Find an equation of a line that is perpendicular to 5X minus Y equals one and is located search that the area of the triangle formed by this line in the ex and Y axis is equal to five
Answers
The equation of a line is y = \(\frac{-x}{5}\) ± √2.
What is an equation of a line?The set of points that make up a line in a coordinate system are represented algebraically by a line's equation.The slope of the line and a point on the line can be used to create the equation of a line.The slope of the line, which can be stated as a numeric integer, fraction, or tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.Given Line : 5x - y = 1
slope of line = \(\frac{-5}{-1}\) = 5
product of slopes of two perpendicular lines is - 1.
m₁ × 5 = -1
slope of required line m₁ = \(\frac{-1}{5}\)
Let the equation of the required line be
y = mx + c where m is slope
y = \(\frac{-x}{5}\) + c
Area of the triangle formed by a line with intercepts a,b = \(\frac{1}{2} ab\)
Here, x-intercept = 5c
y-intercept = c
Area of triangle = \(\frac{1}{2} (5c)(c)\)
=\(\frac{5c^{2} }{2}\)
Given area = 5
⇒ \(\frac{5c^{2} }{2}\) = 5
⇒ c² = 2
⇒ c = ±√2
Hence, The equation of a line is y = \(\frac{-x}{5}\) ± √2.
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Related Questions
A runner's journal shows the number of miles run each day for a week:
Sunday: 1 miles
Monday: 4 miles
Tuesday: 7 miles
Wednesday : 10 miles
Thursday: 13 miles
Friday: 16 miles
Saturday:
Based on the arithmetic sequence how many miles are planned for Saturday?
Answers
The number of miles planned on Saturday is 19 milea
What is an arithmetic sequence?This means the sequence where the difference between one term and the next term is a constant.
In this case, the following information are illustrated:
Sunday: 1 miles
Monday: 4 miles
Tuesday: 7 miles
Wednesday : 10 miles
Thursday: 13 miles
Friday: 16 miles
As we can see there's a difference of three between them. This can be seen as:
= 4 miles - 1 mile
= 3 miles
Therefore, the number planned on Saturday will be:
= Friday + 3 miles
= 16 miles + 3 miles
= 19 miles
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The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude,
in feet, of the airplane and x represents the number of minutes the plane has been descending:
y=-1025x + 30,750
Part A:
Create a table for the values when x = 0, 5, 8, 10, 30.
Include worked-out equations used to identify the values within the table.
Part B:
Identify the altitude after 5 minutes and after 30 minutes. Use 1-2 sentences to explain the altitude at these two times and
describe what is happening to the airplane at these time intervals.
Answers
Part A:
Look at photo
Part B:
After 5 minutes, the altitude of the airplane is 20,500 feet. This means that the airplane has been descending for 5 minutes and has lost an altitude of 10,250 feet.
After 30 minutes, the altitude of the airplane is -29,250 feet. This means that the airplane has been descending for 30 minutes and has lost an altitude of 60,000 feet. The negative value of the altitude indicates that the airplane has landed or is close to landing.
At both 5 minutes and 30 minutes, the airplane is descending. The rate of descent is constant, as represented by the slope of the equation, and is equal to -1025 feet per minute. At 5 minutes, the airplane is still at a high altitude, while at 30 minutes the airplane has landed or is close to landing, as indicated by the negative value of the altitude.
Answer:
Step-by-step explanation:
Part A:
x | y | Equation
0 | 30,750 | y = -1025*0 + 30,750
5 | 27,250 | y = -1025*5 + 30,750
8 | 23,750 | y = -1025*8 + 30,750
10 | 20,250 | y = -1025*10 + 30,750
30 | -20,250 | y = -1025*30 + 30,750
Part B:
After 5 minutes, the altitude is 27,250 feet. This means that the airplane has been descending steadily for 5 minutes and is now at a lower altitude than when it started.
After 30 minutes, the altitude is -20,250 feet. This means that the airplane has been descending steadily for 30 minutes and is now much lower than when it started. The airplane is close to the ground and about to land.
The graph shows the distribution of the number of text messages young adults send per day.
A graph titled daily text messaging has number of text on the x-axis, going from 8 to 248 in increments of 30. Data is distributed normally. The highest point of the curve is at 128.
Which statement describes the distribution?
A) The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 98 messages.
B) The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 30 messages.
C) The distribution is approximately Normal, with a mean of 30 messages and a standard deviation of 128 messages.
D) The distribution is uniform, with a mean of 128 messages and a standard deviation of 30 messages.
Answers
The statement that describes the distribution based on the given information is:
A) The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 98 messages.
The statement that describes the distribution based on the given informationThe graph shows a normal distribution, as indicated by the shape of the curve. The highest point of the curve (the peak) is at 128, which represents the mean of the distribution.
The standard deviation measures the spread of the data, and based on the information given, it is 98. Therefore, option A accurately describes the distribution.
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PLEASE HELP!! The price of a pair of headphones is $39.99 before tax. Dalton bought the headphones for 30% off. He then paid 6% sales tax on the discounted price. Part A: How much did Dalton pay in sales tax? Show all work and steps in your solution. (5 points) Part B: What is the total amount that Dalton paid for the headphones? Show all work and steps in your solution. (5 points) Source StylesFormatFontSize
Answers
Answer:
Step-by-step explanation:
A)
This is the 30% discount:
$39.99 x .30 = $11.997; The discount is $11.997
Price of headphones after the discount:
$39.99 - $11.997 = $27.99
Now we need to calculate the 6% sales tax on the discounted price.
$27.99 x .06 = $1.68 (rounded off)
Dalton paid $1.68 in sales tax on the discounted price.
B)
The total price Dalton paid for the headphones will be the discounted price plus the sales tax.
$27.99 + $1.68 = $29.67
Total price Dalton paid: $29.67
The Hiking Club plans to go camping in a State park where the probability of rain on any given day is 50%. What is the probability that it will rain on exactly one of the three days they are there? Round your answer to the nearest thousandth.
Answers
The probability that it will rain on exactly one of the three days they are there is 0.375.
Given that Hiking Club plans to go camping in a State park where the probability of rain on any given day is 50%.
The binomial distribution is used when there are exactly two outcomes of a trial that are mutually exclusive.
Use binomial probability:
P = ⁿCʳ pʳ (1−p)ⁿ⁻ʳ
where n is the number of trials,
r is the number of successes,
and p is the probability of success.
probability of rain on any given day =p =0.50
total number of ways,n=3
let X is number of days with rain out of 3 days
So, \(X\sim Bin(3,0.50)\)
P(x=X)=ⁿCₓpˣ(1-p)ⁿ⁻ˣ
P(x=1)=³C₁(0.50)¹(1-0.50)³⁻¹
P(x=1)=3×0.50×(0.5)²
P(x=1)=1.5×0.25
P(x=1)=0.375
Hence, the probability that it will rain on exactly one of the three days they are there where the probability of rain on any given day is 50% is 0.375.
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Statistical data of breakdowns of computer XXX show that the duration for trouble-free operation of the machine can be described as a gamma distribution with a mean of 40 days and a standard deviation of 10 days. The computer is occasionally taken out for maintenance in order to insure operational condition at any time with a 95% probability.
1. How often should the computer be scheduled for maintenance? Should it be shorter or longer than the mean of 40 days?
2. Three XXX computers were acquired at the same time by an engineering consulting firm. The computers are operating under the same environment, workload, and regular maintenance schedule. The breakdown times between the computers, however, may be assumed to be statistically independent. What is the probability that at least one of the three machines will break down within the first scheduled maintenance time?
Answers
1. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.
2. Probability of no breakdowns = (reliability of a single machine)^3. Probability of at least one breakdown = 1 - Probability of no breakdowns
1. To determine how often the computer should be scheduled for maintenance, we need to consider the reliability and the desired level of operational condition. Since the duration for trouble-free operation follows a gamma distribution with a mean of 40 days, this means that, on average, the computer can operate for 40 days before a breakdown occurs.
To ensure operational condition with a 95% probability, we can calculate the maintenance interval using the concept of reliability. The reliability represents the probability that the machine will not break down within a certain time period. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.
Using the gamma distribution parameters, we can find the corresponding reliability for a specific time duration. By setting the reliability equation equal to 0.95 and solving for time, we can find the maintenance interval:
reliability = 0.95
time = maintenance interval
Using reliability and the gamma distribution parameters, we can calculate the maintenance interval.
2. To calculate the probability that at least one of the three machines will break down within the first scheduled maintenance time, we can use the complementary probability approach.
The probability that none of the machines will break down within the first scheduled maintenance time is given by the reliability of a single machine raised to the power of the number of machines:
Probability of no breakdowns = (reliability of a single machine)^3
Since the breakdown times between the machines are statistically independent, we can assume that the reliability of each machine is the same. Therefore, we can use the reliability calculated in the first part and substitute it into the formula:
Probability of at least one breakdown = 1 - Probability of no breakdowns
By calculating this expression, we can determine the probability that at least one of the three machines will break down within the first scheduled maintenance time.
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The graph shows the distribution of the lengths (in seconds) of videos on a popular video-streaming site. The distribution is approximately Normal, with a mean of 264 seconds and a standard deviation of 75 seconds.
A graph titled Streaming Videos has length (seconds) on the x-axis, going from negative 36 to 564. The highest point of the curve is at 264.
What percentage of videos on the streaming site are between 264 and 489 seconds?
0.15%
49.85%
95%
99.7%
Answers
According to the properties of the standard normal distribution, approximately 99.7% of the values lie within three standard deviations of the mean. Therefore, the answer is 99.7%.
To determine the percentage of videos on the streaming site that are between 264 and 489 seconds, we need to calculate the area under the normal curve within that range. Since the distribution is approximately normal with a mean of 264 seconds and a standard deviation of 75 seconds, we can use the properties of the standard normal distribution to find the desired percentage.
First, we need to convert the values 264 and 489 to z-scores, which represent the number of standard deviations a particular value is away from the mean. The z-score formula is given by:
z = (x - μ) / σ
where x is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:
z1 = (264 - 264) / 75 = 0
z2 = (489 - 264) / 75 = 3
Next, we can use a standard normal distribution table or a calculator to find the area under the curve between z = 0 and z = 3. The area represents the percentage of videos falling within that range. The answer is 99.7% .
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solve the system by elimination 4x-y=2 and x+3y=7
Answers
Answer:
x=1 y=2
Step-by-step explanation:
Isolate x for 4x -y=2: X=2+y/4
Substitute x= 2+y/4
(2+y/4 )+3y=7
simplify 2+13y/4=7
Isolate y for 2+13y/4=7
y=2
Forx= 2+y/4
Substitute y = 2
x= 2+2/4
Simplify
X=1
Based on the table, what is the best prediction of the weight of a person of 62 inches?
Answers
Answer:
128lbs
Step-by-step explanation:
60% of 120lbs+40% of 140lbs
72+56
128
In the Country A legal system, a defendant is presumed innocent until proven guilty. Consider a nullhypothesis, H0, that the defendant is innocent, and an alternative hypothesis, H1, that the defendant is guilty. A jury has two possible decisions: Convict the defendant (i.e., reject the nullhypothesis) or do not convict the defendant (i.e., do not reject the null hypothesis). Explain the meaning of the risks of committing either a Type I or Type II error in this example.
Answers
Using error concepts, it is found that in this problem, a type I error would be finding an innocent person guilty, while a type II error would be finding a guilty person innocent.
What are Type I and Type II errors?Type I: Rejection of a true null hypothesis. The null hypothesis is true, but from a sample, you get enough evidence to reject.Type II: Non-rejection of a false null hypothesis. The null hypothesis is false, but from a sample, you do not get enough evidence to reject.Hence:
In this problem, a type I error would be finding an innocent person guilty, while a type II error would be finding a guilty person innocent.
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Please help! 15 points!
Suppose the sample space for a continuous random variable is 0 to 200. If the area under the density graph for the variable from 0 to 50 is 0.25, then the area under the density graph from 50 to 200 is also 0.25. O A. True B. False SUBMIT
Answers
Answer:
I guess it's False...Hope it helps you.
Answer:
true
Step-by-step explanation:
How do you do this question?
Answers
Answer:
9.29
Step-by-step explanation:
S₄ is the area using Simpson's rule and 4 intervals.
Simpson's rule can be calculated as:
Sᵢ = Δx/3 (f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + ... + 4f(xᵢ₋₂) + 2f(xᵢ₋₁) + f(xᵢ))
Or, Simpson's rule can be calculated as a combination of midpoint and trapezoid sums:
S₂ᵢ = (2Mᵢ + Tᵢ) / 3
Using the first method:
Δx = (4−0)/4 = 1
S₄ = 1/3 (1.00 + 4(1.41) + 2(2.24) + 4(3.16) + 4.12)
S₄ = 1/3 (27.88)
S₄ ≈ 9.29
Using the second method:
S₄ = (2M₂ + T₂) / 3
The midpoint area for 2 intervals is:
M₂ = (2) (1.41) + (2) (3.16) = 9.14
The trapezoid area for 2 intervals is:
T₂ = ½ (1.00 + 2.24) (2) + ½ (2.24 + 4.12) (2) = 9.60
Therefore:
S₄ = (2 (9.14) + 9.60) / 3
S₄ ≈ 9.29
e
B
0
14. The table shows the number of inches of
rain over five months. What would be an
appropriate display of the data? Explain.
(Lesson 2)
Month
Number
of Inches
of Rain
Jan. Feb. Mar.
1.5
2.2
3.6
Apr.
5.3
May
4.8
Answers
The graph of the given function is attached.
Given is a function for the rainfall in 5 months in inches.
We need to display the data,
So, as we can see that the data is not showing any proportion or pattern,
So, it can be displayed as a line chart.
Hence the chart is attached for the function.
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Let f(X)=3√x
if g(x) is the graph of the f(x) shifted down 1 units and left 5 units write a formula for g(x)
g(x)=
Answers
g(x) = 3√(x-5) -1
The process of altering a graph to produce a different version of the preceding graph is known as graph transformation. The graphs can be moved about the x-y plane or translated. They may also be stretched, or they may undergo a mix of these changes.
Horizontal stretching: It means the graph is elongated or shrink in x direction.
Vertical stretching : It means the graph is elongated or shrink in y direction
Vertical translation : It means moving the base of the graph in y direction
Horizontal translation : It means moving the base of the graph in x direction
According to rules of transformation f(x)+c shift c units up and f(x)-c shift c units down.
Therefore, in order to move the graph down 1 units, we need to subtract given function by 1 , we get
g(x) = 3√x -1
According to rules of transformation f(x+c) shift c units left and f(x-c ) shift c units right.
Therefore, in order to move the graph left by 5 units, we need to add given function by 5 , we get
g(x) = 3√(x-5) -1
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simplify each algrebraic expression. drag tiles to correct boxes to complete the pairs.
-5x-2 5x+2 5x-2 -5x+2
Answers
(a) The algebraic expression, -5x - 2 + 5x + 2 is simplified as 0.
(b) The algebraic expression, 5x -2 - (5x + 2) is simplified as -4.
What is the simplification of the algebraic expression?The given algebraic expression is simplified by adding similar terms together, as it will make the expression to be in simplest form.
The given algebraic expressions are;
-5x - 2 + 5x + 2
5x -2 - (5x + 2)
The first algebraic expression is simplified as follows;
-5x - 2 + 5x + 2
collect similar terms;
(-5x + 5x) + (-2 + 2)
= 0 + 0
= 0
The second algebraic expression is simplified as follows;
5x - 2 - (5x + 2)
= 5x - 2 - 5x - 2
collect similar terms;
= (5x - 5x) + (-2 - 2)
= 0 - 4
= - 4
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Write the slope-intercept form of the equation of the line.
Answers
9514 1404 393
Answer:
y = x + 2
Step-by-step explanation:
We observe that the line crosses the y-axis at y=2, so the y-intercept is 2.
The line has a rise of 1 grid square for each run of 1 grid square to the right. The slope is the ratio of rise to run:
m = rise/run = 1/1 = 1
The slope and intercept can be put into the slope-intercept form:
y = mx + b . . . . . line with slope m and y-intercept b
y = 1x +2 . . . . . . line with slope 1 and y-intercept 2
y = x +2 . . . . . . . simplified
The cost of a jacket increased from $75.00 to $84.75. What is the percentage increase of the cost of the jacket?
A.
1.3%
B.
87%
C.
13%
D.
9.75%
Answers
Answer:
c) 13%
Step-by-step explanation:
Given information,
→ The cost of a jacket increased from the price $75.00 to $84.75.
Now we have to,
→ find the % increase of cost of jacket.
Let's solve the problem,
→ ((84.75 - 75)/75) × 100
→ (9.75/75) × 100
→ 0.13 × 100
→ 13%
Hence, the answer is 13%.
The dimensions of a cylinder are shown in the diagram
Round to the nearest whole number , what is the total surface area of the cylinder in cubic centimeters
Answers
Answer:
S = 2π(3^2) + 2π(3)(8.2) = 67.2π = 211 cm^3
Question 9 of 60
Which symbol correctly compares the fractions below? 3/7 ? 4/14
O A. =
B. >
O C. <
OD. None of these are correct.
SUBMIT
Answers
Statistics
TOPIC NAME
Weighted mean: Tabular data
no idea how to solve this i dont understand alek's explanation
Answers
Considering the information, the mean number of books read is approximately 3.06 books.
How to find the mean number of books read?We need to calculate the sum of the number of books read by each student and divide it by the total number of students:
Mean = (1 × 5 + 3 × 9 + 4 × 15 + 7 × 4) / (5 + 9 + 15 + 4)= 101 / 33≈ 3.06Therefore, mean, also known as the average, is a measure of central tendency that represents the sum of a set of values divided by the total number of values. In this case, we have a sample of 33 students, and we want to find the mean number of books they read. We can conclude that the mean number of books read is approximately 3.06 books.
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Approximate -10 + √30 to the nearest tenth.
O-5.5
O-4.5
04.5
O5.5
Answers
Answer:
(b) -4.5
Step-by-step explanation:
Choosing the correct answer here is not the same as knowing what the correct value is.
EstimateYou know that √30 < √100 = 10, so the sum must be negative. That is, 10 subtracted from a positive number less than 10 will give a negative result.
You know that 25 < 30 < 36, so √25 < √30 <√36. That is, √30 will be between 5 and 6. If we say √30 ≈ 5.5, then the sum is ...
-10 +√30 ≈ -10 +5.5 = -4.5
__
Additional comment
Of course, a calculator can tell you the value to the desired precision.
What percentage of values are between 25 and 45
Answers
Answer:
I'm not that good at this but I'll try.
The difference between 25 and 40 is 15
The difference between 80 and 5 is 75
So, 15/75 = 0.20 or 20%
Sorry, that all I can come up with
Step-by-step explanation:
PLEASE HELP IM SO LOST
Answers
Answer: f(x) has an axis of symmetry at x = 4 and h(x) has an axis of symmetry at x = -2
Step-by-step explanation:
You can easily find the axis of symmetry by investigating around which line the functions are symmetrical about
for instance, in h(x), the graph is symmetrical on either side of x = -2, meaning that the line x = -2 cuts the parabola in 'half'
in f(x), this is a little harder to think about, but if you know how the graph will be shifted on the x-axis you can figure it out! In this case (x-4)^2 means that the graph will be shifted on the x-axis 4 units to the right (or from the origin to +4 on the X axis)
as such the line x = 4 will cut the function f(x) in 'half'
(5+5)x2-12 divided by 4
Answers
Answer:
(5+5)x2-12 = 8
Step-by-step explanation:
5+5=10, 10×2= 20-12 = 8
A drone flying over a field of corn identifies a dry area. The coordinates of the vertices of the area are shown. To what coordinates should the portable irrigation system be sent to water the dry area? Explain your reasoning.
Answers
The coordinates to which the portable irrigation system should be sent to water the area are:
(495.75, 672).
Where to send the portable irrigation system?The portable irrigation system should be sent right to the middle of the dry area given by the rectangle at the end of the answer.
Hence the coordinates are given as follows:
x-coordinate: Mean of the x-coordinates of x = 56, x = 144, x = 888, x = 895.y-coordinate: Mean of the y-coordinates of y = 289, y = 332, y = 1012, y = 1055.Hence the x-coordinate of the point to which the system should be sent is:
x = (56 + 144 + 888 + 895)/4 = 495.75.
(the mean is given by the sum of the observations divided by the number of observations).
The y-coordinate of the point to which the system should be sent is:
y = (289 + 332 + 1012 + 1055)/4 = 672.
Missing InformationThe area is given by the image at the end of the answer.
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A point in the table for the transformed function is
Answers
Answer:
linear function
Step-by-step explanation:
straight line then add up
Evaluate 5x-3y when x=7 y=1/3
Answers
Answer:
34
Step-by-step explanation:
(5*7)-(3*1/3) =
35-1 = 34
Answer:
34
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
5x - 3y
x = 7
y = 1/3
Step 2: Evaluate
Substitute: 5(7) - 3(1/3)Multiply: 35 - 1Subtract: 34HELPPPP PLEASEEEE When writing a proof, how do you construct the first statement?
A) By writing the justification for the first statement in the right column.
B) By copying the “prove” statement(s) from the original problem.
C) By writing the next logical statement from the current one.
D) By copying the “given” statement(s) from the original problem.
Answers
Answer:
By copying the given statements from the original problem
No. D
I hope it helped you.
Please Mark me the brainliest
Answer:
Hey, when writing a proof, the first statement should be based on the given information or assumptions, and it should be written in the left column of the proof. To get started, it's best to look at the "given" statements from the original problem and use those as your starting point. This first statement sets the foundation for the logical progression of the proof.
It's important to remember that each subsequent statement should be logically connected to the previous ones, and should lead towards the final statement or conclusion that you're trying to prove. To make your proof convincing, you should also include a justification for each statement that you make, which goes in the right column of the proof.
Overall, constructing a proof can take some time and effort, but by following a clear and logical progression, you can create a solid and convincing argument for your claim.
Step-by-step explanation:
Find the length of major arc PQ
Answers
The length of major arc PQ is 35π units.
What is major arc?
In geometry, an arc is a portion of the circumference of a circle. A major arc is an arc that spans more than 180 degrees of the circle. In other words, a major arc is an arc that is greater than a semicircle (which spans exactly 180 degrees).
we know that,
length of arc = s = 2 π r (θ/360°)
where, r is the radius and θ is the angle of arc.
we have, r = 30
θ = 210
so, length of major arc PQ :
= 2 π r (θ/360°)
= 2 π × 30 × (210/360)
= 60 π × 7/12
= 35π units.
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Finding the derivative of a function at a point x gives
A.) The slope of the secant line of the function at x
B.) A line parallel to the function
C.) The slope of the tangent line of the function at x
D.)None of the above
Answers
Answer:
C.)
Step-by-step explanation:
that is exactly the definition of the derivative.
the derivative is the limit of
(f(x+h) - f(x))/((x+h) - x) = (f(x+h) - f(x))/h
with h going to 0.
this is the limit of the standard rate of change concentrated on a single point = the slope of the tangent at that point.