Graph the function and analyze it for domain, range, continuity, increasing or decreaseing behavior, symmetry, boundedness,
extrema, asymptotes, and end behavior.
f(x)=3•e^2x
Answers
A graph is a collection of points and the connections between some subset of those points that may or may not be empty in mathematical terms.
What are the values of the terminologies of the graph ?The given function is f (x ) = [tex]3e^{2x}[/tex]
1. Domain :
The function has no undefined points or domain constraints . Therefore the domain is -∞ < x < ∞ .2.Range :
The range of the exponential function is of the form f(x) > kSince k = 0, f(x) > 03.Continuity:
The graph is a single, continuous curve (i.e. a curve that can be drawn in one movement without taking your pen off the paper). We can observe that the function is basically continuous.4.Behaviour that is either increasing or decreasing:
For any x in the domain, as x grows, f(x) shrinks. This indicates that the function behaves in a diminishing manner.5.Symmetry:
It is clear to see the graph of f(x) has no symmetry.6.Boundedness:
When we choose negative values, the graph of f(x) expands upward exponentially, showing that it is unbounded above.7.Extrema:
There are no extreme points for the function.8.Asymptotes:
This curve does not have any vertical asymptotes, despite the way it seems. Simply put, the curve's negative-x region is expanding so swiftly that it resembles an asymptote. For any x < 0, there is a value for f(x). However, a horizontal asymptote exists , y = 0.9.End behaviour :
As [tex]\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty[/tex] As,[tex]\:x\to \:-\infty \:,\:f\left(x\right)\to \:0[/tex]Refer image for graph.To learn more about Asymptotes , refer:
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Related Questions
a tower that is 124 feet tall casts a shadow 138feet long. find the angle of elevation of the sun to the nearest degree.
Answers
The angle of the elevation comes to be 41.94 degrees.
What is Angle of Elevation ?The angle of elevation is the angle that is to be formed between the horizontal line and the given line of sight. If the line of sight is upward from the given horizontal line, then the angle formed is an angle of the elevation.
What is Trigonometry ?The most crucial area of mathematics is trigonometry. Combining the Greek "Trigonon" and "Metron," which respectively mean "triangle" and "measure," creates the word "trigonometry." It is the examination of the relationship between a right-angled triangle's sides and angles. By employing formulas and identities based on this relationship, it is thus possible to determine the measure of a right-angled triangle's unknown dimensions.
As in the case of right angled Triangle
From Trigonometry,
tan (α) = [tex]\frac{124}{138}[/tex]
α = arctan( [tex]\frac{124}{138}[/tex] )
α = 41.94 degrees
and in radians = 0.732
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STEP BY STEP please help me asap please !!!???
Answers
Answer:
(A) 19 times, 16 people.
Step-by-step explanation:
There are 374 people in line and 16 people leave the line without riding, so there are 374 - 16 = <<374-16=358>>358 people who want to ride the Caterpillar.
The Caterpillar seats 18 people, so it must run 358/18 = <<358/18=19.89>>19.89 times to accommodate all the riders.
Since the Caterpillar cannot run a fraction of a time, it must run 19 times.
There are 358 people who want to ride and the Caterpillar can accommodate 19 x 18 = <<19*18=342>>342 of them, so there are 358 - 342 = <<358-342=16>>16 people on the last ride.
Therefore, the Caterpillar runs 19 times and there are 16 people on the last ride, so the answer is (A) 19 times, 16 people.
Tell me if this helped :)
A cereal box says that now it contains 20% more originally it came with 18.5 ounces of cereal how much cereal does the box come with now
Answers
Answer:
Step-by-step explanation:
Step-by-step explanation: the original weight of a cereals is ounces. Now according to question, new weight of cereals is more of original weight of cereals. Therefore, New weight of cereals will be formulated as Hence, the new weight of cereals is ounces.
Given 4 and one tenth times negative 4 times 5 over 12, determine the product.
Answers
The word problem 4 and one tenth times negative 4 times 5 over 12 have a product of negative 8 and one fifth
How to find the product of the word problemMultiplication is one of the basic mathematical operator which is used to solve the given problem. It is the inverse of division. the result of multiplication is called the product
Rewriting the word problem 4 and one tenth times negative 4 times 5 over 12 to figures
4 1/10 * -4 * 5/10
solving the equation
= 4 1/10 * -4 * 5/10
= 41/10 * -4 * 5/10
= -41/5
= -8 1/5
The product of the multiplication is negative 8 and one fifth
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you're selling vegetarian sandwiches for $3 each and turkey sandwiches for $4 each. you sell 25 sandwiches for a total of $85. how many vegetarian and how many turkey sandwiches did you sell
Answers
Answer:
You sold 15 vegetarian sandwiches and 10 turkey sandwiches.
Step-by-step explanation:
First, let's call the number of vegetarian sandwiches sold "V" and the number of turkey sandwiches sold "T".
We can set up the following equation: 3V + 4T = 85
Next, we need to find the values of V and T that satisfy this equation. To do this, we can use the fact that V and T must be whole numbers since we cannot sell a fraction of a sandwich.
We can start by trying V = 1 and T = 6. Plugging these values into the equation, we get: 3(1) + 4(6) = 18 + 24 = 42
Since 42 is not equal to 85, this means that V and T cannot both be 1 and 6.
We can try other values of V and T that are whole numbers until we find a combination that satisfies the equation. One way to do this is to use trial and error.
For example, we can try V = 2 and T = 5, which gives us: 3(2) + 4(5) = 6 + 20 = 26 This is still not equal to 85, so we can try other values. We can also use the fact that V + T = 25 (since we sold a total of 25 sandwiches) to help us solve the equation.
If we set V + T = 25, then we can rewrite the original equation as: 3V + 4(25 - V) = 85 Solving for V, we get: 3V + 100 - 4V = 85 Combining like terms, we get: -V = 15 Dividing both sides by -1, we get: V = 15
Since V + T = 25, this means that T = 25 - 15 = 10
Therefore, we sold 15 vegetarian sandwiches and 10 turkey sandwiches.
!!30 Points, Pls help ASAP!!
Divide using synthetic division
x^4 – 3x^3 – 7x + 1 ÷ x + 2
Answers
The quotient of x⁴ – 3x³ – 7x + 1 ÷ x + 2 is x³ - 5x² + 3x and the remainder is 5
How to perform the synthetic division?From the question, we have the following parameters that can be used in our computation:
x^4 – 3x^3 – 7x + 1 ÷ x + 2
Rewrite as
x⁴ – 3x³ – 7x + 1 ÷ x + 2
This means that
Divisor = x + 2
Dividend = x⁴ – 3x³ – 7x + 1
Using the synthetic division, we have the following setup
-2 | 1 -3 -7 1
Bring down the first factor
-2 | 1 -3 -7 1
1
Multiply by -2
-2 | 1 -3 -7 1
-2
1
Repeat the above steps as follows
So, we have
-2 | 1 -3 -7 1
-2 10 -6
1 -5 3 5
The last number represents the remainder of the division
This means that
Remainder = 5
Quotient = x³ - 5x² + 3x
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suppose that a product is designed to function for 10,000 hours with a 3% chance of failure. find the average number of failures per hour and the mttf.
Answers
A product is designed to function for 10,000 hours with a 3% chance of failure , then Average number of failures per hour = 0.03/10000 = 0.000003 and MTTF = 1/0.000003 = 333,333 hours
Given,
Chance Product is designed to function for 10,000 hours
of failure is 3%
To find,
Average number of failures per hour
MTTF
Solution,
Average number of failures per hour = Chance of failure/Total hours of function
= 3%/10000
= 0.03/10000
= 0.000003
MTTF = 1/Average number of failures per hour
= 1/0.000003
= 333,333 hours
The product is designed to function for 10,000 hours with a 3% chance of failure. This means that the average number of failures per hour is 0.000003 and the Mean Time To Failure (MTTF) is 333,333 hours. This means that, on average, the product should last 333,333 hours before it fails.
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yes Are these polygons congruent? 1.5 cm 4 cm 3 cm no 2 cm
Answers
This is because in order to be congruent, the sides need to be the same lengths
3 ^ 21 is how many time as great value of 3 ^ 19
Answers
The exponent [tex]3^{21}[/tex] is 9 times greater than the exponent [tex]3^{19}[/tex]
What are Exponents?
Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself.
Solution:
To solve this type of question all we need to know are the Rules of Exponents with their help any question of this type can be solved
Since we are required to find the number of times the value os greater so we will divide the numbers
3^21 / 3^19
By rule of exponents if a^b/a^c then we can write it as a^(b-c)
Similarly 3^21 / 3^19 = 3^(21 - 19) = 3^2 = 9
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Need help and fast please and thank you.
y= 0.141(15) + 0.842 =
Answers
y = 2.115 + 0.842
= 2.957
no explanation
Tommy is flying his kite one afternoon and notices that he has let out
the entire 130 ft of string. The angle his string makes with the ground
is 48°. How high, to the nearest foot, is his kite at this time?
Answers
If Tommy is flying his kite one afternoon and notices that he has let out
the entire 130 ft of string. The height , to the nearest foot, is his kite at this time is : 144 ft.
How to find the height?Given data:
String = 130 ft
Angle = 48°
Let h represent the height
Hence,
Tan48° = h/130
h= 130 tan48°
h = 130 (1.11061251483)
h = 144 ft
Therefore we can conclude that the height is 144ft.
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A pool has some initial amount of water in it. Then it starts being filled so the water level rises at
a rate of 6 centimeters per minute. After 20 minutes, the water level is 220 centimeters.
Graph the relationship between the pool's water level (in centimeters) and time (in inches minutes).
Answers
Answer:
To graph the relationship between the pool's water level and time, we can start by creating a table of values for the water level at different times. Here is an example of such a table:
Time (minutes) Water Level (centimeters)
0 0
1 6
2 12
3 18
4 24
5 30
6 36
7 42
8 48
9 54
10 60
11 66
12 72
13 78
14 84
15 90
16 96
17 102
18 108
19 114
20 120
We can then plot these values on a graph, with the time on the x-axis and the water level on the y-axis. The resulting graph would be a straight line that slopes upwards, starting at the origin (0, 0) and ending at (20, 120).
The graph shows that the water level in the pool increases linearly with time. The slope of the line represents the rate at which the water level is increasing, which in this case is 6 centimeters per minute.
Step-by-step explanation:
An isosceles triangular prism has a triangular
end with a base of 16 feet, an altitude of 6 feet,
and a side length of 10 feet. The height of the
prism is 18 feet. What is the surface area of the
prism?
a- 520
b- 850
c- 744
d- 635
Answers
An isosceles triangular prism, its surface area becomes: 568 feet²
What is an isosceles triangular prism?The faces of a polyhedron called an isosceles triangular prism are made up of polygons. It has six edges, five faces, and five vertices. Isosceles triangles make up the two portions at the base that face each other and rectangles make up the vertical faces of the five faces.
where the isosceles triangle's base has equal sides measured in "a" units, each triangle's base measured in "b" units, the triangle's height measured in "h" units, and the length of the congruent rectangles measured in "l" units.
The surface area of an isosceles triangular prism is:
Surface area = (b × h) + (2× l × a) + (l × b)
here, b = the base of each of the triangle = 16 feet
h = the height of the triangle = 18 feet
l = length of the congruent rectangles = 10 feet
a = isosceles triangle in the base have the equal sides be "a" units = 6 feet
Now, Surface area = (16 × 18) + (2 × 10 × 6) + (10 × 16)
or, Surface area = 568 feet²
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Which equation is represented by the graph below
Answers
Answer: pls show list of equations
Step-by-step explanation:
Find the value of a if the line line y=-x+4 is tangent to the graph of f(x) = x^2 - 5x +a
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
If the line y=-x+4 is tangent to the graph of f(x) = x^2 - 5x + a, it means that the line and the graph of the function are just touching at a single point, and are not intersecting at any other points.
To find the value of a, we can start by setting the equation for the line and the equation for the function equal to each other:
y = -x + 4
f(x) = x^2 - 5x + a
Then, we can substitute the equation for the function into the equation for the line:
-x + 4 = x^2 - 5x + a
We can then solve this equation for a by moving all the terms to one side:
-x + 4 - x^2 + 5x = a
-x^2 + 6x - 4 = a
We can see that the left-hand side of this equation is a quadratic expression in x, and we know that a quadratic function is tangent to a line when the line is a horizontal tangent. This occurs when the derivative of the function is equal to the slope of the line.
The derivative of f(x) = x^2 - 5x + a is 2x - 5, so we can set this equal to the slope of the line, which is -1:
2x - 5 = -1
2x = -6
x = -3
Now that we know the value of x, we can substitute it back into the equation for the function to find the value of a:
f(-3) = (-3)^2 - 5(-3) + a
f(-3) = 9 + 15 + a
f(-3) = 24 + a
Since the line and the function are just touching at this point, the y-value of the function at x=-3 must be equal to the y-value of the line at x=-3. We can substitute these values into the equation for the line to find the value of a:
y = -(-3) + 4
y = 3 + 4
y = 7
Substituting this back into the equation for the function, we get:
f(-3) = 24 + a = 7
a = 7 - 24
a = -17
Therefore, the value of a is -17.
what do you mean by tangent?
A tangent is a line that touches a curve at a single point, but does not intersect the curve at any other points. In other words, it is a line that is just "skimming" the curve, rather than crossing it.
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Ma Baker's Pies charges $12 for a pumpkin pie and $14 for an apple pie. Last week, they sold a third as many pumpkin pies as apple pies, for a total of $5,400. How many pumpkin pies were sold last week?
20 POINTS!!!!
Answers
The Ancient Egyptians were the first to invent a dish close to what we know as a pie today. They had a honey filling covered in a crusty cake made from oats,
Who was the first American author of a recipe for pumpkin pie?This type of pie appears to have been made by some of the early colonists as well—but, by 1796, when Amelia Simmons' American Cookery, the first cookbook written by an American and published in America, appeared, pumpkin pie had evolved into a familiar form that we would recognize today.The cost of one apple pie = $6They stewed pumpkins or filled a hollowed out pumpkin shell with milk, honey and spices, and then baked it in hot ashes. Northeastern Native American tribes grew squash and pumpkins. The Native Americans brought pumpkins as gifts to the first settlers, and taught them the many uses for pumpkin.Types of squashes were first introduced to Europe in the form of Pumpkin seeds brought back from the Americas by Columbus himself. The introduction of pumpkins affected the way food was consumed in Europe. In both Italy and Spain, pumpkins were used in puddings and soups, making food much tastier and more enjoyable.And cost of one pumpkin pie = $8
Let the cost of one apple pie be $x
And cost of one pumpkin pie be $ y.
According to given problem,
For Lisa : sold 8 apple pies and 4 pumpkin pies for a total of $80
8x + 4y = 80 ------------(1)
For Shreya : sold 8 apple pies and 3 pumpkin pies for a total of $72
8x + 3y = 72 ---------------(2)
Solving equation (1) and (2), to get x and y.
Subtract equation (2) from equation (1)
i.e 8x + 4y - (8x +3y) = 80 - 72
or 8x - 8x + 4y - 3y = 8
or y = 8
And x = 6 { 8x + 4×8 = 80 or x = (80 - 32)/8 = 48/8 = 6 }
Hence, the cost of one apple pie = x = $6
And cost of one pumpkin pie = y =$8
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2 √ 3 + 3 √ 3 can you help me solve this equation in simplest form
Answers
The simplest form of [tex]2\sqrt{3} + 3\sqrt{3}[/tex] is found to be 8.66025403784 .
What is the simplest form of a equation ?A fraction is in its simplest form when the numerator and the denominator have no common factors besides one.
Reducing equation is a method of rewriting the equation in a simpler form. Certain equations in mathematics are not in the form of linear equations but they can be put in the form of linear equations by performing some mathematical operations on them. After reduction of these equations in linear form they can be solved and the value of unknown can be calculated easily.
Given the equation is;
[tex]2\sqrt{3} + 3\sqrt{3}[/tex]
Now solving it ,
[tex]2\sqrt{3} + 3\sqrt{3}[/tex]
By adding this we get,
[tex]5\sqrt{3}[/tex] (∵ [tex]\sqrt{3}[/tex] is common in both )
= 8.66025403784
The decimal (or) simplified value of [tex]2\sqrt{3} + 3\sqrt{3}[/tex] is 8.66025403784.
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a car and a motorcycle leave at noon from the same location, heading in the same direction. the average speed of the car is mph slower than twice the speed of the motorcycle. in two hours, the car is miles ahead of the motorcycle. find the speed of both the car and the motorcycle, in miles per hour.
Answers
The speed of car is 50 miles per hour and the speed of the motorcycle is 40 miles per hour.
Let M = speed of the motorcycle.
Hence, speed of the car = 2M - 30.
Distance covered = Time taken x Speed.
Hence in 2 hours,
Distance covered by motorcycle = 2M
Distance covered by car = 2(2M-30).
Given, the car is 20 miles ahead of the motorcycle.
Hence,
2(2M-30) = 2M + 20
4M-60 = 2M + 20
2M = 80
M = 40
2M-30 = 2(40)-30 = 80-30 = 50
Therefore, speed of motorcycle is 40 miles per hour and speed of car is 50 miles per hour.
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Part A: Given the function g(x) = |x-5 ,describe the graph of the function, including the vertex, dom
Part B: If the parent function f(x) = |x| is transformed to h(x) = |x| + 3, what transformation occurs from
Answers
The vertex domain of g(x)=|X-7| is (7,0) (-∞,∞) and (0,∞) and the function f(x)=|x| is vertically shifted.
What is graph of the function?In mathematics, the set of ordered pairs with the (x,y)(x,y) is known as the graph of a function, where f(x)=y. x and f are Cartesian coordinates of points in two-dimensional space, and in the typical scenario where they are real numbers, they constitute a subset of this plane.Instead of the pairs ((x,y),z) and ((x,y),z) as in the definition above, the graph for functions of two variables, i.e. functions whose domain consists of pairs (x,y), (x,y), is typically the set of ordered triples (x,y,z) and (x,y,z) where A surface for a continuous real-valued function of two real variables, this set is a subset of three-dimensional space.Hence, The vertex domain of g(x)=|X-7| is (7,0) (-∞,∞) and (0,∞) and the function f(x)=|x| is vertically shifted.
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Graph the line −2x − 3y = 12.
The graph shows a line through the points 0 comma 4 and 6 comma 0.
The graph shows a line through the points 0 comma negative 4 and 6 comma 0.
The graph shows a line through the points 0 comma 4 and negative 6 comma 0.
The graph shows a line through the points 0 comma negative 4 and negative 6
Answers
Answer:
its d I did the test hope its helps
Nick has two pet rabbits.His Flemish giant rabbit weighs 5 times as much as his Holland lop rabbit,If nich's Flemish rabbit weighs 12 more pounds than his Holland lop rabbit,how much does his Flemish giant rabbit weight?
Answers
Answer:The Flemish giant rabbit weighs 32 pounds.
Step-by-step explanation:
one number is 431 more than the other, their sum is 679, find the two numbers
Answers
Answer:
Step-by-step explanation:
Let's call the two numbers x and y. We can set up the following equation to represent the problem:x + y = 679y = x + 431Substituting the second equation into the first equation, we get:x + (x + 431) = 679Combining like terms, we get:2x + 431 = 679Subtracting 431 from both sides, we get:2x = 248Dividing both sides by 2, we get:x = 124Substituting this value back into the equation y = x + 431, we get:y = 124 + 431 = 555Therefore, the two numbers are 124 and 555.
write an equation in slope-intercept form for the line that passes through (9,12) and is parallel to y=4
Answers
An equation in slope-intercept form for the line that passes through (9,12) and is parallel to y=4 is y= 4x -24.
What is Parallel lines?
Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.
Parallel lines will have the same slope but different y-intercepts so again we can use the coordinates to determine the y intercept of the new equation.
So we know that the slope intercept formula is y=mx + b where m is the slope and b is the y-intercept so we will input the x and y coordinates to solve for b.
12 = 4(9) + b
12 = 36 + b
b = -24
The equation will be y= 4x -24.
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Select the equation for the line crossing the points (3,¹/2) and (5,5).
Answers
The equation of the line is (b) y = 2.25x - 6.25
How to determine the equation of the lineFrom the question, we have the following parameters that can be used in our computation:
Points = (3, 1/2) and (5, 5)
A linear equation can be represented as
y = mx + c
Substitute the known values in the above equation, so, we have the following representation
1/2 = 3m + c
5 = 5m + c
Subtract the equations
2m = 4.5
Divide by 2
m = 2.25
Substitute m = 2.25 in 5 = 5m + c
5 = 5 * 2.25 + c
So, we have
c = 5 - 5 * 2.25
Evaluate
c = -6.25
Recall that
y = mx + c
So, we have
y = 2.25x - 6.25
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Complete question
Select the equation for the line crossing the points (3,1/2) and (5,5).
(a) y = 5x + 2
(b) y = 2.25x - 6.25
(c) y = 2.25x + 6.25
(d) y = -5x - 2
Solve the equation -3.5(x-14)+9x=5.5x + 49. Which statement is true ?
Answers
Answer:
Step-by-step explanation:
Answer:
-3.5(x-14)+9x=5.5x + 49 is a TRUE statement that equals 0. It has infinite solutions.
Step-by-step explanation:
k3-4j=12,wen k =8,j=2
Answers
With the Application of Arithmetic operators the value of given equation is 492.
what is Arithmetic operators?
an operator that works with groups and numbers in arithmetic. The prefix and the binary plus (+) and minus (-) symbols are the only arithmetic operators in AHDL that are supported for Boolean expressions.
solution:
sub k =8,j=2 in equation k^3-4j = 12
Therefore, (8)^3 - 4 (2) = 12
512 - 8 - 12 = 0
492 is the value.
Therefore the value of given equation is 492
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Complete Question:
What Is The Answer
k3 - 4j +12, when k=8, j=2
Please help asap ill give brainlest
Answers
The solutions to the equation word problems are as follows;
1) Amount jane will have is 50 + 2d
2) Amount Elis will have = 24 + 6d
3) The equation is; 50 + 2d = 24 + 6d
4) Amount each has saved = $63
How to solve Algebra Word Problems?We are given that;
Amount Jane has = $50
Amount Elis has = $24
Amount saved by Jane each day = $2
Amount saved by Elis each day = $6
1) After d days of saving, amount jane will have is;
A = 50 + 2d
2) After d days of saving, amount Elis will have is;
A = 24 + 6d
3) The equation that will be used to show when Joan and Elis would have saved same amount is;
50 + 2d = 24 + 6d
4) 50 + 2d = 24 + 6d
26 = 4d
d = 26/4
d = 6.5 days
Amount each has saved = 50 + 2(6.5) = $63
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Identify the slope and y-intercept of each linear function's equation. X -3=4 slope = 1; y-intercept at -3 y=1-3x slope =-3; y-intercept at 1 y = 3x. - 1 slope =-1; y-intercept at 3 -x+3=y slope = 3; y-intercept at -1
Answers
Using slope-intercept form, the slope and y-intercept of the equation are 1 and - 7 respectively
Slope and Y-interceptThe slope-intercept formula is often used to calculate or identify the slope, the y-intercept, the x-intercept, or the equation of a straight line in the equation.
The slope of the line is defined as the rate of change of the y - axis to the change in the x - axis.
The formula is represented as;
m = Δy / Δx
where Δ represent the change
The y-intercept of a line is the point at which the line touches the y-axis of the graph.
With these information, we can write a slope-intercept form of a straight line which is given as;
y = mx + c
m = slopec = y-interceptIn the given question;
x - 3 = 4
Let's collect like terms
x - 3 - 4 = x - 7
The equation can be rewritten as y = x - 7
In this case, the slope is 1 and the y-intercept is - 7
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Use arrow notation to describe the translation of point P(–10, 1) to point P′(–16, –1).
Answers
Answer: In order to describe a translation using arrow notation, we need to specify the direction and distance of the translation. In the case of the given translation, point P is translated to point P' by moving 6 units to the left and 2 units down. This can be represented using arrow notation as follows:
P' = P ← 6 ↓ 2
Here, the symbol ← represents a leftward movement, and the symbol ↓ represents a downward movement. The numbers 6 and 2 indicate the distance of the movement in the respective directions. This means that point P is translated to point P' by moving 6 units to the left and 2 units down from its original position.
Water is flowing into a tank at a rate of R(t) where t is measured in seconds. Is there ever a time where the R'(t) = 0? If so, what time interval does t occur in? Justify your answer using the Mean Value Theorem. t R(t) 0 70 1 72 2 78 3 80 4 83 5 78 6 82
Answers
On solving the provided question, we can say that - by equation, total amount of water removed was = 1.R(0) + 2.R(1) + 3.R(3) = 1(1340) + 2(1190) + 3(950) + 2(740) = 8050 liters
What is equation?An equation is a mathematical formula that expresses equality by joining two expressions together with the equal symbol =. A formula that claims two formulae are equal is the definition of an equation in algebra in its most basic form. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. An equal sign is a part of all mathematical formulas, including equations. Often, algebra is used in equations. In mathematics, algebra is employed when we don't know the precise quantity to calculate.
R'(2) = R(3) - R(1) /3-1 = 950-1190/2 = /120L/hr
total amount of water removed was = 1.R(0) + 2.R(1) + 3.R(3) = 1(1340) + 2(1190) + 3(950) + 2(740) = 8050 liters
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