Answers
Part (a)
The locus is the set of points that satisfy the given conditions. Namely that the point P needs to be 1 unit from the line given.
Think of a median along a highway. Then imagine the two shoulders of the road. The locus describes the two parallel lines that are to this given median. In other words, the median is y = x+2 and the road shoulders are unknown for now.
Though we do know that parallel lines have equal slopes (but different y intercepts).
Therefore, the answers to the next section will be of the form y = x+k for some real number k.
=============================================================
Part (b)
Use your favorite graphing tool to plot y = x+2. I recommend GeoGebra since I use it all the time, and it's what I used to make the drawing below. Desmos is another tool you can use. Both are free.
Note that point A(0,2) is on the line y = x+2. The line perpendicular to y = x+2 and goes through (0,2) is y = -x+2. From here, plot a circle centered at (0,2) with radius 1. The equation of this circle is x^2 + (y-2)^2 = 1
The intersection points of the circle and y = -x+2 will provide starting points, so to speak, for the two shoulder lines I mentioned in part (a).
The approximate locations of those points are:
B = (0.71, 1.29)
C = (-0.71, 2.71)
From here, it shouldn't be too hard to find the y = mx+b forms of the locus lines. Let me know if you need help with that, or if you need me to check your answers.
Side note: Why is it called a locus? I'm not sure, but my gut feeling tells me it has to do with the insects of a similar sounding name (locus the math term and locust the insect). Imagine millions of them forming various shapes in the sky, similar to how many points are used in the 2D plane to create various curves.
Related Questions
Rectangle A has a length of 2 and a width of 10. Rectangle B has a length of 4
and a width of 5. Rectangle A and Rectangle B (doing a test please answer fast)
Answers
Answer: dang bro i never do flvs that early in school. Sorry my guy i got no answer to that. Im quite dumb myself in math
Step-by-step explanation:
cual es la raiz cuadrada de 64???
Answers
Hey there! Hola!
Let's find the square root of 64:
[tex]\sqrt{64}[/tex]
Basically, what number times itself equals 64? that's the answer.
That number is 8.
Hence, the square root of 64 is 8.
La raiz cuadrada de 64 es 8.
Hope everything is clear.
Let me know if you have any questions!
#KeepLearning
[tex]\tt{Amiable}[/tex]
Choose bank, credit union, or both for each statement below:
Must be part of a specific member group to join
Profits are given to shareholders
Offer checking and savings accounts, CDs, loans
Deposits are insured up to $250,000
Fees tend to be higher
Interest customers earn on deposits tends to be higher
Answers
Answer:
Must be part of a specific member group to join . - CREDIT UNION.
Credit Unions require that you are a member of a member group to join as well as other entry requirements unlike a bank where the qualification rules are less stringent.
Profits are given to shareholders . - BANK.
A Bank is owned by its investors and shareholders so they will have to distribute profits to them unlike a Credit Union that is owned by its members.
Offer checking and savings accounts, CDs, loans . BOTH.
Both Credit Unions offer these financial products and accounts.
Deposits are insured up to $250,000 - BOTH.
Both of these types of Institutions are insured up to $250,000 by the United States Governments. Credit Unions are insured by the National Credit Union Share Insurance Fund (NCUSIF) and banks are insured by the FDIC (Federal Deposit Insurance Corporation).
Fees tend to be higher . BANKS.
Banks are for profit institutions so they will charge higher fees to make more profit for their investors.
Interest customers earn on deposits tends to be higher. - CREDIT UNIONS.
Credit Unions earn higher deposit interest for customers because they are not-for-profit so do not have to offer less rates to keep more money for their investors.
Bank, credit union, or both have been for each of the statements below:
Credit Union: Must be part of a specific member group to join. Banks: Profits are given to shareholders. Both: Offer checking and savings accounts, CDs, loans. Both: Deposits are insured up to $250,000. Banks: Fees tend to be higher. Credit Unions: Interest customers earn on deposits tends to be higher.Meaning of Banks and Credit UnionBanks are financial institutions that have licenses to accept deposits from customers and provide loans when the conditions are met.
Credit Unions, on the other hand, are not operated for the purpose of making profits. They are formed by members who hold an agreement and their methods of operation are similar to the commercial banks.
In the given points above the similarities and differences between these two financial institutions are shown.
Learn more about Banks here:
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Finding the slope intercept form of the line passing through the point ( 7,-2 ) and parallel to the line
Answers
Answer:
y = -8x + 54
Step-by-step explanation:
Since the lines are parallel, their slopes are the same, leaving you with y = -8x.
That equation at x = 7 would make y -56, but we want it to be -2. Therefore we add a 54 in the end, leaving you with y = -8x + 54.
I hope this helped.
answer quick! ......................
Answers
Answer:
10 units up
Step-by-step explanation:
An example of this is where the graph changes from (0,0) to (0,10)
Have an amazing day!
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7. Given b= 4, c = 10, and A = 34 degrees, use the Law of Cosines to solve for a. Round your answer to the nearest whole number.
8. Given a = 11, C = 131 degrees, and b = 8, use the Law of Cosines to solve for c. Round your answer to the nearest tenth.
9. Given c = 9.6, b = 5.9, and a = 10.5, use the Law of Cosines to solve for C. Round your answer to the nearest degree.
Answers
Answer: (7) 7.0 (8) 17.3 (9) 64.7°
Step-by-step explanation:
Law of Cosines is: a² = b² + c² - 2bc · cos A
or: b² = a² + c² - 2ac · cos B
or: c² = a² + b² - 2ab · cos C
7) b = 4, c = 10, ∠A = 34
a² = b² + c² - 2bc · cos A
= 4² + 10² - 2(4)(10) · cos 34°
= 16 + 100 - 80 (0.829)
= 116 - 66.323
= 49.677
a = [tex]\sqrt{49.677}[/tex]
a = 7.0
8) a = 11, b = 8, ∠C = 131
c² = a² + b² - 2ab · cos C
= 11² + 8² - 2(11)(8) · cos 131°
= 121 + 64 - 176 (-0.656)
= 185 + 115
= 300
c = [tex]\sqrt{300}[/tex]
c = 17.3
9) a = 10.5, b = 5.9, c = 9.6
9.6² = 10.5² + 5.9² - 2(10.5)(5.9) · cos C
92.16 = 110.25 + 34.81 - 2(10.5)(5.9) · cos C
92.16 = 145.06 - 123.9 cos C
-52.9 = -123.9 cos C
0.427 = cos C
cos⁻¹ (0.427) = C
64.7° = C
Answer:
Answer:
A.
B.
C.
Step-by-step explanation:
We have been given inverse trigonometric functions. We are asked to find the value of each function.
A.
We will use inverse sin to solve our given equation as:
Round to nearest degree:
B.
We will use inverse tann to solve our given equation as:
Round to nearest degree:
C.
We will use inverse cosine to solve our given equation as:
Round to nearest degree:
Step-by-step explanation:
21. A store display will have 6 rows, with 12 containers in each row.
If 39 containers has been set up so far, explain how to find the
number of containers that still need to be set up. Then solve the
problem.
Answers
I need explain in this one please and i need the answers
Answers
Check the picture below.
Subtract 3 2/5 from 5 3/4
Answers
Answer:
[tex]-2\frac{7}{20}[/tex]
Step-by-step explanation:
Given the following question:
[tex]3\frac{2}{5} -5\frac{3}{4}[/tex]
To find the answer we first need to convert the mixed numbers into improper fractions, find the common denominator, subtract the denominators, and of course convert the improper fraction back into a mixed number.
[tex]3\frac{2}{5} -5\frac{3}{4}[/tex]
[tex]3\frac{2}{5}=5\times3=15+2=17=\frac{17}{5}[/tex]
[tex]5\frac{3}{4} =4\times5=20+3=23=\frac{23}{4}[/tex]
[tex]\frac{17}{5} -\frac{23}{4}[/tex]
Find the common denominator:
[tex]CD=20[/tex]
[tex]\frac{17}{5} \times4=\frac{68}{20}[/tex]
[tex]\frac{23}{4} \times5=\frac{115}{20}[/tex]
[tex]\frac{68}{20} -\frac{115}{20}[/tex]
[tex]68-115=-47=-\frac{47}{20}[/tex]
[tex]=-\frac{47}{20}[/tex]
Convert the improper fraction into a mixed number:
[tex]-\frac{48}{20}[/tex]
[tex]-\frac{47}{20} =47\div20=-2\frac{7}{20}[/tex]
[tex]=-2\frac{7}{20}[/tex]
Your answer is "-2 7/20."
Hope this helps.
[tex]2\frac{7}{20}[/tex] is the mixed number we get by subtracting [tex]3\frac{2}{5}[/tex] from [tex]5\frac{3}{4}[/tex].
To subtract [tex]3\frac{2}{5}[/tex] from [tex]5\frac{3}{4}[/tex], we first need to convert both mixed numbers to improper fractions.
[tex]5\frac{3}{4}[/tex] = (4 × 5 + 3) / 4 = 23/4
[tex]3\frac{2}{5}[/tex] = (5 × 3 + 2) / 5 = 17/5
Now we can subtract the two fractions:
23/4 - 17/5
To subtract fractions, we need to have a common denominator.
The common denominator for 4 and 5 is 20.
We'll convert both fractions to have a denominator of 20:
23/4 = (23 × 5) / (4 × 5) = 115/20
17/5 = (17 × 4) / (5 × 4) = 68/20
Now we can subtract the fractions:
115/20 - 68/20
= (115 - 68) / 20
= 47/20
=[tex]2\frac{7}{20}[/tex]
To learn more on Fractions click:
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The graph of y = f ′(x), the derivative of f(x), is shown below. List the intervals where the graph of f is concave down.
(–4, –2) U (2, 4)
(–2, 2)
(–4, 0)
(0, 4)
Answers
Answer:
(a) (–4, –2) U (2, 4)
Step-by-step explanation:
A graph is concave down where its second derivative is negative. That will be where the slope of the first derivative is negative.
Your graph shows the first derivative has negative slope at the left and right ends. The function f(x) will be concave downward on those intervals:
(–4, –2) U (2, 4)
What is the correct interpretation of the probability of getting an 11 when a pair of dice is rolled? Interpret an event as significant if its probability is less than or equal to 0.05.
Answers
Answer:
1/18
Step-by-step explanation:
We are considering that we have 2 dices with 6 faces each (so, the probability to getting any face in any dish is 1/6). To get an 11, we only have two ways to obtain it:
Dice 1= 6 and Dice 2 =5 or Dice 1= 5 and Dice 2 =6
So, the probability of the event is given as:
P(Dice1=5 ∧ Dice2=6) ∪ P(Dice1=6 ∧ Dice2=5) = P(Dice1=5) x P(Dice2=6) + P(Dice1=6) x P(Dice2=5) = 1/6 x 1/6 + 1/6 x 1/6 = 1/36 + 1/36 = 2/36 = 1/18.
As 1/18 = 0,055, and 0,055 > 0,05, we consider the event as not significative (according to the definition of significance in the sentence).
find the simple interest for Rs 500 in 3 years at rate of 10% per year find it with solution
Answers
[tex]\\ \sf\longmapsto I=\dfrac{PRT}{100}[/tex]
[tex]\\ \sf\longmapsto I=\dfrac{500(3)(10)}{100}[/tex]
[tex]\\ \sf\longmapsto I=5(30)[/tex]
[tex]\\ \sf\longmapsto I=Rs.150[/tex]
A restaurant has square tables. Only one person can sit on either end of the table.
Now
Write out the formula to show how you to work out the "number of people" from the number of tables.
Someone making the booking for 20 people. How many tables must be pushed together?
Answers
Answer:
10
Step-by-step explanation: Because 10x2=20
so in this case if they were to push the tables togther only 1 can sit at one square table if there pushed together
unless each table held 2 people like one on one side and one on the other it would be the same formula because 10 on one side of the tables and 10 on the other side would be 10x2
10+10=20 or 10x2=20
ethier one would be the same
hope this helps you!
how do i graph 3/2 on the number line?
Answers
Answer:
by drawing a number line then simpifly 3/2 than mark it down
Step-by-step explanation:
7. Which of the following is true about the set of all solutions for f(x) = 4x?
Select all that apply.
A. It is continuous,
B. It is linear
C. It is exponential
D. The point (1,4) falls on the graph,
E. The point (4,0) falls on the graph,
Answers
Answer:
B.It is linear 180=3x2+24x+36
Step-by-step explanation:
What is the constant rate of change of the
function represented in the table?
Answers
Answer: it is -4 or c
Step-by-step explanation:
The following data are the distances between a sample of 20 retail stores and a large distribution center. The distances are in miles.
29; 32; 38; 40; 58; 67; 68; 69; 76; 81; 85; 95; 96; 96; 99; 106; 112; 127; 145; 150
Find the value that is one standard deviation below the mean. (Round your answer to one decimal place.)
Please help!!!!
Answers
Mean = sum of all numbers / 20 = 1669 / 20 = 83.45
Standard deviation = 7.86
Z-score = -1
So...
Z = (x - mean) / standard deviation
x = Z * standard deviation + mean = -1 * 7.86 + 83.45 = 75.59
Rounded: 75.6
plus help me its really simple ill give you the brainiest
Answers
Answer:
Whole Numbers
Step-by-step explanation:
Whole numbers is the only set of numbers in the following choices that don't include negative numbers (only positive integers and zero). Therefore, since -7 is negative, it doesn't belong to whole numbers!
Your friend has a bag of marbles. Your friend says that there is a 100% chance that you pick out a red marble and a 0% chance that you pick a green one.
What can you conclude about the colors of the marbles inside of your friend's bag?
Can you determine exactly how many marbles are in the bag? Why or why not?
Answers
Answer:
1. They are all red. 2. There is no possible way to come to a conclusion
Step-by-step explanation:
If there is a 100% chance you will draw a red marble, they all have to be red or it would not be a 100% chance.
We can't conclude how many marbles are in the bag because the question states nothing about how many marbles there are.
Six chicken sandwiches and four drinks cost $16.00. Six chicken sandwiches
and two drinks cost $14.00. How much is a chicken sandwich?
Answers
Answer:
$2.67
Step-by-step explanation:
16 ÷ 6 = 2.66666666667
2.67 x 6 = 16.2
(well, it was close.)
Sorry if it's wrong.
Bye, have a great day.
Which number is a prime number? (1 point) 9 15 19 22
Answers
Answer:
The only prime number is 19
Payton bought new headphones originally listed for $90.99. They are 25% off. Which equation can be used to find the amount Payton will save?
Answers
Answer:
90.99x25/100
Step-by-step explanation:
or 90.99x25%
An aeroplane X whose average speed is 500°km/hr leaves kano airport at 7.00am and travels for 2 hours on a bearing 050°. It then changes its course and flies on a bearing 120° to an airstrip A. Another aeroplane Y leaves kano airport at 10.00am and flies on a straight course to the airstrip A. both planes arrives at the airstrip A at 11.30am. calculate the average speed of Y to three significant figures. the direction of flight Y to the nearest degree
Answers
Answer:
72
Step-by-step explanation:
Suppose we want to choose 2 colors, without replacement, from the 3 colors red, blue, and green.
Answers
Okay, I am going to answer this question personally.
Suppose we want to choose 3 colors, without replacement, from the red, blue, green, and purple.
(a) How many ways can this be done, if the order of the choices is taken into consideration?
(b) How many ways can this be done, if the order of the choices is not taken into consideration?
Answer
(a) 6 choices
(b) 3 Choices
Given:
3 Colors
Order of choice : Red, Blue, Green
(a) Order of the choices taken into consideration :
When we are picking the first colour there are 3 color choice.
When we are picking second colour there are 2 choice and so on.
Therefore, total choices are = 3*2 = 6 choices
(b) Order of the choices not taken into consideration :
When to take this option we choose as and the remove the duplicates
Therefore, choices are 3 Choices
Consider giving Brainliest, please.
A driver averages 42 miles per hour and took 15 hours to travel between two cities what is the distance between the two cities
Answers
Answer:
The distence bettween the two cities is 630miles
Step-by-step explanation:
So you take 42 and multiply it by 15 and you get 630.
mikes deli just sold 328 ham sandwiches this week. around how many ham sandwiches did mike sold every day this week?
Answers
Answer:
46.9
Step-by-step explanation:
328/7 = 46.9
To double check: 46.9 x 7 = 328
Have an amazing day!!
PLEASE RATE!!
x <-8
Graph the inequality
Answers
Answer:
<--------
<----|---|---|---|---|---|---|----------
-9 -8 -7 -6 -5 -4 -3
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAINLIEST TY
You go to the doctor and he gives you 15 milligrams of radioactive dye. After 20 minutes, 7.25 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm.
If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived?
Give your answer to the nearest minute.
How many minutes will you spend at the doctor's office?
Answers
Answer:
=34 minutes.
Step-by-step explanation:
Done according to my own understanding!
15mg - 7.25mg = 7.75mg
7.75mg / 20min = 0.3875mg per minute
7.25mg - 2mg = 5.25mg
5.25mg / 0.3875mg = 13.5483871 minutes
13.5483871 minutes + 20 minutes = 33.5483871 minutes
=34 minutes.
Suppose you were to collect data for each pair of variables listed below. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and strength. a) Cell phone data plans for a person who wants a large file size: file size, cost b) Lightning strikes by a person watching a lightning storm: distance from lightning, time delay of the thunder c) A streetlight that you are approaching: its apparent brightness, your distance from it d) Cars being catalogued at a dealership: weight of car, age of owner
Answers
Answer and explanation:
1. Cost is response variable while file size is explanatory variable. Cost is response variable here because it is the dependent variable and the other is the independently variable that affects the dependent variable cost. The scatter plot will show how much cost increase with each change in file size. Scatter plot is in positive direction and strong
2. Time of delay of thunder is response variable while distance from lightning is explanatory variable. Time of delay is dependent variable while the other is independent variable which affects it. Scatter plot shows how much delay of thunder changes with change in distance from lightning. Positive scatter plot and strong
3. Your distance from it is explanatory variable while apparent brightness is response variable. Distance from it is independently variable while the the other is dependent variable. Scatter plot shows change of brightness with each change of distance. Negative direction as distance increase results in brightness decrease. It is strong.
4. weight of car is response variable while age of owner is explanatory variable. Weight of car is dependent variable while the other is independent variable. Scatter plot shows change of weight of car with change of age of owner. Positive direction as one increases the other increases. Strong
Pick which graph satisfies the given conditions.
Degree 5 with 1 x-intercept and a positive leading coefficient.
Answers
Answer:
graph c.
Step-by-step explanation:
it has 5 degrees and it does a 80 angle.