Answers
The area of triangle ABC is 23.5 square units and the perimeter is 20.4174 units.
To find the area and perimeter of the given triangle ABC, we need to apply the following formulas:Formula for Distance between two points:
The distance between two points (x1, y1) and (x2, y2) is given by:
AB = √(x2-x1)²+(y2-y1)²BC = √(x3-x2)²+(y3-y2)²AC = √(x3-x1)²+(y3-y1)²
Formula for Area of Triangle: If we know the length of the three sides of a triangle then,
using Heron's formula, we can calculate the area of the triangle as:
area = √s(s-a)(s-b)(s-c)where a, b, and c are the lengths of the sides of the triangle and s is the semi-perimeter of the triangle, which is given as s = (a+b+c)/2
Formula for Perimeter of Triangle: The perimeter of the triangle is the sum of the lengths of its sides.
That is: perimeter = AB + BC + ACArea of ΔABCAB
= √(1 - (-2))² + (5 - (-4))²AB
= √3²+9² = √90BC
= √(2 - 1)² + (2 - 5)²BC
= √1²+3² = √10AC
= √(2 - (-2))² + (2 - (-4))²AC
= √4²+6²
= √52Semi-Perimeter (s)
= (AB + BC + AC)/2
= (√90 + √10 + √52)/2
= 12.8572Area of ΔABC
= √s(s-a)(s-b)(s-c)
= √12.8572(12.8572-√90)(12.8572-√10)(12.8572-√52)
= 23.5
Perimeter of ΔABC = AB + BC + AC = √90 + √10 + √52 = 20.4174
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Related Questions
Carleigh, Inc., is a pork processor. Its plants, located in the Midwest, produce several products from a common process: sirloin roasts, chops, spare ribs, and the residual. The roasts, chops, and spare ribs are packaged, branded, and sold to supermarkets. The residual consists of organ meats and leftover pieces that are sold to sausage and hot dog processors. The joint costs for a typical week are as follows: Direct materials $84,500 Direct labor 29,000 Overhead 20,000 The revenues from each product are as follows: sirloin roasts, $68,000; chops, $71,000; spare ribs, $33,000; and residual, $9,800. Carleigh’s management has learned that certain organ meats are a prized delicacy in Asia. They are considering separating those from the residual and selling them abroad for $52,000. This would bring the value of the residual down to $2,650. In addition, the organ meats would need to be packaged and then air freighted to Asia. Further processing cost per week is estimated to be $27,500 (the cost of renting additional packaging equipment, purchasing materials, and hiring additional direct labor). Transportation cost would be $12,100 per week. Finally, resource spending would need to be expanded for other activities as well (purchasing, receiving, and internal shipping). The increase in resource spending for these activities is estimated to be $3,120 per week.
Answers
Carleigh, Inc. should separate the organ meats from the residual and sell them abroad, as it would increase their total revenue by $17,150 per week.
To determine whether Carleigh, Inc. should separate the organ meats and sell them abroad, we need to calculate the incremental revenue and incremental costs associated with this decision.
The incremental revenue would be the revenue generated from selling the organ meats abroad, which is $52,000 per week. The incremental cost would include the cost of further processing ($27,500 per week), transportation cost ($12,100 per week), and the increase in resource spending for other activities ($3,120 per week).
Therefore, the incremental cost would be $42,720 per week. Subtracting this from the incremental revenue of $52,000, we get an incremental profit of $9,280 per week.
However, this decision would also decrease the value of the residual from $9,800 to $2,650 per week. Therefore, we need to subtract this decrease in value from the incremental profit. This gives us a net increase in profit of $17,150 per week ($9,280 - $7,130).
Thus, it would be beneficial for Carleigh, Inc. to separate the organ meats and sell them abroad.
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Annabelle is going to a carnival that has games and rides. Each game costs $1.75 and each ride costs $3.50. Annabelle spent $28 altogether at the carnival and the number of games she played is 7 more than the number of rides she went on. Graphically solve a system of equations in order to determine the number of games Annabelle played, x,x, and the number of rides Annabelle went on, yy.
Answers
Answer:
$15.75
Step-by-step explanation:
1.75 x 7 = 12.25
28 - 12.25 = 15.75
Add dollar sign. Final answer is $15.75
Answer:
y=-1/2x+8
y=x-7
(10,3)
10 games played and 3 rides
Step-by-step explanation:
The line y = 2 is ______.horizontalon the y-axisverticalon the x-axis
Answers
We need to identify the direction of the line:
\(y=2\)This line corresponds to the points (x,2), i.e., all the points that have the y-coordinate equal to 2, for any value of x:
As we can see, this line is parallel to the x-axis. Therefore, it is horizontal.
Answer: horizontal
Please do fast doesn't have to be long explanation
Answers
1. The Mean and Standard Deviation should be used by the restaurant manager to measure the volume of soap served in each cup per day.
2. To determine the most popular car type, the Highway officer should use the Mode.
3. To compute the yearly salary of all employees in a company, the researcher should use the Median and Quartiles.
4. The actuary should use the Mean and Standard Deviation to record the reported age at death of residents in the state.
5. To determine the most common gas price, the researcher should use Mode.
What is the mean?The mean is the average of a data set.
Standard deviations are squared variations from the mean.
What is the mode?The mode is the value with the most often common occurrence in a data set.
What are median and quartiles?The median is a division of a data set into a lower half and an upper half.
Quartiles represent middle values or the median.
The lower and upper quartiles are the middle values of the lower half and the upper half, respectively.
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39.4% of us homes continue to use a landline in addition to cell phone service. What is the probability that 5 randomly selected homes all continue to use a landline
Answers
The probability that 5 randomly selected homes all continue to use a landline is approximately 0.0094 or 0.94%.
Binomial probability distribution:In this case, the binomial distribution is used to calculate the probability of getting exactly k successes in n trials with a probability of success p.
The formula for the binomial probability distribution is used to calculate the probability of all 5 randomly selected homes continuing to use a landline. The binomial probability distribution formula is given by
\(P(X = k) = (n, k) \times p^{k} \times (1 - p)^{n-k}\)
Here we have
39.4% of us homes continue to use a landline in addition to cell phone service
Assuming that each household is independent and has the same probability of using a landline, we can model the number of households that continue to use a landline as a binomial random variable x with parameters n = 5 (the number of trials) and p = 0.394 (the probability of success on each trial).
The probability of getting exactly k successes in n trials can be calculated using the binomial probability formula:
\(P(X = k) = (n, k) \times p^{k} \times (1 - p)^{n-k}\)
For k = 5, the probability of all 5 households continuing to use a landline
=> P(X = 5) = (5, 5) × 0.394⁵ × (1 - 0.394)⁽⁵⁻⁵⁾
= 0.394⁵ ≈ 0.0094
Therefore,
The probability that 5 randomly selected homes all continue to use a landline is approximately 0.0094 or 0.94%.
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The total cost of an electronic photo
display comes to $100. The price
y plus the tax of $6 equals $100.
Write an equation to find the price
of the electronic photo display.
Answers
Answer:
P = y * 1.06
Step-by-step explanation:
Let y be the net price (no tax), t the tax (as a factor) and P the total price (tax included),
P = y * t
From the info provided, we know that for each 100 USD, 6 USD is tax, so 6%,
TIP: By multiplying by 1.06 we add the 6% to the net price (6% is 0.06)
P = y * 1.06
A square wrestling mat has a perimeter of (12x−32)
feet. Write an expression in simplest form that represents the side length (in feet) of the mat.
Answers
Answer:
The perimeter of a square is given by the formula P = 4s, where s is the side length. In this case, we are given that the perimeter is (12x - 32) feet, so we can set up an equation:
P = 4s
(12x - 32) = 4s
To solve for s, we can divide both sides by 4:
(12x - 32)/4 = s
Simplifying the expression on the left:
3x - 8 = s
Therefore, the expression in simplest form that represents the side length of the square wrestling mat is 3x - 8 feet.
Answer:
Step-by-step explanation:
the answer would be 3 x − 8 3x-8 3x−8 ft
What is the slope of (-1,-9) and (0,-3)
Answers
Answer:
i belive the awnser to this is m=6
There is a 5 by 5 square in the top right square is your home in the bottom left square is your school there are >100 ways and you can’t go through corners and the way Can only be 10 blocks no more or less
Answers
Answer:
there is a 5 by 5 square
Step-by-step explanation:
Answer:
In plane Euclidean geometry, a rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equalStep-by-step explanation:
assume that there is a party consisting of people between the ages of 18 and 24 inclusive. how many people would have to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year? note: assume the range of birth years include 2 leap years. (
Answers
The minimum number of people that would need to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year is Three (3).
To find the number of people that would need to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year, we need to consider the number of possible birthdays that exist within the given age range (18 to 24 inclusive).
There are 12 months in a year, and each month has between 28 and 31 days (depending on the month). Therefore, there are a total of 12 * 31 = 372 possible birthdays within a given year.
There are 7 possible birth years within the given age range (18 to 24 inclusive), which means there are a total of 7 * 372 = 2596 possible birthdays within the given age range.
Since we want to guarantee that at least three people share the same birthday, we need at least 3 people to be at the party.
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Complete Question:
Assume that there is a party consisting of people between the ages of 18 and 24 inclusive. How many people would have to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year? Note: assume the range of birth years include 2 leap years.
The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 247.9 and a standard deviation of 64.7. (All units are 1000 cells/μL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 118.5 and 377.3? b. What is the approximate percentage of women with platelet counts between 53.8 and 442.0?
Answers
Answer:
A) Approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 118.5 and 377.3 = 95%
B) approximate percentage of women with platelet counts between 53.8 and 442.0 = 99.7%
Step-by-step explanation:
We are given;
mean;μ = 247.9
standard deviation;σ = 64.7
A) We want to find the approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 118.5 and 377.3.
Now, from the image attached, we can see that from the empirical curve, the probability of 1 standard deviation from the mean is (34% + 34%) = 68 %.
While probability of 2 standard deviations from the mean is (13.5% + 34% + 34% + 13.5%) = 95%
Thus, approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 118.5 and 377.3 = 95%
B) Now, we want to find the approximate percentage of women with platelet counts between 53.8 and 442.0.
53.8 and 442.0 represents 3 standard deviations from the mean.
Let's confirm that.
Since mean;μ = 247.9
standard deviation;σ = 64.7 ;
μ = 247.9
σ = 64.7
μ + 3σ = 247.9 + 3(64.7) = 442
Also;
μ - 3σ = 247.9 - 3(64.7) = 53.8
Again from the empirical curve attached, we cans that at 3 standard deviations from the mean, we have a percentage probability of;
(2.35% + 13.5% + 34% + 34% + 13.5% + 2.35%) = 99.7%
The equation 5w+16=61 models how many weeks, w, it takes a puppy to reach a weight of 61 ounces after being born. If the puppy gains the same amount of weight each week, how many weeks does it take the puppy to reach 61 ounces?
Answers
Answer:
9 weeks
Step-by-step explanation:
5 x 9= 45
45+16=61
5x9+16=61
Which BEST analyzes the nuances of word choice in line 21 of this play
excerpt?
The use of the word "customary" by Algernon signals
to the audience that necessary background
A
information will follow in order to help explain the
refreshment choices offered by Lane
The stage direction indicating that Algernon is to
B)
express his line "stiffly" is meant to help the audience
recognize the character's sense of being offended by
a previous comment made by Jack
The question that is presented by Algernon functions
as a subtle warning to Jack that Algernon suspects
him of misdeeds and has heard unsettling gossip
about Jack's activities over the last week
Algernon uses the words "slight refreshment' to
D)
emphasize the idea that Jack should not expect the
amount or variety of foods available at a formal
dinner during his brief visit to Half-Moon Street.
C
Answers
Answer: C
Step-by-step explanation:
nick uses 8 dowels to make one birdhouse. if he bought 1,581 dowels, about how many birdhouses will he be able to make? (EXPLAIN) !!
Answers
Which of the following is a perfect square trinomial?
O A. 25x2 - 30xy +9y2
O B. 25x2 + 16xy - 9y2
O C. 25x2 - 16xy + 9y2
O D. 25x2 + 30 xy - 9y2
What is the answer I can’t find it
Answers
Answer:A
Step-by-step explanation:
Of the stamps in a book, 5/12 came from Brian's collection and 24 came from Amy's. Of the rest, 15 were Jo's, 3/10 were Carl's and 27 were purchased. How many stamps are there in the book? HELPPP
Answers
Algebraic expressions are mathematical statements that consist of both number(s) and alphabet(x). Thus the number of stamps in the book is 66\(\frac{43}{60}\) (67).
Algebraic expressions are mathematical statements that consist of both number(s) and alphabet(x). Majorly, the alphabet in the expression is referred to as the unknown value which has to be determined.
When the power of any of the alphabets contained in an algebraic expression is more than one, then it can be referred to as a polynomial.
In the given question, let the number of stamps in the book be represented by N.
So that;
N - 5/12 + 24 + 15 + 3/10 + 27 = 0
N - (5/12 + 24 + 15 + 3/10 + 27) = 0
N - \(\frac{8006}{120}\) = 0
N - 66\(\frac{43}{60}\) = 0
N = 66\(\frac{43}{60}\)
= 66.72
N ≅ 67
Therefore the number of stamps in the book is approximately 67.
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Please help with this math question!
Answers
Answer:
5. Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
Sam is driving on the highway. He begins the trip with 12 gallons of gas in his car. The car uses up one gallon of gas every 35 miles.
Let G represent the number of gallons of gas he has left in his tank, and let D represent the total distance (in miles) he has
traveled. Write an equation relating G to D, and then graph your equation using the axes below.
Answers
equation and graph attached
Caleb’s parents gave him a used car, and he pays his own insurance, which is $110 a month. His gas and maintenance expenses usually run $65 a month. He also has a cell phone and pays his parents $30 each month for his share of the family plan.
What are Caleb's total regular monthly expenses?
Answers
110 + 65 + 30 = $205
Answer: Calebs total regular monthly expenses would be $205
Step-by-step explanation:
Hope this helps
I need help asap!
Question 1,
What is the correct equation for this word problem? Jorge had received some crayons for his birthday. He gave 12 crayons to his friend and had 14 left, how many crayons did he receive as a gift?
A, x - 12 = 14
B, 14 + x = 12
C, x + 14 = 12
D, 12 - x = 14
question 2
Match the terms below to the correct meaning.
Alone, by itself,
Opposite,
1, inverse
2, isolate
Question 3
what is the correct equation for this word problem? Charlie and some friends are playing a game online. They start with 13 people and some sign out and leave. They are left with 5 people how many if his friends signed out?
A, g + 13 = 5
B, 5g = 13
C, 13/g = 5
D, 13 - g = 5
Question 4
What is the correct equation for this word problem? Jaime and her friends are going out for pizza. For 30$ total, they can buy p pizzas. Each pizza costs $6.
A, 6/p = 30
B, 30 - p = 6
C, 6p = 30
D, p + 6 = 30
Question 5
Solve the word problem. Write just the number in the blank.
Mr. Green is buying an app for his class. The app costs a dollars per student and he has 32 students. He spends a total of 96$. How much is the app per student?
Sorry it’s so much! I need help asap!!!
Answers
Answer:
Question 1: A. x-12=14
Question 2: Alone=isolate, by itself=isolate, opposite=inverse
Question 3: D. 13-g=5
Question 4: C. 6p=30
Question 5: $3
Hope this helped :)
Step-by-step explanation:
PLEASE HELP!!! BRAINLIEST FOR CORRECT
If t = 0 refers to 12:00 pm (noon), at what time does the maximum price occur?
A) 2:00 pm
B) 6:00 pm
C) 11:00 pm
D)4:00 am
Answers
Explanation:
The highest point on the curve occurs when x = 11, which is 11 hours after the 12:00 pm noon marker. This represents the time 11:00 PM
what is (1/2 + isqrt3/2)^5?
Answers
Answer:
\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)
Step-by-step explanation:
Convert 1/2 + i√3/2 to rectangular form
\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)
Use DeMoivre's Theorem
\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)
Graph the solution to this inequality on the number line. −18 ≤−3p
Answers
The solution to the inequality −18 ≤−3p, is shown in the graph in the attachment which is p ≤ 6.
How to Graph the Solution to an Inequality?To graph the solution of a given inequality, we have to first solve the inequality to determine what the solution will be.
Given the inequality, -18 ≤ -3p, solve to find p:
-18 ≤ -3p
Divide both sides by -3
-18/-3 ≥ -3p/-3 [the sign will change because we're dividing by a negative value]
6 ≥ p
It can be rewritten as p ≤ 6. The graph of this solution is a number line having a closed circle on point 6 that points towards the left.
See the diagram in the attachment which shows the solution of the inequality.
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explain how the sum of a fraction or a rational number and its additive inverse is equal to zero
Answers
If we use a simple example, the additive inverse of 5 is -5. This is because -5 + 5 = 0.
It is the same with fractions, if we take one half, \(-\frac{1}{2}\) + \(\frac{1}{2}\) = 0
A rational number is a number that can be written as an integer or a fraction without having a 0 in the denominator.
("In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. ")
Basically, the sum of a fraction / rational number and its additive inverse is equal to 0 because you are adding together "opposites" with regards to negative / positive. They are the same number, just different sides of the number line.
six options. Each of these six options leads to a menu with four options. For each of these four options, three more options are available. For each of these three options, another three options are presented. If a person calls the 800 number for assistance, how many total options are possible
Answers
Answer:
Hence the total number of possible options available to a person who calls the 800 number is 216.
Step-by-step explanation:
Given that the caller 10 800 telephone system has six options. For each of these four options, three more options are available. For each of these three options, another three options are presented.
Hence the total number of possible options available to a person who calls the 800 number = \(6 \times 4 \times 3 \times 3 = 216\).
The figure shows four box-and-whisker plots. These represent variation in travel time for four different types of transportation from the beginning to the end of one route.
Conrad is at one end of the route. He is trying to decide how to get to an appointment at the other end. His appointment is in 30 minutes. Which type of transportation is LEAST likely to take more than 30 minutes?
Select one:
a.
bus
b.
car
c.
subway
d.
train
Answers
Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.
How to Interpret a Box-and-whisker Plot?
In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.
The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.
Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.
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dont understand this
Answers
Answer:
165 degrees
Step-by-step explanation:
1 is opposite of 6
1 is 15 degree
half circle is 180 degree
you subtract 15 you got 165
1 and 5 they both will be 15 degree and 6 and 2 they both will be 165 degree
g if we want to calculate a confidence interval of the difference of two proportions what is the standard error (do not pool for this answer)
Answers
Answer:
The standard error is \(s = \sqrt{\frac{\pi_1(1-\pi_1)}{n_1}+\frac{\pi_2(1-\pi_2)}{n_2}}\), in which \(p_1,p_2\) are the proportions and \(n_1,n_2\) are the sample sizes.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which
z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).
The standard error is:
\(s = \sqrt{\frac{\pi(1-\pi)}{n}}\)
For the difference of proportions:
For proportion 1, the standard error is:
\(s_1 = \sqrt{\frac{\pi_1(1-\pi_1)}{n_1}}\)
For proportion 2, the standard error is:
\(s_2 = \sqrt{\frac{\pi_2(1-\pi_2)}{n_2}}\)
For the difference:
The standard error is the square root of the sum of the squares of each separate standard error. So
\(s = \sqrt{(\sqrt{\frac{\pi_1(1-\pi_1)}{n_1}})+(\sqrt{\frac{\pi_2(1-\pi_2)}{n_2}})^2} = \sqrt{\frac{\pi_1(1-\pi_1)}{n_1}+\frac{\pi_2(1-\pi_2)}{n_2}}\)
The standard error is \(s = \sqrt{\frac{\pi_1(1-\pi_1)}{n_1}+\frac{\pi_2(1-\pi_2)}{n_2}}\), in which \(p_1,p_2\) are the proportions and \(n_1,n_2\) are the sample sizes.
Answer 396,397,398,399
Answers
Answer:
yes you are right I think
SOLVE THESE PROBLEMS CORRECTLY TO BE MARKED BRAINLIEST!
1. Sophie wrote a two-digit number on the board. Max wrote the digit 3 to the right of it and got a number that is bigger than the Sophie's number by 372. What number did Sophie write on the board?
2. Some kids went on a bike ride. The ride was six hours long and the kids traveled 54 miles. For part of the ride they biked at a speed of 7 mph and for part of the ride they biked at a speed of 11 mph. For how long did they bike at the first speed, and for how long at the other speed?
3. I left Boston for Washington, DC, at 7:00 am. At first, my speed was 55 mph; then it was 75 mph. I traveled 630 miles in 10 hours. At what time did I begin to drive faster?
Thanks!
Answers
Answer: 1= 41
2= 3 hours biking at the other speed.
3= We began to drive at 75 mph at 1:00 p.m
Step-by-step explanation:
3= x/55 + (630 - x)/75 = 10
75x + 55 * (630 - x) = 41,250 (4,125 as Lowest common multiple)
75x + 34,650 - 55x = 41,250
20x = 41,250 - 34,650 (Subtracting 34,650 at both sides)
20x = 6,600
x = 6,600/20
x = 330 ⇒ 630 - x = 300
Time we drove at 55 mph = 330/55 = 6 hours
Time we drove at 75 mph = 300/75 = 4 hours
We began to drive at 75 mph at 1:00 p.m. (7 am + 6 hours)
hope this helps :)