)
\(SA=96\)
The surface area(SA) of the square pyramid is 96 sq. mi
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What is the area of 6ft and 5ft
Answers
Answer:
30 ft
Step-by-step explanation:
6 x 5 = 30
you multiply 6 times 5 and you get 30
Step-by-step explanation:
Opportunity cost and production possibilities Crystal is a skilled toy maker who is able to produce both cars and drums. She has 8 hours a day to produce toys. The following table shows the daily output resulting from various possible combinations of her time. On the following graph, use the blue points (circle symbol) to plot Crystal's initial production possibilities frontier (PPF). On the following graph, use the blue points (circle symbol) to plot Crystal's initial production possibilities frontier (PpF). Suppose Crystal is currently using combination D, producing one car per day. Her opportunity cost of producing a second car per day is per day. Now, suppose Crystal is currently using combination C, producing two cars per day. Her opportunity cost of producing a third car per day is per day. From the previous analysis, you can determine that as Crystal increases her production of cars, her opportunity cost of producing one mare car Suppose Crystal buys a new tool that enables her to produce twice as many cars per hour as before, but it doesnt affect her ability to produce drums Use the green points (triangle symbol) to plot her new PPF on the previous graph. Because she can now make more cars per hour, Crystal's opportunity cost of producing drums is
Answers
The opportunity cost of producing a second car per day for Crystal, who is currently using combination D and producing one car per day, is one drum per day. The opportunity cost of producing a third car per day for Crystal, who is currently using combination C and producing two cars per day, is two drums per day.
As Crystal increases her production of cars, her opportunity cost of producing one more car increases. This is reflected in the fact that the opportunity cost of producing a second car is one drum, while the opportunity cost of producing a third car is two drums. The increasing opportunity cost indicates that Crystal must give up more and more drums in order to produce additional cars. This is due to the limited resources and time she has available. When Crystal buys a new tool that allows her to produce twice as many cars per hour, her PPF shifts outward, indicating an increase in her production capabilities. With the ability to make more cars per hour, Crystal's opportunity cost of producing drums decreases. This means that she now needs to give up fewer drums to produce additional cars. The decreased opportunity cost is shown by the lower number of drums associated with each additional car on the new PPF. Crystal's improved efficiency in car production allows her to allocate more time and resources towards making cars without sacrificing as many drums.
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What is the equation of the hyperbola with center (0,0) and with a=4 and b=10 that opens vertically?
Answers
Answer:
The answer is the third option.
y^2/16 - x^2/100 = 1
Step-by-step explanation:
Calculate value of expressions when
A= -5,b= -4, c= -3 and d=-2
3a+4b+6c+3d
Answers
Answer:
-55
Step-by-step explanation:
3*(-5)+4*(-4)+6*(-3)+3*(-2)=(-15)+(-16)+(-18)+(-6)=(-55)