Answer:
-6
Step-by-step explanation:
3x * 2 = 6x - 1 = -6
The required result of the given expression is 2x - 5.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now the given expression is,
Add 3 to x, double what you have, then subtract 1
So, we can write,
Add 3 to x = 3 + x
Double = 2(3 + x)
Subtract from = 1 - 2(3 + x)
Simplifying we get,
1 - 6 + 2x
solving we get,
1 - 6 + 2x = 2x - 5
this is the required result.
Thus, the required result of the given expression is 2x - 5.
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Eight pounds of peanuts cost $24.00. Six pounds of walnuts cost half as much.
Which is more expensive and by how much?
Answer:
24 is more expensive by $18.00
Step-by-step explanation:
Answer:
The eight pounds of peanuts are more expensive, by $1.
Step-by-step explanation:
If eight pounds of peanuts cost $24.00, then one pound of peanuts costs $24.00/8 = $3.00.
If six pounds of walnuts cost $12.00 (half as much), then one pound of walnuts costs $12.00/6 = $2.00.
A store sells white scarves and red scarves.
• A white scarf costs $3.
• A red scarf costs $5.
On Monday, the store sold 12 scarves for a total of $50.
The store sold 7 red scarfs and 5 white Scarfs
5+5+5+5+5+5+5+3+3+3+3+3=50
This Maths question involves formation and solution of a system of equations, where equations are representing the number and total cost of scarves sold. The variables used are 'w' for white scarves and 'r' for red scarves, forming two equations: w + r = 12, and 3w + 5r = 50.
Explanation:This question can be approached by using a system of equations. A system of equations is a set of two or more equations that have the same variables. You can think of this problem as having two equations:
The total number of scarves (both white and red) sold is 12.The total amount made from selling all the scarves is $50.
Let's represent the number of white scarves sold as 'w' and the red scarves sold as 'r'. So, our first equation would become: w + r = 12
And knowing the cost of each scarf, the second equation would be: 3w + 5r = 50
Now with these two equations, one can solve for 'w' and 'r'. This type of problem is often seen in algebra and is an example of linear equations.
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Which pairs of angles are congruent because they are vertical angles? Check all that apply.
◽Angle 1 and Angle 4
◽Angle 14 and Angle 12
◽Angle 7 and Angle 8
◽Angle 10 and Angle 8
◽Angle 3 and Angle 5
◽Angle 8 and Angle 12
Answer:
◽Angle 14 and Angle 12
◽Angle 10 and Angle 8
Step-by-step explanation:
Vertical angles are opposite to each other on a pair of intersecting lines.
◽Angle 1 and Angle 4
These angles are not on the same two intersecting lines.
◽Angle 14 and Angle 12
These angles are on the same two intersecting lines. They are also opposite to each other.
◽Angle 7 and Angle 8
These angles are on the same intersecting lines, but they are not opposite to each other.
◽Angle 10 and Angle 8
They are on the same pair on lines, and opposite to each other.
◽Angle 3 and Angle 5
They are not on the same pair of intersecting lines.
◽Angle 8 and Angle 12
These angles are not on the same pair on intersecting lines. (However, they are also equal because they are corresponding, on the insides of an "F" pattern).
Answer:
A and D
Step-by-step explanation:
Edge 2020
If you erased 1/4 of the shaded part below. How much of the original figure will be shaded?
Answer:1/2
Step-by-step explanation: i dont really have a explanation but its right
Step-by-step explanation:
uhhh link an image please?
3x+3=2x+1 what is the value of x
Answer:
Answer: 3x + 3 = 2x + 1
Answer: 3x + 3 = 2x + 1 <=>3x - 2x = 1 - 3
Answer: 3x + 3 = 2x + 1 <=>3x - 2x = 1 - 3 <=> x = -2
Find the missing value in the ratio table
Answer: y-value=36
Step-by-step explanation:
If you take the unit rate of these set of numbers, (it can be any set of the numbers on the table), let's use 2 and 12. To find the unit rate all you have to do is divide. 12 divided by 2 is 6. This also works for 4 and 24. 24 divided by 4 is 6. Therefore 6 times any number in the x column will give you the y-value.
Plugging in the unit rate would look look this 6(6)=y
36=y
Therefore your missing value, or the y-value that is not filled in would be 36.
Compared with the rest of Europe, northern Italy had many
churches.
cities.
farms.
forests.
Step-by-step explanation:
compared with the rest of Europe northern Italy had many cities
When compared with the rest of Europe, one will notice that Northern Italy has a lot of cities.
The Northern part of Italy is much more developed than the South and is so developed that it has one of the highest rates of developments in all of Europe.
This is due to the high density of cities located there such as:
Milan Genoa Turin Venice etcThere are about 23 cities in Northern Italy alone which leads us to conclude that in Europe, Northern Italy has one of the highest number of cities.
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Write 144 as a product of primes.
Use index notation where appropriate
Answer:
144=2x2x2x2x3x3
Step-by-step explanation:
Answer:
[tex]2^4\cdot3^2[/tex]
Step-by-step explanation:
The first step is to break this down. 144=12^2 or 12*12. Now you can break down 12. 12=4*3=2*2*3. This means that 144=2*2*3*2*2*3=[tex]2^4\cdot3^2[/tex]. Hope this helps!
The perimeter of a rectangle is 35 cm. The rectangle s area in sq. cm) as a function of its length (in cm) is
graphed
What is the approximate average rate at which the area decreases, as the rectangle's length goes from 13 cm
to 16 cm?
Answer: 11 1/3
Dhdgdhdhd
To find the rate at which the area of the rectangle decreases as its length changes, use the formula for the area of a rectangle and evaluate the area at the two lengths. Then, calculate the average rate of decrease by taking the change in an area divided by the change in length.
Explanation:The problem involves understanding the properties of rectangles and how the changes in one dimension (length in this case) can affect another (area). Let's consider a rectangle with a perimeter of 35 cm. If 'L' is the length and 'W' is the width, the perimeter = 2*(L+W) which equals 35 cm.
Next, we figure out that W= 17.5 - L as we isolate W in the equation. The area of the rectangle is then given by A = L * W = L * (17.5 - L). If we plug in L = 13 cm and L = 16 cm, we get two area values. The decrease in area ΔA = A2 - A1.
Finally, the average rate of change, or the rate at which the area decreases, as the length goes from 13 cm to 16 cm is calculated by ΔA / ΔL.
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What is the height of a cylinder with a base area of 12 cm squared and a volume of 144 cubic cm?
Answer:
12
Step-by-step explanation:
h = V / A
Height equals volume divided by (base) area.
144 / 12 = 12
The height of the cylinder is 12 cm.
To find the height of the cylinder, we can use the formula for the volume of a cylinder, which is given by:
[tex]\[ V = B \times h \][/tex]
where [tex]\( V \)[/tex] is the volume, [tex]\( B \)[/tex] is the base area, and [tex]\( h \)[/tex] is the height of the cylinder.
Given that the base area [tex]\( B \)[/tex] is 12 cm² and the volume [tex]\( V \)[/tex] is 144 cm³, we can solve for the height [tex]\( h \)[/tex] by rearranging the formula:
[tex]\[ h = \frac{V}{B} \][/tex]
Substituting the given values:
[tex]\[ h = \frac{144 \text{ cm}^3}{12 \text{ cm}^2} \][/tex]
[tex]\[ h = 12 \text{ cm} \][/tex]
Therefore, the height of the cylinder is 12 cm.
A random sample of people was asked to report the age and distance driven of their primary car. A line was fit to the data to model the relationship.
Answer:
y= 12x + 5 for part A, part B is 89 thousand miles
Step-by-step explanation:
Just copy the answer you nerd.
a statistics professor finds that when she schedules an office hour for student help, an average of 2.4 students arrive. find the probability that in a randomly selected office hour, the number of student arrivals is 2
Answer:
P=0.2613
Step-by-step explanation:
-Notice that this is a poison probability distribution problem.
-The Poisson probability function is expressed as:
[tex]P(X=x)=\frac{\lambda^x e^{-\lambda}}{x!}[/tex]
where:
x=0,1,2,3[tex]e[/tex] Euler's constant[tex]\lambda[/tex] =mean number of occurrences.Given that x= 2 and [tex]\lambda=2.4[/tex], the probability is calculated as:
[tex]P(X=2)=\frac{\lambda^xe^{-\lambda}}{x!}\\\\=\frac{2.4^2e^{-2.4}}{2!}\\\\\\=0.2613[/tex]
Hence, the probability that in a randomly selected office hour, the number of student arrivals is 2 is 0.2613
Final answer:
To find the probability that in a randomly selected office hour, the number of student arrivals is 2, we can use the Poisson distribution. The average number of student arrivals is 2.4.
Explanation:
To find the probability that in a randomly selected office hour, the number of student arrivals is 2, we can use the Poisson distribution. The average number of student arrivals is 2.4, so the parameter λ for the Poisson distribution is 2.4.
The probability of getting exactly 2 student arrivals can be calculated using the formula:
P(X=k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of student arrivals, k is the desired value (2 in this case), and λ is the average number of student arrivals per office hour.
Calculate e^-λ: e is the base of the natural logarithm and λ is 2.4. e^-2.4 ≈ 0.0908.
Calculate λ^k: 2.4^2 ≈ 5.76.
Calculate k!: 2! = 2.
Plug in the calculated values into the formula: P(X=2) = (0.0908 * 5.76) / 2 ≈ 0.2613.
So, the probability that in a randomly selected office hour, the number of student arrivals is 2 is approximately 0.2613 or 26.13%.
Select the correct answer.
Which sequence of transformations proves that shape I is similar to shape II?
Answer:
c
Step-by-step explanation:
im not explaining im taking the test
The quality control team of a company checked 800 digital cameras for defects. The team found that 20 cameras had lens defects, 25 cameras had charging defects, and 6 cameras had both defects. What is the probability that a camera has a lens defect given that it has a charging defect?
Answer:
6/25
Step-by-step explanation:
Given two events A and B, the conditional probability of event A is the probability that event A occurs given that event B has occurred. It is calculated as
[tex]p(A|B)=\frac{p(A\cap B)}{p(B)}[/tex]
where
[tex]p(A\cap B)[/tex] is the probability that both A and B occur at the same time
[tex]p(B)[/tex] is the probability that B occurs
In this problem, we call:
A = the camera has a lens defect
B = the camera has a charging defect
Here we have:
a = 20 is the number of cameras with lens defects
b = 25 is the number of cameras with charging defects
c = 6 is the number of cameras having both defects
n = 800 is the total number of cameras
So we have:
[tex]p(A\cap B)=\frac{c}{n}=\frac{6}{800}[/tex] is the probability that the camera has both lens and charging defect
[tex]p(B)=\frac{b}{n}=\frac{25}{800}[/tex] is the probability that the camera has a charging defect
So the conditional probability is
[tex]p(A|B)=\frac{6/100}{25/100}=\frac{6}{25}[/tex]
Why is the value of x limited to 0 in. < x < 4.25 in.?
Answer:
Lengths can't be negative
Step-by-step explanation:
Dimensions of the base are:
(8.5-2x) × (11 - 2x)
Since length cannot be negative:
x > 0
8.5 - 2x > 0
2x < 8.5
x < 4.25
11 - 2x > 0
x < 5.5
The set of values of x which satisfies all is:
0 < x < 4.24
-5x -4y = -15 and -x + 4y = -3
So the first thing you would want to do is rewrite the equation like so.
−x+4y=−3;−5x−4y=−15
once you done that you'll have to think about what variable are you trying to get be itself which in this case it'll be x. So now you'll be solving this equation.
−x+4y=−3
next you'll add -4y to both sides
Once you done so you should have this written down
-x over -1 = 4y- 3 over -1
divide -1 to both sides and you should end up with x= 4y+3
Now you have to substitute 4y+3 for x in -5x-4y=-15
So it should look like this now
−5(4y+3)−4y=−15
The next step is to simplify both sides with the following equation
−24y−15=−15
After simplifying add 15 to both sides, It then should look like this
−24y=0
Divide -24 to both sides and your answer should be this
y=0
hope this helps :)
correct answer gets brainliest
Answer:
C
Step-by-step explanation:
Answer:
C. 24 degrees
Step-by-step explanation:
The 3 angles inside ∠ABE: ∠ABC,∠DBC and∠EBD must add to 126 degrees
∠ABC+∠DBC+∠EBD =126
We already know that ∠DBC is 30 degrees, and ∠EBD is 72 degrees, so we can substitute them in
∠ABC+30+72=126
Combine like terms
∠ABC+102=126
Subtract 102 from both sides
∠ABC=24
So, ∠ABC equals 24 degrees, and C is the correct choice
Jeremy is packaging a stew containers.There are 8 3/4 cups of stew that need to put into 5 to go containers equally.How many cups of stew will be in each container?
Answer:
1 3/4 cups
Step-by-step explanation:
In order to be able to equally divide the stew into 5 containers we need to turn everything into the same format, in this case it would be by multiplying the whole number and the denominator and then adding the numerator like so
(8 * 4) + 3 = [tex]\frac{35}{4}[/tex]
Now we can divide the numerator by 5 (container) in order to calculate how much stew each container will get.
[tex]\frac{35}{4} / 5 = \frac{7}{4}[/tex]
So each container will get 7/4 of the Stew or 1 3/4 cups
Answer:
Each container = 1 3/4 cups
Step-by-step explanation:
*** There are 8 3/4 cups of stew that MUST be put into five containers EQUALLY.
*** We are basically required to calculate the number of cups of stew that must be in each container.
Since 8 3/4 cups of stew needs to be equally distributed and placed in just about five containers, we will need to first convert 8 3/4 cups which is in mixed fraction into improper fraction in order to enable us to calculate successfully.
8 3/4 = [(4×8)+3]/4
= 35/4
We will now use a little bit of the principle of proportion to get through this:
If 8 3/4 cups must be equal in five containers, then one container will have ? number of cups:-
5 containers --------- 35/4 cups
1 container ---------- ? cups.
1/5 × 35/4
= 7/4 cups.
We will now convert it back to mixed fractions and we will have 1 3/4 cups.
Therefore, each container we will contain 1 3/4 cups
Charlene and Gary want to make perfume. In order to get the right balance of ingredients for their tastes they bought 3 ounces of rose oil at $4.03 per ounce, 2 ounces of ginger essence for $3.42 per ounce, and 4 ounces of black currant essence for $3.92 per ounce. Determine the cost per ounce of the perfume. The cost per ounce of the perfume is $ (Round to the nearest cent.)
Answer:
$3.85 per ounce
Step-by-step explanation:
If we assume that all of the purchased ingredients are used in a mixture, their total cost is ...
3(4.03) +2(3.42) +4(3.92) = 34.61
The total quantity of mix is ...
3 + 2 + 4 = 9 . . . ounces
Then the cost per ounce is ...
$34.61/(9 oz) ≈ $3.85 /oz
The cost per ounce of the perfume that Charlene and Gary made is $3.85. This is calculated by adding the total cost of each ingredient and dividing by the total quantity of all ingredients.
Explanation:To find the cost per ounce of the perfume that Charlene and Gary wish to make, you need to determine the total cost of all the ingredients first, then divide by the total quantity of the perfume produced.
First, calculate the total cost of each ingredient:
Rose oil: 3 ounces * $4.03/ounce = $12.09Ginger essence: 2 ounces * $3.42/ounce = $6.84Black currant essence: 4 ounces * $3.92/ounce = $15.68Total cost is thus $12.09 + $6.84 + $15.68 = $34.61.
The total quantity of the perfume is 3 ounces (rose oil) + 2 ounces (ginger essence) + 4 ounces (black currant essence) = 9 ounces.
Therefore, the cost per ounce of the perfume is $34.61 / 9 ounces = $3.85 per ounce (rounded to the nearest cent).
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Mia says that two adjacent angles are supplementary and drew the figure on the left.
Ethan says that adjacent angles are not supplementary and drew the figure on the right.
Who is correct?
Explain your answer.
Answer:
Ethan
Step-by-step explanation:
Supplementary angles are angles which add up to 180 degrees.Two or more angles are Adjacent when they have a common side and a common vertex.In the scenario presented, Ethan is right to say that adjacent angles are not supplementary. This is as a result of the fact that no other condition was attached.
Adjacent angles are only supplementary "if they are all on a straight line" as in Mia's case. This is a special case and an extra condition has been imposed.
definicion de Funcion Polinomica
Answer:
Ejemplos de funciones polinómicas son: , la cual es de grado 3, ya que el exponente mayor es 3. , que es una función polinómica de grado 2, o sea cuadrática, cuya gráfica es una parábola. ... Muchas veces a partir de la gráfica de un polinomio se puede deducir la ecuación de la función.
Step-by-step explanation:
Una función polinómica es una expresión matemática compuesta por términos de variables elevadas a exponentes no negativos con coeficientes.
Una función polinómica es una función matemática definida por una expresión polinómica, que es una combinación lineal de variables elevadas a exponentes no negativos, multiplicadas por coeficientes constantes. Formalmente, una función polinómica [tex]\( f(x) \)[/tex]se expresa como:
[tex]\[ f(x) = a_n x^n + a_{n-1} x^{n-1} + \ldots + a_1 x + a_0 \][/tex]
Donde:
[tex]- \( n \)[/tex] es un número entero no negativo (grado del polinomio).
[tex]- \( a_n, a_{n-1}[/tex], [tex]\ldots, a_1, a_0 \)[/tex] son coeficientes constantes.
[tex]- \( x \)[/tex] es la variable independiente.
Por ejemplo, [tex]\( f(x) = 2x^3 - 3x^2 + 5x - 7 \)[/tex] es una función polinómica de grado 3. Las funciones polinómicas son un tipo importante de funciones en matemáticas y se utilizan en una variedad de campos, incluyendo álgebra, cálculo, estadística y física.
The perimeter of a triangle is 24inches. The longest side is 4 more than the middle side , and the smallest side is half the length of middle side. What are the lengths?
Answer:
Step-by-step explanation:
the length of the smallest side is 4 inches.
the length of the middle side is 8 inches.
the length of the longest side is 12 inches.
Step-by-step explanation:
Let x represent the length of the middle side of the triangle.
The longest side is 4 more than the middle side. It means that the length of the middle side is x + 4.
The smallest side is half the length of middle side. It means that the length of the smallest side is
x/2
The formula for determining the perimeter of a triangle is
Perimeter = a + b + c
Where a, b and c are the lengths of each side of the triangle. The perimeter of the triangle is 24 inches. It means that
x + 4 + x + x/2 = 24
Multiplying both sides of the equation by 2, it becomes
2x + 8 + 2x + x = 48
5x = 48 - 8
5x = 40
x = 40/5
x = 8 inches
The length of the longest side is
8 + 4 = 12 inches
The length of the smallest side is
8/2 = 4 inches
The radioactive element carbon-14 has a half-life of 5750 years. The percentage of carbon-14 present in the remains of plants and animals can be used to determine age. How old is a skeleton that has lost 50% of its carbon-14?
Answer:
A skeleton that has lost 50% of its carbon-14 is 5750 years old.
Step-by-step explanation:
The halflife on an element is the amount it takes to decrease to half it's original amount, that is, when the amount is 50% of the initial amount.
How old is a skeleton that has lost 50% of its carbon-14?
If the skeleton lost 50% of its carbon-14 it has the other 50%, that is, it is in it's half-life.
The radioactive element carbon-14 has a half-life of 5750 years.
This means that a skeleton that has lost 50% of its carbon-14 is 5750 years old.
A skeleton that has lost 50% of its carbon-14 is 5,730 years old, which corresponds to one half-life of carbon-14 (C-14).
Explanation:The age of a skeleton that has lost 50% of its carbon-14 can be determined using carbon-14 dating. Since the half-life of carbon-14 (¹⁴C) is 5,730 years, if a skeleton has only 50% of the original carbon-14 remaining, it would mean that one half-life has passed. Therefore, the skeleton would be 5,730 years old. Carbon-14 dating measures the radioactive decay of ¹⁴C in formerly living matter to estimate its age. This method is effective for dating biological tissues up to about 50,000 to 60,000 years old.
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Nancy spent half of her allowance going to the movies. She washed the family
car and earned 7 dollars. What is her weekly allowance if she ended with
16 dollars ?
Subtract 6 from me. Then multiply by 2. If you subtract 49 and then divide by 4, you get 8. What number am I?
Answer:
46.5
Step-by-step explanation:
Chandni has 3 pieces of orange yarn that are 1.25 feet long each and 2 pieces of blue yarn that are 2.75 feet long each. She uses all 5 pieces of yarn for an art project. What is the total length of yarn, in feet, that Chandni uses for her art project
Answer:
9.25 feet.
Step-by-step explanation:
Given:
Chandni has 3 pieces of orange yarn that are 1.25 feet long each and 2 pieces of blue yarn that are 2.75 feet long each.
She uses all 5 pieces of yarn for an art project.
Question asked:
What is the total length of yarn, in feet, that Chandni uses for her art project ?
Solution:
By unitary method:
Length of 1 piece orange yarn = 1.25 feet
Length of 3 pieces orange yarn = 1.25 feet [tex]\times[/tex] 3 = 3.75 feet
Length of 1 piece blue yarn = 2.75 feet
Length of 2 piece blue yarn = 2.75 feet [tex]\times[/tex] 2 = 5.5 feet
As she uses all 5 pieces of yarn for an art project:-
Total length of yarn, she uses for her art project = 3.75 feet + 5.5 feet = 9.25 feet
Thus, the total length of yarn, she uses for her art project = 9.25 feet.
Please I need help with the following question, How can you obtain the graph of ( + )from the graph of ?
Answer:
B) Translate the graph [tex] k [/tex] units to the left.
A certain television is advertised as a 17-inch TV(the diagonal length). If the width of the TV is 8 inches, how many inches tall is the Tv?
Answer:
15
Step-by-step explanation:
Two sides and an angle are given below. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. b equals 6 comma c equals 8 comma Upper B equals 30 degrees
The information given results in one triangle. By applying the law of sines and trigonometric relation, we find the angles A=107.52, B=30, C=42.48 degrees for a triangle with sides b=6, c=8.
Explanation:The problem deals with the Law of Sines which can be used to determine if a triangle exists given two sides and a non-included angle. According to the law of sines, ratio of the length of a side to the sine of the opposite angle is the same for all three sides of a triangle. Using this, we can determine whether the given conditions lead to a valid triangle.
Given: b = 6, c = 8, B = 30 degrees
1. Compute the value of sin(B) = sin(30) = 0.5 (using standard angle values).
2. Apply the law of sines to compute the missing angle. You get sin(C) = c*sin(B)/b = 8*0.5/6 = 0.67
3. Check sin(C): if sin(C) is greater than 1 or less than -1, no triangle exists. If sin(C) = 0.67, we get C = arcSin(0.67) = 42.48 degrees.
4. To find the third angle A, use the relationship 'Sum of angles in a triangle' equals 180. Hence, A = 180 - B - C = 180 - 30 - 42.48 = 107.52 degrees. We know that in a triangle, no angle can exceed 180 degrees, hence A=107.52 degrees confirms that the triangle is possible.
Hence given information results in one triangle with sides b=6, c=8 and angles A=107.52, B=30 and C=42.48
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The given information results in one triangle. To solve the triangle, we can use the Law of Sines.
Explanation:The given information of b=6, c=8, and B=30 degrees results in one triangle.
To solve the triangle, we can use the Law of Sines.
By plugging in the values, we can find the length of side a using the formula: a = (b * sin(A)) / sin(B).
After substituting the values, we find that the length of side a is approximately 3.464 units.
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Goes through every edge exactly one; starts and stops at different places. a Hamiltonian Path b Hamiltonian Circuit c Euler Path d Euler Circuit
Answer:
D. Euler Circuit.
Step-by-step explanation:
An Euler Circuit goes through every edge exactly once; starts and stops at the same vertex.
According to the Euler's Theorem, A graph has an Euler path if there are two 2-degree vertices without odd degrees and all other vertices have even degrees.
Mathematically, it is given as;
V+F=2-E
where;
F is the number of faces
V the number of vertices
E the number of edges.
Final answer:
An Euler Path traverses every edge of a graph exactly once and can start and end at different vertices, fitting the student's question.
Explanation:
The student's question hints at two different types of paths in graph theory: the Euler Path and the Hamiltonian Path. An Euler Path goes through every edge exactly once and can start and stop at different vertices. This path doesn't have to cover all vertices, but it must include every edge.
Here's a breakdown of the terms:
Hamiltonian Path: A path that visits every vertex exactly once, but it may start and end at different vertices.
Hamiltonian Circuit: A path that visits every vertex exactly once and starts and ends at the same vertex (creating a cycle).
Euler Path: A path that uses every edge exactly once, but it may start and end at different vertices.
Euler Circuit: A path that uses every edge exactly once and starts and ends at the same vertex (creating a cycle).
On the other hand, a Hamiltonian Path also goes through every vertex exactly once, but it is not concerned with edges.
In this case, since the definition provided in the question states the requirement is about edges and not vertices, the correct answer is c. Euler Path.