Answers
By using the parallelogram method, the addition of the vectors [tex]\vec a + \vec b[/tex] is (3, 1).
How to add vectors by using the head to tail method or parallelogram method?In Mathematics, a vector typically comprises two (2) points. First, is the starting point which is commonly referred to as the "tail" and the second (ending) point that is commonly referred to the "head."
Furthermore, the head to tail method of adding two (2) vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).
By adding the given vectors algebraically, we have the following:
[tex]\vec a + \vec b[/tex] = (2, -3) + (1, 4)
[tex]\vec a + \vec b[/tex] = [(2 + 1), (-3 + 4)
[tex]\vec a + \vec b[/tex] = (3, 1).
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Related Questions
the principal spends 96 minutes talking to the teachers and 48 minutes talking to the students. what is the basic ratio of minutes spent talking to teachers to minutes spent talking to students
Answers
The proportion is solved and ratio of minutes spent talking to teachers to minutes spent talking to students is given by 2 : 1
Given data ,
The principal spends 96 minutes talking to the teachers
And , the principal spends 48 minutes talking to students
Now , the basic ratio of minutes spent talking to teachers to minutes spent talking to students, we need to simplify the ratio by dividing both values by their greatest common factor
So , A : B = 96 : 48
On simplifying the proportion , we get
A : B = 2 : 1
Hence , the proportion is 2 : 1
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Madam Antiowwah at oseikakookrom charged her phone to full (100%). She browse two hours. The battery life fell to 60% How many hours later would the phone or She continues to browse?
Answers
Answer:
Phone dies in 6 hours
Step-by-step explanation:
Please help with this one as well,,,
Answers
The whisker plot with the data provided should includes a range that goes from 7 to 49, and a median of 23.
How to draw a whisker plot?A whisker plot, also known as a box plot, is a graphical representation of a data set that shows the distribution of the data along with some important statistical information, such as the median, quartiles, and outliers. It is particularly useful for comparing the distribution of different data sets or for identifying potential outliers in a data set.
To create a whisker plot, follow these steps:
Collect the data you want to represent and arrange it in order from smallest to largest.Find the median, which is the middle value of the data set. If the data set has an even number of values, the median is the average of the two middle values.Find the lower quartile (Q1), which is the median of the lower half of the data set.Find the upper quartile (Q3), which is the median of the upper half of the data set.Calculate the interquartile range (IQR), which is the difference between Q3 and Q1.Learn more about whisker plots in https://brainly.com/question/2742784
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The cost of 8 T-shirts and 3 jackets is $135. The cost of 7 T-shirts and 5 jackets is $149.
Enter the cost of one T-shirt and one jacket in the response boxes below.
T-shirt: S
jacket: $
Answers
The cost of one T-shirt and one jacket is $12 and $13 respectively.
What is the cost of one T-shirt and one jacket?Let
cost of one t-shirt = x
cost of one jacket = y
8x + 3y = 135
7x + 5y = 149
Multiply (1) by 5 and (2) by 3
40x + 15y = 675
21x + 15y = 447
Subtract the equations to eliminate y
40x - 21x = 675 - 447
19x = 228
divide both sides by 19
x = 228/19
x = 12
Substitute x = 12 into (1)
8x + 3y = 135
8(12) + 3y = 135
96 + 3y = 135
3y = 135 - 96
3y = 39
y = 39/3
y = 13
Hence, a T-shirt and a Jacket cost $12 and $13 respectively.
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Use a net to find the surface area of the prism.
A. 469 in.2
B. 315 in.2
C. 539 in.2
D. 784 in.2
Answers
Answer:
2(1/2)(11)(7) + 11(14) + 14(8) + 14(9) = 469 in.^2
The correct answer is A.
Brennan knew his parents had set up their will some years ago. Neither he nor his sister, Maureen, had ever discussed the will with their parents. When both parents passed away, they met with the family lawyer about the will. What they found was that the money their parents had been giving them over the last few years was a gift and part of their estate planning. The gifts reduced the size of the estate to ensure the value of the estate upon their passing would be under the tax-free limit.
Their parents had not really talked with Brennan or Maureen about how the “gift” money they had been receiving would affect their final inheritance. As they listened to
the estate lawyer give them details of their inheritance, they were shocked to learn there was less than what they had thought.
1. Discuss your thoughts on how Brennan’s and Maureen’s parents handled the informationin the will prior to their passing. Should the parents have explained more clearly about the “gift” money and how it affected their inheritance?
2. What responsibility did Brennan and Maureen have to discuss the will with their parents?
3. What experience do you have with a family member’s will? How would you approach
the topic of writing a will with a family member?
Answers
Open and clear communication is crucial when discussing estate planning and wills with family members to prevent misunderstandings and hurt feelings.
1. It is understandable that Brennan and Maureen feel shocked and disappointed with the reduced inheritance.
While it is not required for parents to disclose every detail of their estate planning to their children, it would have been helpful if they had discussed the impact of the gifts on their estate and their final inheritance.
Clear communication can prevent misunderstandings and hurt feelings in the future.
2. Brennan and Maureen have a responsibility to discuss the will with their parents. It is essential to have an open and honest conversation about their parents' wishes and intentions to avoid any confusion or disputes in the future.
While it can be uncomfortable to talk about death and inheritance, it is a crucial conversation to have.
3. It can be a difficult and emotional topic to discuss, but it is important to have open communication to ensure that everyone's wishes are respected and honored. It may be helpful to consult with a lawyer or financial advisor to ensure that the will is properly drafted and that everyone's needs are addressed.
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3+3=???
A: 3113
B: 33
C. 6 ( I did the math and never got this answer)
D. 9
please help !!!!!
Answers
Answer:
D
Step-by-step explanation:
gimme the points
cuz
scientific
8 The events committee wants to survey students about a school dance. The committee is
meeting in the gym, where the girls' basketball team is practicing. They survey the
players on the girls' basketball team.
Answers
The events committee is surveying only 1.5% of the student population by asking the girls' basketball team about the school dance.
How to solveTo calculate the percentage of the student population being surveyed, you can use the formula:
Percentage = (Number of students surveyed / Total number of students) * 100
In this case, the number of students surveyed is 15 (girls' basketball team), and the total number of students is 1,000.
Percentage = (15 / 1,000) * 100 = 1.5%
So, the events committee is surveying only 1.5% of the student population by asking the girls' basketball team about the school dance.
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The events committee wants to survey students about a school dance. The committee is
meeting in the gym, where the girls' basketball team is practicing. They survey the
players on the girls' basketball team.
If there are 1,000 students in the school, and the girls' basketball team has 15 players, what percentage of the student population is being surveyed by the events committee about the school dance?
All but 36 of the 120 state capitals have an interstate highway serving them. What percent of the capitals do not have interstates?
Answers
Therefore, 70% of state capitals do not have interstate highways serving them.
What is percent?Percent is a way of expressing a number as a fraction of 100. The term "percent" means "per hundred". Percentages are usually denoted by the symbol %, which is placed after the numerical value. Percentages are used in many fields, including finance, science, and everyday life, to represent proportions, rates, and changes in quantities.
Here,
If all but 36 of the 120 state capitals have an interstate highway serving them, then the number of capitals that do not have interstates is 120 - 36 = 84.
To find the percentage of capitals that do not have interstates, we need to divide the number of capitals without interstates by the total number of capitals and then multiply by 100:
84 / 120 x 100% = 70%
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100 POINTS!!!
Question:
Answers
for KW 1 calculation output are 15,17,19,21,23for KW 2 calculation output are 61,63,65 for KW 3 calculation are 16,23,30,37,114,121,128, just by substituting to equation we can get answer
what is equation ?
An equation is a mathematical statement that asserts that two expressions are equal. It is typically written using an equal sign (=) between the two expressions. An equation can contain variables, which are symbols that represent unknown values.
In the given question,
for table 1 calculation is as below
output x=0 is 15+2x=15+2*0=15
output x=1 is 15+2x=15+2*1=17
output x=2 is 15+2x=15+2*2=19
output x=3 is 15+2x=15+2*3=21
output x=4 is 15+2x=15+2*4=23
for table 2 calculation is as below
output x=1 is 60+2x=60+2*1=61
output x=2 is 60+2x=60+2*2=63
output x=3 is 60+2x=60+2*3=65
for table 3 calculation is as below
output x=0 is 16+7x=16+7*0=16
output x=1 is 16+7x=16+7*1=23
output x=2 is 16+7x=16+7*2=30
output x=3 is 16+7x=16+7*3=37
output x=14 is 16+7x=16+7*14=114
output x=15 is 16+7x=16+7*15=121
output x=16 is 16+7x=16+7*0=128
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for KW 1 calculation output are 15,17,19,21,23for KW 2 calculation output are 61,63,65 for KW 3 calculation are 16,23,30,37,114,121,128, just by substituting to equation we can get answer
what is equation ?
An equation is a mathematical statement that asserts that two expressions are equal. It is typically written using an equal sign (=) between the two expressions. An equation can contain variables, which are symbols that represent unknown values.
In the given question,
for table 1 calculation is as below
output x=0 is 15+2x=15+2*0=15
output x=1 is 15+2x=15+2*1=17
output x=2 is 15+2x=15+2*2=19
output x=3 is 15+2x=15+2*3=21
output x=4 is 15+2x=15+2*4=23
for table 2 calculation is as below
output x=1 is 60+2x=60+2*1=61
output x=2 is 60+2x=60+2*2=63
output x=3 is 60+2x=60+2*3=65
for table 3 calculation is as below
output x=0 is 16+7x=16+7*0=16
output x=1 is 16+7x=16+7*1=23
output x=2 is 16+7x=16+7*2=30
output x=3 is 16+7x=16+7*3=37
output x=14 is 16+7x=16+7*14=114
output x=15 is 16+7x=16+7*15=121
output x=16 is 16+7x=16+7*0=128
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What is the solution to
√7x-4 = 2√x
O A.4/3
O B. -4/4
O C. 4/5
O D. -4/3
Answers
Answer:
B
Step-by-step explanation:
take square on both sides
7x-4 = 4x
x = 4/3
If I save 300 a week how much will I have at the end of the year?
Answers
15,653 much will I have at the end of the year in linear equation.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with power 1 variables are known as linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.
Earning $300 a week equals $15,587 a year. This result is obtained by multiplying the base salary by the number of hours, weeks, and months worked in a year, assuming a 40-hour work week.
15,653 much will I have at the end of the year in.
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PQRSTU is plotted on a coordinate plane with vertices p(-1,0) Q(-1,3) R(1,4) S(2,5) T(4,4) and U(4,0) what is the hexagons area
Answers
First, we can find the length and width of the rectangle by finding the distance between points R and T, and between points Q and U, respectively.
Length of the rectangle RT = sqrt((4-1)^2 + (4-5)^2) = sqrt(10)
Width of the rectangle QU = sqrt((4-(-1))^2 + (0-3)^2) = sqrt(50)
The area of the rectangle is then:
Area of rectangle = Length x Width = sqrt(10) x sqrt(50) = 10sqrt(2)
To find the area of the two triangles, we can use the formula for the area of a triangle:
Area of triangle = 1/2 x Base x Height
Triangle 1 has base PQ, which has length 3, and height 1, which is the distance between PQ and RS. The area of triangle 1 is:
Area of triangle 1 = 1/2 x 3 x 1 = 3/2
Triangle 2 has base RS, which has length sqrt((4-1)^2 + (5-4)^2) = sqrt(10), and height 1, which is the distance between PQ and RS. The area of triangle 2 is:
Area of triangle 2 = 1/2 x sqrt(10) x 1 = sqrt(10)/2
Therefore, the total area of the hexagon is:
Area of hexagon = Area of rectangle + Area of triangle 1 + Area of triangle 2
= 10sqrt(2) + 3/2 + sqrt(10)/2
= 10sqrt(2) + (3+sqrt(10))/2
So the area of the hexagon is approximately 19.55 square units.
A medical researcher claims that the proportion of people taking a certain medication that develop serious side effects is 12%. To test this claim, a random sample of 900 people taking the medication is taken and it is determined that 93 people have experienced serious side effects. The following is the setup for this hypothesis test: H0:p=0.12 Ha:p≠0.12 Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places. The following table can be utilized which provides areas under the Standard Normal Curve:
Answers
The p-value from the hypothesis is 0.0583 which is not significant at p<0.05
What is the p-valueTo determine the p-value of the hypothesis, we need to use the formula;
z = (x - a) / √(a(1 - a)/n)
a = hypothesized proportionx = sample proportionn = sample sizex = 93 / 900 = 31/300 = 0.103
a = 12% = 12/100 = 0.12
n = 900
Substituting the values into the formula;
z = (0.103 - 0.12)/√(0.12(1 - 0.12)/900)
z = -0.017 / √0.0001173
z = -1.569
Using a standard normal distribution table;
p-value = 0.058324
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A car and a bus left Sunrise Village for Sunset Village of the same time, travelling along the
same route. After travelling for 4 h, the car reached Sunset Village, but the bus had only
completed 5/8 of the journey. The bus travelled at a speed which was 30 Km/h slower than the car
a) Find the distance between the two villages.
b) Find the average speed of the bus.
Answers
Answer:
a) 192Km
b) 50
Step-by-step explanation:
1. Bill scored the following number of points in a basketball games: 22, 18, 19, 16, 32, 24, 19, 20, 22 and 22
a. Box and Whisker plot:
b. What is the range:
c. Are there any outliers?
IQR:
Answers
b. The range is 32 - 16 = 16. and IQR 4
c. 32
how to find range?a. Here is a box and whisker plot to represent the given data:
The horizontal axis shows the range of the data, and the vertical axis represents the frequency. The box represents the middle 50% of the data, with the bottom of the box being the 25th percentile and the top of the box being the 75th percentile. The whiskers represent the lowest and highest values within 1.5 times the interquartile range (IQR) of the box, and any points outside the whiskers are considered outliers.
b. The range is the difference between the highest and lowest values in the data set. In this case, the range is 32 - 16 = 16.
c. There is one outlier in the data set, which is the value of 32. It is outside the whiskers of the box and is considered to be an outlier.
The interquartile range (IQR) is the difference between the 75th and 25th percentiles of the data set. In this case, the IQR is:
IQR = Q3 - Q1
= 22 - 18
= 4
where Q1 is the first quartile (the value below which 25% of the data falls), and Q3 is the third quartile (the value below which 75% of the data falls).
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The rectangles in the figure below are folded along the dotted lines at 90 * angles to make a completely closed rectangle box with no overlap. What is the volume of the resulting box?
Answers
The Volume of the resulting rectangular box is calculated as: 72 cubic units.
What is the Volume of a Rectangular Box?A rectangular box's volume can be calculated using the formula expressed below:
Volume = length * width * height.
Using the image of the net of the rectangular box, when folded, the dimensions of the box would be:
Length = 6 units
Width = 10 - 6 = 4 units
Height = 11 - 4 - 4 = 3 units
Plug in the values:
Volume of rectangular box = 6 * 4 * 3 = 72 cubic units.
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HELP ME PLEASE!!!!!
Answers
Answer:
1. True
2.True
3.True
4.False
5.False
6.True
7.True
8.True
Step-by-step explanation:
1. The area of a rectangle is found by the formula A=bh.
2. There are 4 rectangles making up the lateral area of the prism. 2+3=5. 5*6=30, and multiply by 2 since there are two of the 2x6 and two of the 3x6 rectangles to get 60. The bases of the prism have an area of 6 square inches each.
60+12+12=84
3. 3*5=15
4. The base is not a square, so you cannot multiply by 4 to get the area of all the triangles. You can multiply by two, and also multiply 1/2(3)(4) by 2 to get the area of the other two triangles.
5. The base is a triangle. 1/2(3)(4)=6.
6. 2[1/2(3)(4)]=12. 2(8*5)=80. 3*8=24. 80+24+12=116
7. A cube has 6 identical sides, so you can find the area of one side and multiply by 6 to get the surface area of the cube.
8. 9^2=81. 81*6=486.
Is c = 3 a solution to the inequality below?
122 c
yes
no
Answers
The value c = 3 is not a solution to the inequality
Checking if c = 3 is a solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
122 c
Express properly
So, we have
1 ≥ c
When this inequality is rewriiten. we have
c ≤ 1
This means that the values of c do not exceed 1
The number 3 exceeds 1
So, it means that c = 3 is not a solution to the inequality
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Help please!!!!
Whoever answers right gets brainliest!
Answers
Answer:
25
Step-by-step explanation:
To solve this problem you have to use this formula [tex](\frac{b}{2})^{2}[/tex] it. So in this case b is the term next to the x term. This number is 10. So all we have to do is insert it into the formula. This would give us:
[tex]=(\frac{10}{2})^{2}\\\\=(5)^{2}\\\\= 25[/tex]
The constant term is 25.
Could I get Brainilest, please? I'm trying to get to the expert level
use the standard normal distribution table to determine the percent of data less than
z= 1.67
The percent of the data less than Z = 1.67 is ?
Answers
Step-by-step explanation:
Look at the table for z = 1.67
You have the wrong table.......the table you posted is for negative z-scores
for z -score = + 1.67 , the value is .9535 = 95.35 %
Today's clients are ages 15, 72, 8, 89, 14, 16, 24, and 38. What is the range of the clients' ages?
Answers
Answer:
81
Step-by-step explanation:
The difference between the maximum and minimum values in a collection of data is known as the range. We must first determine the lowest and maximum values before we can determine the age range of the clients.
the minimum age is 8, and the maximum age is 89.
Therefore, the range of the clients' ages is:
Max age - Min age = 89 - 8 = 81
So the range of the clients' ages is 81.
Solve the equation 4/3 (x + 6) = 2x – 3 + x.
Answers
The solution to the equation is x = 33/5.
We can start by simplifying both sides of the equation using the distributive property and combining like terms:
4/3 (x + 6) = 2x - 3 + x
4/3 x + 8 = 3x - 3
Next, we can isolate the variable x on one side of the equation by subtracting 4/3 x and adding 3 to both sides:
4/3 x - 3x = -8 - 3
-5/3 x = -11
Finally, we can solve for x by dividing both sides by -5/3:
x = -11 / (-5/3)
x = 33/5
Therefore, the solution to the equation is x = 33/5.
Eliza plans on constructing a confidence interval for the slope of a regression line. She creates the residual plot shown to check the conditions for creating the interval. Which of the following conditions appear to be met based on the residual plot?
I.The true relationship between x
and y
is linear.
II.The standard deviation of y
is constant for different levels of x
.
III.The value of 0 is contained in the confidence interval.
Answers
Answer:
Based on the residual plot, we can check for the following conditions:
I. The true relationship between x and y is linear:
We can check this condition by looking at the pattern of the residuals in the plot. If the residuals are randomly scattered around zero, without any discernible pattern, then it suggests that the true relationship between x and y is linear. If there is a pattern in the residuals, then it suggests that the true relationship is not linear. Since we are not given a residual plot to examine, we cannot determine whether this condition is met.
II. The standard deviation of y is constant for different levels of x:
We can check this condition by looking at the spread of the residuals in the plot. If the spread of the residuals is roughly the same for all values of x, then it suggests that the standard deviation of y is constant for different levels of x. If the spread of the residuals increases or decreases as x increases, then it suggests that the standard deviation of y is not constant for different levels of x. From the residual plot, we cannot determine whether this condition is met.
III. The value of 0 is contained in the confidence interval:
This condition refers to the confidence interval for the slope of the regression line. If the confidence interval includes 0, then it suggests that the slope is not significantly different from 0 and there is no significant linear relationship between x and y. From the residual plot, we cannot determine whether this condition is met.
Therefore, based on the given information, we cannot determine which conditions appear to be met based on the residual plot.
HELP FAST! EASY ALGEBRA 2!
Answers
A graph of the functions with the asymptotes is shown in the image below.
The pre-image of the function y = log₂(x + 1) was horizontally shifted to the left by 1 unit.
The pre-image of the function y = log₂(x) + 4 was vertically shifted up by 4 units.
What is a translation?In Mathematics, the translation a geometric figure or graph to the left means subtracting a numerical value to the point on the x-coordinate of the pre-image;
g(x) = f(x + N)
In Mathematics and Geometry, the translation a geometric figure upward means adding a numerical value to the point on the positive y-coordinate (y-axis) of the pre-image;
g(x) = f(x) + N
Since the parent function f(x) was horizontally translated 1 unit left, we have the following transformed function;
y = log₂(x + 1)
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1/2x^2+3x-5 min or max
Answers
The function f(x) = (1/2)x^2 + 3x - 5 has a minimum value
Classifying the function as min or maxTo determine whether the function f(x) = (1/2)x^2 + 3x - 5 has a minimum or maximum value, we can use the fact that the vertex of a quadratic function represents the minimum or maximum point of the function.
To find the x-coordinate of the vertex, we can use the formula x = -b/2a, where a and b are the coefficients of the quadratic term and the linear term, respectively.
In this case, a = 1/2 and b = 3, so we have:
x = -b/2a = -(3)/(2(1/2)) = -3
To find the corresponding y-coordinate, we can substitute x = -3 into the function:
f(-3) = (1/2)(-3)^2 + 3(-3) - 5 = -9.5
Since the coefficient of the quadratic term is positive, we know that the parabola opens upward and the vertex represents a minimum value.
Therefore, the minimum value of the function is -9.5, which occurs at x = -3.
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HELP THIS IS ALL!!!HELPPP
Answers
Answer:
247
Step-by-step explanation:
A store has 300 televisions on order, and 90% are high definition. How many televisions on order are high
definition? You may find the bar model useful in completing this problem.
20% 30% 40%
70%
0%
0
10%
30
The store has
50% 60%
high-definition televisions on order.
80%
90%
100%
300
Answers
Answer:
90% of 300 = .90 × 300 = 270 high- definition televisions on order.
A pair of standard dice are rolled. Find the
probability of rolling a sum of 7 with these dice.
Answers
Answer:
6 out of 36 or 1 out of 6
Step-by-step explanation:
There are 36 possible ways two dice can roll, so the probability of the sum of seven is 6 out of 36, or 1/6.
[tex]\boxed{\sf 16.67\%}.[/tex]
Step-by-step explanation:1. Determine the total amount of different outcomes.So since we have a pair of dice, assuming they are standard 6 faced dices, the total amount of outcomes is given by just multiplying the number of faces or different numbers that the dices can present:
6 x 6 = 36 possible outcomes.
2. Determine the amout of outcomes that meet the requirement of adding up to 7.Now, here we need to count all the possible cases where the outcome of both dices will equal 7. And there are said cases:
1 + 6 = 7
Explanation. Here the first dice presented number 1 and the second presented number 6, adding up to 7.
Other cases that meet the requirement:
2 + 5 = 7
3 + 4 = 7
4 + 3 = 7
5 + 2 = 7
6 + 1 = 7
So the total amount of events that will meet the requirement is 6.
3. Find the probability.So if we have an event with 36 possible outcomes, and only 6 of those 36 outcomes will mean a success on the experiment. Then, to find the probability of those 6 events from happening all we need to do is divide the amount of events considered "success" which is the numbers adding up to 7 by the total amout of outcomes (36).
So, the probability of rolling a sum of 7 with 2 dices is:
[tex]\sf P(\dfrac{6}{36} )=\dfrac{1}{6} =\boxed{\sf 16.67\%}.[/tex]
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Trigonometry homework help
Answers
A. The distance she must walk to return to the starting point is approximately 1912.325 ft, or 1912 ft 3 in.
B. She is walking towards the north, the heading is N 1° 20' W.
C. Acreage = 7.55 acres (rounded to 3 decimal places).
How did we get these values?A. Convert the angles to decimal degrees:
N. 27° 40′ E. = 27.667°
N. 56° 31′ E. = 56.517°
S. 4° 26′ W. = -4.433°
Now, calculate the distances between the points:
AB = √(696.2917² + 3.5² - 2*696.2917*3.5*cos(27.667°)) = 696.2227 ft
BC = √(487.9792² + 11.75² - 2*487.9792*11.75*cos(56.517°)) = 487.9385 ft
CD = √(1691.125² + 1.5² - 2*1691.125*1.5*cos(-4.433°)) = 1691.1415 ft
B. Finding the distance from D back to A, calculate the distance and angle between AD:
AD = √(AB² + BD² - 2*AB*BD*cos(θ)) where θ = 180° - 4°26' - 27°40' = 147.9°
Substituting AB and BD:
AD = √(696.2227² + 1691.1415² - 2*696.2227*1691.1415*cos(147.9°)) = 1912.3246 ft
Therefore, the distance she must walk to return to the starting point is approximately 1912.325 ft, or 1912 ft 3 in.
C. Finding the heading she walks from D back to A, calculate the angle between AD and the north-south axis:
θ' = atan((AB*sin(27.667°) - BD*sin(θ))/AD) = atan((696.2227*sin(27.667°) - 1691.1415*sin(147.9°))/1912.3246)
θ' = -1.344°
Since she is walking towards the north, the heading is N 1° 20' W.
Lastly, to calculate the acreage of this plot of land, we use Heron's formula to determine the area of triangle ABC:
s = (AB + BC + AC)/2 = (696.2227 + 487.9385 + 1392.625)/2 = 788.8931 ft
A = √(s(s-AB)(s-BC)(s-AC)) = 328756.0207 ft²
Convert to acres:
Acreage = 328756.0207/43560 = 7.55 acres (rounded to 3 decimal places).
learn more about distance: https://brainly.com/question/28551043
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