Distance from point (0, -3) to the line y = x - 1 = [tex]\sqrt{2}[/tex]
Given:
Point =(0,-3) => x = 0; y = -3
Line = y = x - 1 => a= 1, b= -1, c=-1
How is the distance from the point to the line calculated?
Let us consider the distance to be d,
[tex]d= \frac{ax+by+c}{\sqrt {a^{2}+b^{2}} } \\\\=\frac{1(0)-1(-3)-1}{\sqrt{2} } \\\\=\frac{2}{\sqrt{2} } = \sqrt{2}[/tex]
What is the distance from a point to a line?
The distance between a point and a line in Euclidean geometry is the shortest path between any two points on an infinite straight line. The length of the line segment connecting the point to the closest point on the line, measured perpendicularly to the line, is the distance between them.If the variances of the dependent and independent variables are equal, then Deming regression, a form of linear curve fitting, produces orthogonal regression, in which each data point's degree of fit error is expressed as the angle of the point from the regression line.To learn more about distance from a point to a line, refer:
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you have a rectangular plot measuring 16 by 25 feet in a community garden. you want to grow tomato plants that each need 8 square feet of space and pepper plants that need 5 square feet. write an equation that models how many tomato plants and how many pepper plants you can grow
Considering a rectangular plot measuring 16 by 25 feet in a community garden the equation that models the the number of tomato plant and the number of pepper plant is 8x + 5y = 400
How to write the model of number of tomato plant and pepper plantgiven data
a rectangular plot measuring 16 by 25 feet
area to grow tomato plants = 8 square feet
area to grow pepper plants = 5 square feet
From the given data the total area is
Area = 16 * 25
Area = 400 square feet
let the number of area required by tomato plant be x and the area required by pepper plant be y
The equation that models how many tomato plants and how many pepper plants you can grow can be written as
8x + 5y = 400
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Prior Knowledge Problems:
1. On the first math test, Jamaya
answered 19 out of 25 questions
correctly. On the second test she got
17 out of 20 correct. On which test did
she get a better grade?
a. Write a ratio in fraction form to
compare the number correct to the
total questions for each test.
b. Can you compare these two ratios
as they are written?
a) Ratio in fraction form to compare the number correct to the total questions for each test is [tex]\frac{17}{20}[/tex].
b) Yes, we compare these two ratios as they are written.
How to calculate the above question?Jamaya got a better answer on the test on her second test, and you could compare these two ratios as they are written.
a)
First: Convert the each of scores into the percentages:
How do you convert the ratios to percentages? Well, first we have to convert ratio to a decimal or a fraction. Let's convert it to fraction. So, 19 out of 25 will become fraction [tex]\frac{19}{25}[/tex], and 17 out of 20 will become fraction [tex]\frac{17}{20}[/tex] . To convert fraction to percentage:
Divide numerator by denominator:
19 ÷ 25 = 0.76 AND 17 ÷ 20 = 0.85
Multiply the quotient by 100
0.76 x 100 = 76 AND 0.85 x 100 = 85
Add percent sign
76% AND 85%
Now, two quantities are easier to compare. We can obviously see that 85% is the bigger [and better] than 76%. So, ratio that equals 85% - 17 out of 20 - is a better grade.
b)
Yes, you can compare the these two ratios, just find [positive] difference between the amount that she scored and the total number of scores that could be gained.
25 - 19 = 6
20 - 17 = 3
Since equation with 20 and 17 in it has a smaller difference, it is most likely to have a greater value [because that means that Jamaya got more right and less wrong, which means a greater mark which is also greater quantity].
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-24+12d=2(d-3)+22
D=
The width of a rectangle is 3 units less than the length. The area of the rectangle is 18 units. What is the length, in units, of the rectangle?
Answer:
w=3units l=6 units
Step-by-step explanation:
The required length and width of the rectangle are 6 and 3 units
Given that,
The width of a rectangle is 3 units less than the length. The area of the rectangle is 18 units.
The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.
Here,
Let the length of the rectangle be l and the width of the rectangle is l -3
Now,
area of the rectangle,
18 = l [l - 3]
18 = l² - 3l
l² - 3l - 18 = 0
l² - 6l + 3l - 18 = 0
(l - 6) + 3 (l - 6) = 0
(l - 6)(l + 3) = 0
l = 6 {negative value of the l can be neglected.}
now,
width = 6 - 3 = 3
Thus, the required length and width of the rectangle are 6 and 3 units.
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What is the amplitude of the function y = sin1/2x
since y=AsinKx.......1
so amplitude =|A|=1
If x=-9 and y=3
evaluate the following expression:
2(y-3xy)
Answer:
168
Step-by-step explanation:
= 2[3-{3(-9)(3)}]
= 2[3-{-81}]
= 2(84)
= 168
Hope it helps!!
BTW it was very easy...
Which of the following is most likely the next step in the series
Li Na is preparing for a party. She will have at least 100 guests attending. The venue has small tables that seat 4 people and large tables that seat 6 people.
Write an equation or inequality to represent how many small and large tables Li Na could use
to seat all her guests.
Answer: 100 = 4x + 6y
Step-by-step explanation:
We have a total of 100 guests, small tables seat 4, and large tables seat 6. So for each small table used, 4 guests are subtracted from the total.
x = small tables
y = large tables
A skydiver is planning her jump out of an airplane. Typically, she will jump at a height
of 13,500 feet and she will pull the cord when she is 5000 feet above the ground. If the
equation for distance traveled during freefall is given as d(t) = 16t², how long should
she wait before pulling the cord?
If she will jump at a height of 13500 feet and she will pull the cord when she is 5000 feet above the ground, the equation for distance traveled during freefall is d(t)= [tex]16t^{2}[/tex], then she has to wait 23.05 seconds to pull the cord
The initial height = 13500 feet
The height at which she has to pull the cord = 5000 feet above the ground
The distance traveled to reach 5000 feet above the ground = 13500-5000
= 8500 feet
The equation for the distance traveled during the freefall d(t)= [tex]16t^{2}[/tex]
where d is the distance traveled
t is the time taken
Substitute the values in the equation
8500 = 16 × [tex]t^{2}[/tex]
[tex]t^{2}[/tex] = 8500/16
[tex]t^{2}[/tex] = 531.25
t = [tex]\sqrt{531.25}[/tex]
t = 23.05 seconds
Hence, If she will jump at a height of 13500 feet and she will pull the cord when she is 5000 feet above the ground, the equation for distance traveled during freefall is d(t)= [tex]16t^{2}[/tex], then she has to wait 23.05 seconds to pull the cord
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A deep-sea exploring ship is pulling up a diver at a rate of 25 feet per minute. The diver is 200 feet below sea level. How deep was the diver 10 minutes ago?
What is the solution of the system of equations? 3x+4y=12 2x+y=10
y=10-2x..(3)
[tex]3x+4(10-2x)=12\\\\3x+40-8x=12\\3x-8x=12-40\\-5x=-28\\\frac{-5x}{-5} =\frac{-28}{-5} \\x=\frac{28}{5}[/tex]
[tex]y=10-2(\frac{28}{5} )\\y=10-\frac{56}{5} \\y=-\frac{6}{5}[/tex]
Evaluate the equation
ƒ (n) = −n
ƒ (−6) =
Answer:
6
Step-by-step explanation:
If f(n) is f(-6), that means you need to input -6 in any places that have n in them.
f(-6) = --6
Two negatives make a positive.
f(-6) = 6
Hope this helps! :)
Hello!
To find the value of f(-6)
==> must plug '-6' into n's position in the equation
f(-6) = -(-6) = 6
Hope that helps!
ha bet u u cant ok do it
We can simplify the mathematical expression to get:
[tex]\frac{(5 + \sqrt{3})*(5 - \sqrt{3} ) }{\sqrt{22} } = 4*\sqrt{2/11}[/tex]
How to simplify the given expression?Here we have the mathematical expression:
[tex]\frac{(5 + \sqrt{3})*(5 - \sqrt{3} ) }{\sqrt{22} }[/tex]
Remember the rule:
[tex](a + b)*(a - b) = a^2 + b^2[/tex]
Then the numerator can be rewritten as:
[tex]\frac{(5 + \sqrt{3})*(5 - \sqrt{3} ) }{\sqrt{22} } = \frac{5^2 - \sqrt{3}^2 }{\sqrt{22} } = \frac{25 - 9}{\sqrt{22} } = \frac{16}{\sqrt{22} }[/tex]
notice that 16*16 = 256 then we can rewrite:
[tex]\frac{16}{\sqrt{22} } = \sqrt{\frac{256}{22} } = \sqrt{\frac{128}{11} } = \sqrt{\frac{4*4*2}{11} }= 4*\sqrt{2/11}[/tex]
That is the expression simplified.
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Please help, htis has a time limit
Answer:
Domain: All real numbers
Range: f(x) ≥ 5 or f(x) < 2
Step-by-step explanation:
The given graph is a graph of a piecewise function.
Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.
When graphing piecewise functions:
An open circle is used where the value is not included in the interval.A closed circle is used where the value is included in the interval.An arrow is used to show that the function continues indefinitely.Domain
The domain of a function is the set of all possible input values (x-values).
From inspection of the graph, the arrows show that the function continues indefinitely in both the positive and negative directions.
The value of x = 1 is not included in the left part of the graph, but it is included in the right part of the graph.
Therefore, the domain of the function is all real values of x:
(-∞, ∞)Range
The range of a function is the set of all possible output values (y-values).
From inspection of the graph, there is an open circle at y = 2 and a closed circle at y = 5. Therefore, there are no y-values in the interval:
2 ≤ y < 5.
Therefore, the range of the function is f(x) < 2 or f(x) ≥ 5:
(-∞, 2) ∪ [5, ∞)To make coffee, one small scoop of coffee grounds is added to 2 cups of water. You can draw a ratio table or make a proportion to help find how many cups of water to use for 5 scoops of coffee.
The proportional relation:
y = 2*x
Tells us how many cups of water we need for x scoops of coffee, with this we can see that for 5 scoops we need 10 cups.
How many cups of water do we need for 5 scoops of coffee?We know that for one small scoop of coffee, you need to add 2 cups of water. Then we can write the proportional relation:
y = 2*x
Where x is the number of scoops of coffee and y is the number of cups of water.
if x = 5, then:
y = 2*5 = 10
y = 10
So for 5 scoops of coffee, you need 10 cups of water.
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Please help me !!!!!!!
If one student is chosen at random, the probability that the student was a female and got 'A' is 0.38
What is probability?Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is expressed. To forecast the likelihood of events, probability has been introduced in mathematics.
The likelihood that something will occur is essentially what is meant by probability. This is the fundamental theory of probability, which is also used to calculate the probability distribution, and it is from it that you will learn the likelihood of various outcomes in a random experiment.
The total number of outcomes that can occur should be known before calculating the likelihood that a specific event will occur.
Total numbers of students = 53
Total numbers of females = 34
Total numbers of females of A grades = 20
So probability = 20/53
= 0.38
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Can someone help me solve for
Trisha is saving $25 a week to go on a vacation. She determines that she will need $350 for the vacation,
but she also wants to have over $100 left in her bank account after the trip. How many weeks should
Trisha save?
Answer:
Trisha should save for 18 weeks.
Step-by-step explanation:
1 week = $25
Total = $350
Also wants over $100
350+100 = 450
450 ÷ 25 = 18
Ella is testing out a new studying method and wants to know if it works. She decides to compare her spelling test scores from last week and this week. On last week's test, Ella spelled 16 out of the 20 words correctly. On this week's test, she spelled 13 out of the 15 words correctly. On which test did Ella get a higher ratio of correctly spelled words to total words?
Ella got a higher test score (ratio of correctly spelled words to total words) in the current week when she spelled 13 out of 15 words correctly.
In last week, Ella spelled 16 out of 20 words correctly which is 16:20 in ratio terms and is equivalent to 0.8 (in decimal terms) or 80% in percentage terms.
In current week Ella spelled 13 out of 15 words correctly which is 13:15 in ratio terms and is equivalent to 0.866... (in recurring decimal terms) or 86.7% in percentage terms.
86.7% being greater than 80%, Ella scored higher in current week than in last week's spelling test.
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What are the like terms of 1.4y+5−4.2−5y2+z
Answer:
Step-by-step explanation:
Turn 19/20 into a terminating decimal... PLEASE SHOW WORK EXTRA EXTRAAA POINTS FOR A CORRECT ANSWER WITH SHOWED WORK
Answer:
0.95
Step-by-step explanation:
19/20
19÷2/20÷2
9.5/10
0.95
find the local maximum and minimum values and saddle point(s) of the function. (enter your answers as a comma-separated list. if an answer does not exist, enter dne.)
There is no saddle point (DNE). However, there is local maximum at (1, 1/2) for the given function.
we have function of two variables f(x,y)= 9-2x+4y-x^2-4y^2
we will find the values by partial derivative with respect to x,y,xy
f ₓ= -2 -2x
[tex]f_{y}[/tex] = 4 -8y
to find the saddle point we should first find the critical points so equate
-2 -2x=0 and 4 -8y=0
we get x= 1 and y =1/2 so, critical points are (1,1/2)
to find local maximum or minimum we have to find [tex]f_{xx}[/tex] , [tex]f_{yy}[/tex] and [tex]f_{xy}[/tex]
formula is [tex]f_{xx}[/tex]* [tex]f_{yy}[/tex] - [tex]f_{2xy}[/tex] =0
[tex]f_{xx}[/tex] = -2
[tex]f_{yy}[/tex] = -8
[tex]f_{2xy}[/tex]=0
putting values in formula
(-2)*(-8) -0 =16 > 0, and [tex]f_{xx}[/tex] < 0 and [tex]f_{yy}[/tex] <0
so, here we have local maximum
we have no saddle point for this function by using the same formula we used to find extrema.
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Adriel buys 20 bottles of grapefruit juice at the corner store for a total cost of $7.80.
If each bottle costs the same amount, how much is 6 bottles of juice?
The cost of 6 bottles of juice is $2.34 if the each bottle costs the same.
According to the question,
We have the following information:
Adriel buys 20 bottles of grapefruit juice at the corner store for a total cost of $7.80.
Cost of 20 bottles of juice = $7.80
Now, from here we can find the cost of 1 bottle of juice by dividing the total cost by the number of bottles purchased.
Cost of 1 bottle of juice = $(7.80/20)
Cost of 1 bottle of juice = $0.39
Now, we can easily find the cost of 6 bottles of juice by multiplying the cost of 1 bottle of juice by 6.
Cost of 6 bottles of juice = $(0.39*6)
Cost of 6 bottles of juice = $2.24
Hence, the cost of 6 bottles of juice is $2.24.
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Solve for the value of n
Thank you!!
Answer:
n = 27
Step-by-step explanation:
n + 6 + 2n + 3 + 90 = 180
solve for n then n = 27
hope this helped
have a good day ^^
If you can buy one can of pineapple chunks for $2, then how many can you buy with $10?
(WITH A GRAPH PLEASE)
Answer:
you can buy 5 cans
Step-by-step explanation:
$2 per can
have $10
10 divided by 2
5
First person to respond gets brainliest
ANSWER : 4x-3y
EXPLANATION:
During an local election the ratio of teens to adults who voted was 10:9 If 1,387 people
voted how many were teens?
730 teens voted.
What is ratio?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).
A ratio is the relationship or comparison between two numbers belonging to the same unit in order to determine how much larger one number is than the other. For instance, if a test result is 7 out of 10, the ratio of the number of points earned to the total number of points is 7:10.
Given Data
Teens to adult ratio 10:9
Total people votes = 1387
Ratio of teen vote:
= 1387 × [tex]\frac{10}{19}[/tex]
= 73(10)
= 730
730 teens votes.
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Horizontal and parallel lines e and f are intersected by diagonal and parallel lines g and h. At the intersection of lines g and e, the bottom right angle is angle 2. At the intersection of lines h and e, the bottom right angle is angle 1. At the intersection of lines f and h, the top left angle is angle 3.
Statements Reasons
1. g || h 1. given
2. ∠1 ≅ ∠2 2. corresponding angles theorm
3. ∠2 ≅ ∠3 3. given
4. ∠1 ≅ ∠3 4. transitive property
5. e || f 5. ?
What is the missing reason in the proof?
vertical angles theorem
alternate exterior angles theorem
converse corresponding angles theorem
converse alternate interior angles theorem
The line e is parallel to f by converse alternate interior angles theorem.
What is converse alternate interior angle theorem?
Converse alternate interior angle theorem states that states if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.
What is parallel lines?
Two lines are said to be parallel when they do not meet at any point in a plane. Lines which do not have a common intersection point and never cross path with each other are parallel to each other. The symbol for showing parallel lines is ‘||’.
Given,
angle 1 is congruent to angle 2 and g is parallel to h.
similarly, angle 2 is congruent to angle 3,
by transitive property angle 1 is congruent to angle 3.
By converse alternate interior angle theorem, e is parallel to f.
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Why is the image of the setting sun most likely not described in great detail in "Because I Could Not Stop for Death"?It is a common symbol of death that requires little description.It is a part of the plot that does little to contribute to the theme.It is not meant to be seen as an important symbol within the poem.It is not a significant aspect of the mood created within the poem.
The image of the setting sun most likely not described in great detail in "Because I Could Not Stop for Death" because it is a common symbol of death that requires little description.
Emily Dickinson's lyrical poem "Because I could not stop for Death" was originally printed in Poems: Series 1 in 1890, after her death. We don't know if Dickinson finished "Since I could not stop for Death" or if it was "abandoned" because her writing was never granted permission to be published.
In the poem "Because I could not stop for death the personified Death appears to Dickinson's poem's speaker. The poet's character speaks calmly about Death, the Afterlife, and the tranquility that comes with it. She represents Death as a young guy accompanying her in a carriage. She gives us a quick overview of her previous life while still living as she passes through to the afterlife.
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Question 3: Kylie needs to spend at least 5 hours each week practicing the piano. She has already practiced 2 and 3/4 hours this week. She wants to split the remaining practice time evenly between the last 3 days of the week. Write an inequality to determine the minimum number of hours she needs to practice on each of the 3 days.
Using proportions with mixed numbers, the inequality to determine the minimum number of hours she needs to practice on each of the 3 days is: m ≥ 3/4.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication or division.
One example is the mean of a data-set, as the mean is given by the sum of all observations in the data-set divided by the number of values.
For this problem, we have that:
She has already practiced 2.75 hours, as the decimal part is of 3/4 = 0.75, hence 2 and 3/4 = 2 + 0.75 = 2.75.She needs to practice 5 hours.Hence the minimum number of hours that she still needs to practice is:
5 - 2.75 = 2.25 hours.
The amount is split evenly amount the 3 days, hence the lower bound of the inequality is:
2.25/3 = 0.75 = 3/4.
Hence the amount is given by:
m ≥ 3/4.
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