Write an equation of a line that passes through (-1, 2) and is parallel to a line with
x-intercept (3, 0) and y-intercept (0, 1).
Answers
The equation of the line that passes through (-1, 2) and is parallel to a line with x-intercept (3,0) and y-intercept (0,1) is x - 3y = 5.
To find the equation of a line that passes through the point (-1, 2) and is parallel to a line with x-intercept (3,0) and y-intercept (0,1), we can use the fact that parallel lines have the same slope.
First, we need to find the slope of the line with x-intercept (3,0) and y-intercept (0,1). To do this, we can use the slope-intercept form of the equation of a line, y = mx + b,
where m is the slope and b is the y-intercept. We know that the y-intercept is 1, so we can substitute this value into the equation: y = mx + 1
Next, we need to find the slope. We can do this by using the x-intercept (3,0) and the y-intercept (0,1) to calculate the rise and run: Slope = (change in y) / (change in x) = (0 - 1) / (3 - 0) = -1/3
So the slope of the line with x-intercept (3,0) and y-intercept (0,1) is -1/3.
Since the line we want to find is parallel to this line, it must also have a slope of -1/3. We can use the point-slope form of the equation of a line to find the equation of the line that passes through (-1, 2) with slope -1/3:
y - y1 = m(x - x1)
where (x1, y1) = (-1, 2) and m = -1/3.
Substituting these values into the equation, we get:
y - 2 = (-1/3)(x - (-1))
y - 2 = (-1/3)(x + 1)
Multiplying both sides by -3 to eliminate the fraction, we get: -3y + 6 = x + 1
Subtracting 1 and adding 3y to both sides, we get the equation in standard form: x - 3y = 5
Therefore, the equation of the line that passes through (-1, 2) and is parallel to a line with x-intercept (3,0) and y-intercept (0,1) is x - 3y = 5.
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Related Questions
A grain tank on a farm is composed of a storage portion in the shape of a cylinder anda cone-shaped dispensing area at the bottom. The bottom cone portion has a slantheight of 5.5 feet. The entire exposed surface of the tank is to be painted. What is theapproximate amount of surface area that will receive the painting?8.4 ft12 ft5.5 ft
Answers
To fidn the surface area of the grain tank you need to find the area of:
Cylinder (without one of the bases as there are just one base exposed), use the next formula:
\(A_1=\pi\cdot r^2+h(2\pi r)\)You have for the given cylinder:
h=12ft
r: as the diameter is 8.4ft the radius is 8.4tf/2=4.2ft
\(\begin{gathered} A_1=\pi(4.2ft)^2+12ft(2\pi(\text{4}.2ft)) \\ =17.64\pi ft^2+100.8\pi ft^2 \\ =118.44\pi ft^2 \end{gathered}\)Cone (without the base as the base is not exposed), use the next formula:
\(A_2=\pi\cdot r\cdot s\)You have for the given cone:
r= 4.2ft
s= 5.5ft
\(\begin{gathered} A_2=\pi(4.2ft)(5.5ft) \\ =23.1\pi ft^2 \end{gathered}\)The entire exposed surface of the tank is:
\(\begin{gathered} A_T=118.44\pi ft^2+23.1\pi ft^2 \\ \\ =141.54\pi ft^2 \\ \\ \approx444.66ft^2 \end{gathered}\)The approximate amount of surface area that will receive the painting is 444.66 squared feetsHELP ME SOMEONE PLEASE!!!!!!!!!!!
Answers
Answer:
The probability that they will both break down would be 8%
Step-by-step explanation:
I believe it is 8% (sorry if its wrong) because tractor 1 is 3% and tractor 2 is 5% add them together and that is where you get 8%
Anybody know the answer bro i gotta turn it in 1 hour
Answers
Answer:
The equation y = x/3 describes the relationship.
Step-by-step explanation:
Let's take two points. (0,0) and (3,1)
slope(m) = ((1-0)/(3-0)
= 1/3
now
y=mx+b
or, 1 =1/3 × 3 + b
or, 1 = 1+b
so, b = 0
now
y = mx+b
or, y = 1/3 × x +0
or, y = x/3
Joey built a skateboarding ramp. The base of the ramp along the ground is 13 feet, and the top of the ramp is 7 feet off the ground. What is the length of the ramp's incline?
Answers
Answer:
14.77 feet
Step-by-step explanation:
Using the pythagoras theorem to get the length of the ramp
l² = 13² + 7²
l is the length of the ramp
l² = 169 + 49
l² = 218
l = √218
l = 14.77 feet
Hence the length of the ram is 14.77 feet
Which is the equation that opens downward and has x–intercepts at (-2.5,0) and (1,0)?
Group of answer choices
f(x) = -2x² + 3x - 5
f(x) = -2x² - 3x - 5
f(x) = x² + 3x - 5
f(x) = -2x² - 3x + 5
Answers
As a result, the solution is not one of the available choices as equation has an upward opening with x-intercepts at (-2.5, 0) and (1, 0) .
To have x-intercepts at (-2.5, 0) and (1, 0), the quadratic function must have factors of (x + 2.5) and (x - 1). Therefore, the equation of the quadratic function is:
f(x) = a(x + 2.5)(x - 1)
To determine the value of "a", we can use one of the given points. Let's use the point (1, 0):
0 = a(1 + 2.5)(1 - 1)
0 = a(3.5)(0)
0 = 0
This tells us that when x = 1, the value of f(x) is 0. Therefore, we have:
f(x) = a(x + 2.5)(x - 1) = a(x² + 1.5x - 2.5x - 2.5)
Simplifying, we get:
f(x) = a(x² - 1x - 2.5)
Now, to determine the value of "a", we can use the other given point, (-2.5, 0):
0 = a((-2.5)² - 1(-2.5) - 2.5)
0 = a(6.25 + 2.5 - 2.5)
0 = a(6.25)
a = 0
This means that the equation for the quadratic function is f(x) = 0, which is not a quadratic function that opens downward. Therefore, none of the given answer choices is correct.
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Find the lowest common multiple of 15 and 12
Answers
Answer:
its 60
Step-by-step explanation:
Angel is trying to find the height of a radio antenna on the roof of a local building. He stands at a horizontal distance of 21 meters from the building. The angle of elevation from his eyes to the roof (point A) is 38∘, and the angle of elevation from his eyes to the top of the antenna (point B) is 46∘. If his eyes are 1.66 meters from the ground, find the height of the antenna (the distance from point A to point B). Round your answer to the nearest tenth of a meter if necessary.
Answers
The distance from point A to point B, which is the height of the radio antenna, found using the specified angles of elevations is about 5.3 meters
What is an angle of elevation?
An angle of elevation is an angle formed by a horizontal line and and an observer's line of sight to an object that is above the horizontal line.
Let h₁ represent the height of the top of the roof and let h₂ represent the height to the top of the radio antenna
The height of the radio antenna is therefore; h = h₂ - h₁
The horizontal distance from Angel to the building = 21 meters
Angle of elevation from Angle's eyes to the roof point A = 38°
The angle of elevation from his eyes to the top of the antenna, point B = 46°
Height of Angel's eyes from the ground = 1.66 meters
We get;
tan(38°) = (h₁ - 1.66)/21
h₁ = 21 × tan(38°) + 1.66 ≈ 18.07
tan(46°) = (h₂ - 1.66)/21
h₂ = 21 × tan(46°) + 1.66 ≈ 23.41
The height of the radio antenna = h₂ - h₁ ≈ 23.41 - 18.07 = 5.34
Rounding the response to the nearest tenth of a meter, we get;
The height of the radio antenna ≈ 5.3 meters
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The height of the antenna is 183.4 ( nearest tenth)
What is angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
The distance from the bottom of the pole to the to the point of Angel eyes is calculated as;
Tan38° = x/ 21
0.781 = x/21
x = 21 × 0.781
x = 16.4m
The height of the pole and building at the point of his eyes is calculated as;
The total angle = 38+46 = 84°
tan 84= y/ 21
y = tan84 × 21
y = 199.8
therefore the height of the antenna is calculated as
y-x
= 199.8 - 16.4
= 183.4 ( nearest tenth)
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7^x=3^[x+4] solve x using logarithmic
Answers
By taking advantage of the definition of exponential and logarithmic function and their inherent relationship we conclude that the solution is x = 4 · ㏒ 3/(㏒ 7 - ㏒ 3).
How to solve an exponential equation by logarithms
Exponential and logarithmic functions are trascendental functions, these are, functions that cannot be described algebraically. In addition, logarithmic functions are the inverse form of exponential functions. In this question we take advantage of this fact to solve a given expression:
7ˣ = 3ˣ⁺⁴ Given㏒ 7ˣ = ㏒ 3ˣ⁺⁴ Definition of logarithmx · ㏒ 7 = (x + 4) · ㏒ 3 ㏒ aᵇ = b · ㏒ ax · ㏒ 7 = x · ㏒ 3 + 4 · ㏒ 3 Distributive propertyx · (㏒ 7 - ㏒ 3) = 4 · ㏒ 3 Existence of additive inverse/Modulative and associative propertiesx = 4 · ㏒ 3/(㏒ 7 - ㏒ 3) Existence of multiplicative inverse/Modulative property/ResultBy taking advantage of the definition of exponential and logarithmic function and their inherent relationship we conclude that the solution is x = 4 · ㏒ 3/(㏒ 7 - ㏒ 3).
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Currently Madeline makes $28,800 a year. Based on the following list ofmonthly expenses, find Madeline's adjusted monthly income (AMI).Student Loan:$250 (5 years remaining)Car Loan:$180 (6 months remaining)Personal Loan:$150 (30 months remaining)Apartment Lease: $425 (4 months remaining)>Gas/Electric:~$115 each month
Answers
Given:
yearly salary=28,800
Required:
To calculate adjusted monthly income
Explanation:
student loan
250 dollar
Nico owns 11 instructional piano books. Two are beginner books, six are intermediate books, and three are advanced books.
If two books are randomly chosen from the collection, one at a time, and replaced after each pick, what is the probability that he first chooses an advanced book and then chooses a beginner book?
StartFraction 5 Over 121 EndFraction
StartFraction 6 Over 121 EndFraction
Five-elevenths
Six-elevenths
Answers
The probability that from the 11 books Nico owns, he first chooses an advanced book before then choosing a beginner book, both book chosen with replacement is \(\dfrac{6}{121}\)
What is the probability of choosing with replacement?When the probability of choosing from a collection of items with replacement is being found, the number of options to choose from remain the same during each event.
The given information are;
The number of books Nico owns = 11
The number of beginner books = 2
The number of intermediate books = 6
The number of advanced books = 3
The required probability; That the first book chosen is an advanced book, and the second book chosen is a beginner book, both books chosen with replacement.
Given that the books are chosen with replacement, the probability remains the same after each book is chosen, which gives;
The probability that an advanced book is chosen is; \(P(A) = \dfrac{3}{11}\)
The probability that a beginner book is chosen = \(\dfrac{2}{11}\)
The probability that an advanced book and then a beginner book are chosen is given by \(P(A \cap B) = P(A) \times P(B)\)
Which gives: \(P(A \cap B) = \dfrac{3}{11} \times \dfrac{2}{11} = \dfrac{6}{121}\)
The probability that he first chooses an advanced book then chooses a beginner book is \(\dfrac{6}{121}\)
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Answer:
B
Step-by-step explanation:
Edge 2023 :')
Solve (u+2)^2+6=69 , where u is a real number.
Answers
Answer:
5.94 and -9.94
Explanation:
Use complete the square to answer the question and then type the last line into a calculator to get 5.94 and -9.94
What is the distance between the two endpoints in the graph below? if necessary, round your answer to two decimal places. (2,3) (-3,-2)
Answers
if y varies directly as x and y=32 when x=4. find the constant of variation
Answers
Answer:
k = 8
Step-by-step explanation:
Given that y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 32 when x = 4, then
32 = 4k ( divide both sides by 4 )
8 = k
What is the surface area of the rectangular prism below?
A. 736 units2
B. 812 units2
C. 706 units2
D. 824 units2
Answers
Answer:it’s A
Step-by-step explanation:
took the test
with a linear regression, what is the aim when choosing the model parameters (aka the slope and coefficient(s))?
Answers
The aim when choosing the model parameters:
Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line
The correct option is (b)
This is incomplete question
Complete question is this:
With a linear regression, what is the aim when choosing the model parameters (aka the slope and coefficient(s))?
Only use models that produce values of r = 1Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line Maximize the size of the residualsFind the best fit line that crosses the y- axis at x = 0Choose the correct option:
Now, According to the question:
Hence, The aim when choosing the model parameters:
Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line
The correct option is (b).
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Help pls
2 Answers and I can make brainliest whoever has the correct answer
Answers
Check the picture below.
so if we look at those dimensions in centimeters, let's get the area of the cross-section, keeping in mind the volume of the bar is simply the area of the cross-section times the length.
\(\stackrel{\textit{\Large area of the cross-section}}{(2)(15)cm^2~~ + ~~(2)(15)cm^2~~ + ~~(8)(2)cm^2\implies 76~cm^2} \\\\\\ \stackrel{\textit{\LARGE bar's volume}}{76cm^2\cdot 120cm\implies 9120~cm^3}\)
now, we know the density of the metal for the bar is 8 g/cm³, so let's do a quick conversion for the whole bar
\(\begin{array}{ccll} grams&cm^3\\ \cline{1-2} 8 & 1\\ g& 9120 \end{array} \implies \cfrac{8}{g}~~=~~\cfrac{1}{9120}\implies 72960=g\implies 72.960Kg\)
so if one bar has 72.960 Kg, how many bars are there in 250Kg?
\(\begin{array}{ccll} bars&Kg\\ \cline{1-2} 1 & 72.960\\ b& 250 \end{array} \implies \cfrac{1}{b}~~=~~\cfrac{72.960}{250} \\\\\\ 250=72.96b\implies \cfrac{250}{72.96}=b\implies 3.43\approx b\qquad \textit{so only \underline{three whole bars}}\)
the sampling distribution of a statistic refers to thegroup of answer choicesrange of all possible sample values of the statistic that could be drawn from the parent population under the specified sampling plan.distribution of the variable in the parent population.distribution of the variable in a particular sample.spread of the variable in the parent population.unbiased nature of most sample statistics.
Answers
Answer:
It is the distribution of the statistic if we were to draw all possible samples of a given size from the population and calculate the statistic for each sample.
Step-by-step explanation:
The sampling distribution of a statistic refers to the range of all possible sample values of the statistic that could be drawn from the parent population under the specified sampling plan.
In other words, it is the distribution of the statistic if we were to draw all possible samples of a given size from the population and calculate the statistic for each sample.
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What is the interest earned in a savings account for 12 months on a balance of $4000 of the interest rate is 1.5% APR compounded earlier
Answers
answer: 60.00
Based on the given conditions, formulate:: 4000x
((1.5%+1)12/12-1)
Evaluate the equation/expression:: 60
Round 60 to the required place rounding: 60.00
in general, a change in what causes a movement along a curve in the models we have studied? a change in what causes a shift in the curve?
Answers
In general, a change in the price of the product causes a movement along the demand curve; and a change in production cost and related factors causes a shift in the supply curve.
What is demand curve?The demand curve is a graphical representation of the relationship between the price of a good or service and the quantity demanded for a given period of time. In a typical representation, the price will appear on the left vertical axis of the graph, and the quantity demanded on the horizontal axis.
What is supply curve?The supply curve is a graphic representation of the relationship between product price and quantity of product which a seller is willing and able to supply. Product price is measured on the vertical axis of the graph, and the quantity of product supplied on the horizontal axis.
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last question...this is geometry. 15 points to whoever gets it right and can explain
Answers
which set includes rational numbers but not natural numbers?; are all rational numbers whole numbers; all real numbers are rational numbers; are natural numbers always/sometimes/never rational numbers; is a natural number; are integers irrational numbers; are integers rational numbers
Answers
Option 1 and 2 are the set that includes rational numbers but not natural numbers.
What are Natural numbers?
In arithmetic, the natural numbers are those numbers used for reckoning and ordering. Numbers used for counting are referred to as cardinal numbers, and numbers used for ordering square measure referred to as ordinal numbers.
Main body:
Given are the set of numbers,
Here, the sets (-6, -2, 5/11, 7/8) and (-5, -4, 4, 5) that includes rational numbers but not natural numbers.
Hence, Option 1 and 2 are the set that includes rational numbers but not natural numbers.
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Suppose that you are conducting a survey on how many pets each employee has in his or her household. The mean number of pets is 4 per household, and the standard deviation is 2. Rob only owns cats, and he has 10 of them. Which of the following statements is true? A. Rob's number of pets is 3 standard deviations to the left of the mean. B. Rob's number of pets is 3 standard deviations to the right of the mean. C. Rob's number of pets is 6 standard deviations to the left of the mean. D. Rob's number of pets is 6 standard deviations to the right of the mean.
Answers
Option B is correct, Rob's number of pets is 3 standard deviations to the right of the mean.
We need to calculate the number of standard deviations away from the mean Rob's number of pets is.
Given:
Mean (μ) = 4
Standard Deviation (σ) = 2
Number of pets owned by Rob = 10
To calculate the number of standard deviations (z-score) away from the mean, we use the formula:
z = (x - μ) / σ
where x is the value we want to measure.
For Rob's number of pets:
z = (10 - 4) / 2
z = 6 / 2
z = 3
Therefore, Rob's number of pets is 3 standard deviations to the right of the mean.
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A kite is gliding 74 feet above sea level. There is a stingray coasting 7 feet below sea level. What is the vertical distance between the kite and stingray.
Answers
The vertical distance between the kite and stingray is 81 feet.
Given that, a kite is gliding 74 feet above sea level. There is a stingray coasting 7 feet below sea level.
What is the vertical distance?Vertical distance or vertical separation is the distance between two vertical positions. Many vertical coordinates exist for expressing vertical position: depth, height, altitude, elevation, etc.
The vertical distance between the kite and stingray is
74-(-7)
= 74+7
= 81 feet
Therefore, the vertical distance between the kite and stingray is 81 feet.
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What is the equation of the line that passes through the point (1,7) and has a slope of −1?
Answers
Answer:
y = -x+8
Step-by-step explanation:
can you help me figure to how to get the answer to this question
Answers
Answer:
Step-by-step explanation:
scale factor=3/2
(8,6)
(12,6)
(12,10)
use formula
(x,y)=(kx,ky) (k means scale factor)
(8,6)=(3/2*8 , 3/*6)
=(24/2 , 18/2)
=(12 , 9)
(12,6)=(3/2*12 , 3/2*6)
=(36/2 , 18/2)
=(18 , 9)
(12,10)=(3/2*12 , 3/2*10)
=(36/2 , 30/2)
=(18 , 15)
Answer:
18 ,15
Step-by-step explanation:
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in a pet store, there are 6 puppies, 9 kittens, 4 gerbils and 7 parakeets. if puppies are chosen twice as often as the other pets, what is the probability that a puppy is picked?
Answers
The probability that a puppy is picked from the pet store is 0.375 or 37.5%.
To determine the probability of picking a puppy from the pet store, we need to take into account the relative frequency of puppies compared to the other pets.
According to the problem statement, puppies are chosen twice as often as the other pets. Therefore, we can assign a weight of 2 to each puppy and a weight of 1 to each of the other pets.
This means that the total weight of all the puppies is 6 x 2 = 12, while the total weight of all the other pets is (9+4+7) x 1 = 20.
To calculate the probability of picking a puppy, we need to divide the weight of all the puppies by the total weight of all the pets:
Probability of picking a puppy = Weight of all the puppies / Total weight of all the pets
= 12 / (12+20)
= 12 / 32
= 3 / 8
= 0.375
Therefore, the probability of picking a puppy from the pet store is 0.375 or 37.5%.
It's important to note that this probability assumes that all the pets are equally likely to be chosen, except for the fact that puppies are chosen twice as often.
If there are any other factors that could influence the likelihood of picking a certain pet, such as their position in the store or their visibility, this probability may not accurately reflect the true likelihood of picking a puppy.
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a table or spreadsheet used to systematically evaluate options according to specific criteria is a ________.
Answers
A table or spreadsheet used to systematically evaluate options according to specific criteria is a decision matrix.
A decision matrix is a table or spreadsheet used to systematically evaluate options based on specific criteria. It is a tool commonly used in decision-making processes to objectively assess and compare different choices.
The decision matrix organizes the criteria in rows and the options in columns. Each cell in the matrix represents the evaluation or score of an option based on a particular criterion. The criteria can be weighted to reflect their relative importance in the decision-making process.
By filling out the decision matrix with scores or ratings for each option and criterion, a comprehensive evaluation can be performed. The matrix allows decision-makers to visualize and compare the performance of different options against the criteria, helping them make more informed and structured decisions.
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if each of seven persons in a group shakes hands with each of the other six persons, then a total of forty-two handshakes occurs.
A. True
B. False
Answers
Answer:
B. False
Step-by-step explanation:
You want to know if it is true that when each of seven persons in a group shakes hands with each of the other six persons, a total of forty-two handshakes occurs.
HandshakesThe count of 42 handshakes includes every one of 7 shaking hands with each of the remaining 6, without regard to whether they met before.
The count will include A shaking hands with B, and B shaking hands with A. That handshake will be counted twice, so the number 42 overstates the actual number of handshakes by a factor of 2.
It is false that there will be 42 handshakes. (There will be only 21.)
The rectangle below has been enlarged by a scale of 3.5.
A rectangle with a length of 8 and width of 6.
[Not drawn to scale]
What is the area of the enlarged rectangle?
Answers
Answer:
588
Step-by-step explanation:
Got it right on Edgen
Answer:
588
Step-by-step explanation:
i took the test
Deux pays , le Pays Chaud et le Pays Froid, mènent des enquêtes sur les dépenses de consommation. Au Pays Chaud , les consommateurs achètent 60 bouteilles d'eau, 16 kilos de pain et 8 litres d'huile d'olive par année. Au Pays Froid, les consommateurs n'achètent aucune bouteille d'eau (ils sucent des glaçons qui ne leur coûtent rien), mais ils achètent 84 litres d'huile d'olive et 29 kilos de pain par année. Les prix dans les deux pays sont les mêmes, et mesurés avec la même monnaie, le dollar. Dans l'année de base, l'eau embouteillée coûtait 0,95 $ la bouteille, le pain,4,80$ le kilo, et l'huile d'olive,10,35 $ le litre. Dans l'année courante, l'eau embouteillée coûte 1,95 $ la bouteille, le pain,6,30 $ le kilo, et l'huile d'olive, 11,20 $ le litre. Quel est l'IPC au Pays Chaud dans l'année courante?