The greatest common divisor(GCD) of 10 and 50 is 10.
What is meant by GCD?The greatest common divisor (GCD) of two or more integers, where at least one of them is not zero, is the largest positive integer that is a divisor of both numbers. For example, the GCD of 8 and 12 equals 4.
In the divisibility preorder relation, the GCD of a and b is their greatest positive common divisor. This signifies that a and b's common divisors are the same as their GCD divisors. The Euclidean algorithm or Euclid's lemma are widely used to establish this. This is the definition of "greatest" in the context of GCD generalizations.
Foe calculating the GCD of 10 and 50, we have to find the factors of 10 and 50.
Factors of 10:
1, 2, 5, 10
Factors of 50:
1, 2, 5, 10, 25, 50
From all these factors we have to choose the greatest factor that is exactly divisible by both 10 and 50 are 1, 2, 10, and 5.
So, the greatest factor of 10 and 50 is 10.
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If you have 675 cm? of material to make a box with a square bottom and an open top, find the largest possible volume of this box_ base edges = W height h
The largest possible volume of this box is 1687.5 cm³ with a base edge of 15 cm and a height of 7.5 cm
Let w = length of the base edge
h = height of the box
A box with a square bottom and an open top is to be made from 675 cm² of material. Hence,
675 cm² = w² + 4wh
4wh = 675 cm² - w²
h = (675 cm² - w²)/4w
The volume of the box is the product of the area of the square base and its height. Hence,
V = w²h
Substitute the expression of h to the equation of volume.
V = w²(675 cm² - w²)/4w
V = (675/4)w - (1/4)w³
To obtain the largest volume possible, the first derivative of the volume should be equal to zero.
V'(w) = 0
V = (675/4)w - (1/4)w³
675/4 - (3/4)w² = 0
Simplify and solve for the value of w.
675/4 - (3/4)w² = 0
(3/4)w² = 675/4
w² = 225
w = 15
length of the base edge = 15 cm
Solve for the value of h.
h = (675 cm² - w²)/4w
h = (675 cm² - (15)²)/4(15)
h = 7.5 cm
height of the box = 7.5 cm
Solve for the volume of the box.
V = w²h
V = (15 cm)²(7.5 cm)
V = 1687.5 cm³
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How do you prove that congruent angles are equal?.
Two angles are considered to be congruent if their measures match. You are already aware that the vertical angles created when two lines connect are congruent.
A = B if A and B are both complements of C. We should investigate additional angle correlations. When you reveal these angle correlations, you will formally prove their veracity. For instance, you were given the concept of an angle bisector. It turns out that an angle's bisector separates it into two angles, each of which has a measure equal to half that of the original angle.Two angles are considered to be congruent if their measures match. You are already aware that the vertical angles created when two lines connect are congruent.
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a book contains 1 to 124 pages numbered from 1 to 124 how many times does the digit 7 appear
What are the 3 types of solutions to a system of linear equations?.
The 3 types of solutions to a system of linear equations are Unique Solution, No Solution and Infinitely Many Solutions.
In the given question we have to find the 3 types of solutions to a system of linear equations.
The 3 types of solutions to a system of linear equations are:
(1) Unique Solution: There is only one solution to a linear equation including one variable. The one and only position at which LHS and RHS are similar on substitution is the unique solution of a linear equation.
(2) No Solution: The system of linear equations has no solution if the graphs of the linear equations are parallel. There is no point in this situation when no lines cross one another.
(3) Infinitely Many Solutions: There are infinite solutions to a 2 linear equation. There is a set of infinite solution points for the linear equation system when each equation's L.H.S changes to its R.H.S
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What is the equation of the line that passes through the point (-1, 3) and has a
slope of -3?
Answer:
y=-3x
Explanation:
3=-3(-1)+b
3=3+b
0=b
y=-3x
the difference between the squares of two numbers is 10. the difference between the two numbers is 2. what is their sum?
If the difference between the squares of two numbers is 10 and the difference between the two numbers is 2, their sum would be 5.
How to solve an equation?An equation is an expression that can be used to show the relationship between variables and numbers.
Let a and b represent the two numbers.
The difference between the squares of two numbers is 10. Hence:
a² - b² = 10
(a - b)(a + b) = 10 (1)
The difference between the two numbers is 2, hence:
a - b = 2
Substituting:
(a - b)(a + b) = 10
2(a + b) = 10
(a + b) = 5
Their sum is 5.
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(1 point) a street light is at the top of a 16 foot tall pole. a 6 foot tall woman walks away from the pole with a speed of 4 ft/sec along a straight path. how fast is the tip of her shadow moving when she is 30 feet from the base of the pole?
The tip of the shadow is moving at [tex]4.8\frac{ft}{sec}[/tex]
Consider the image , as depicted below
Based on similar triangle , we have
[tex]\frac{s(t)}{6} =\frac{s(t)+w(t)}{16}[/tex]
⇒ 10s(t) = 6w(t)
⇒ w(t) = [tex]\frac{10}{6} s(t)[/tex]
we are told that a certain time t,
[tex]\frac{d(w(t))}{dt} = 8\frac{ft}{sec}[/tex]
[tex]\frac{d(w(t))}{dt} = \frac{d(\frac{10}{6}.s(t)) }{dt}[/tex]
[tex]= \frac{10}{6}\frac{d(s(t))}{dt}[/tex]
Therefore,
[tex]\frac{10}{6} \frac{d(s(t))}{dt} = 8\frac{ft}{sec}[/tex]
[tex]\frac{d(s(t))}{dt} = 4.8\frac{ft}{sec}[/tex]
Hence, The tip of the shadow is moving at [tex]4.8\frac{ft}{sec}[/tex]
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the amount of snowfall falling in a certain mountain range is normally distributed with a mean of 70 inches and a standard deviation of 10 inches. what is the probability that the mean annual snowfall during 25 randomly picked years will exceed 72.8 inches?
80.8% of the time, the average yearly snowfall across the 25 years that were randomly chosen will be greater than 72.8 inches.
Describe the term Normal Distribution?When we are aware of the normal distribution of the data, we must utilize that normal distribution to calculate probabilities. That is, in order to determine the necessary area under the normal curve, we must use the mean and indeed the population standard deviation.As the question stated;
The z score is estimated as;
z = (x - μ)/σ
In which,
Mean μ = 70 inche
standard deviation σ = 10 inches.
n = 25
z = (72.8 - 70)/(10/√25)
z = 2.8/2
z = 1.40
Use z-score table to find the value;
P(x > 72.8 inches) = P(z > 1.40)
P(x > 72.8 inches) = 1 - P(z < 1.40)
P(x > 72.8 inches) = 1 - 0.9192
P(x > 72.8 inches) = 0.0808
Thus, 80.8% of the time, the average yearly snowfall across the 25 years that were randomly chosen will be greater than 72.8 inches.
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15 ft
10 ft
20 ft
Find the area of the trapezoid
[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=15\\ b=20\\ h=10 \end{cases}\implies A=\cfrac{10(15+20)}{2}\implies A=175~ft^2[/tex]
prove that for every positive integer n, there are n consecutive composite integers. [hint: consider the n consecutive integers starting with (n 1)! 2.]
It is proved that, for every positive integer n, there are n consecutive composite integers.
Given statement,
For every positive integer n, there are n consecutive composite integers.
Proof:
Assume that m is less than n and that both m and n are positive integers. When m is less than n,
n! = 1 ⋅ 2 ⋅ 3 ⋅ ⋅ ⋅ m ⋅ ⋅ ⋅ n,
which is to say that m is a factor of n!
So,
m + n! = m + ( 1 ⋅ 2 ⋅ 3 ⋅ ⋅ ⋅ m ⋅ ⋅ ⋅ n )
= m ((1 ⋅ 2 ⋅ 3 ⋅ ⋅ ⋅ m ⋅ ⋅ ⋅ n) / m + 1)
Since m is a multiple of n!, n!/m is still an integer. Since the integer m is bounded between 1 and n, it follows that any number you choose up to n can divide m + n!, making it composite until the nth integer.
However, since n! contains the nth integer, the nth integer is also composite, meaning you can choose any integer between 1 and n inclusively and it will be composite.
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a. conceptual warmup (25 points) think back to the navier stokes (n.s.) equations. (15 points) note: you do not need to solve the differential equation for problem. consider a thin layer of fluid flowing on a slope, as illustrated in figure. the fluid-solid interface is at y
∂v⃗ ∂t+(v⃗ ⋅∇⃗⃗) v⃗ +1ρ∇⃗ p=g. The viscosity leads to frictional forces within the fluid. Taking the viscosity into account in the Euler equation finally leads to the Navier-Stokes equation.
For the derivation of the Navier-Stokes equations we consider a fluid element and the forces acting on it. At first we will consider only the motion of the fluid in x-direction. The motion of the fluid element is influenced by the pressure forces acting on the front and back surface of the cubic volume element.
These pressure forces basically represent normal stresses and are therefore denoted in the following by the Greek symbol σ instead of p. We will see later that in addition to the pressure forces, viscosity-related forces also act perpendicular to the surfaces and contribute to the normal stress.
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An archaeologit i roping off a rectangular region of land to dig for artifact. The region mut have a perimeter of 440 feet and an area of at leat 8500 quare feet. Decribe the poible length of the region
The possible length of the region after solving the quadratic equation is either 170ft or 50ft.
What is a quadratic equation?
A quadratic equation in algebra is any equation that can be written in the simpler form where x stands for an unknown value and a, b, and c are known quantities. The assumption is that a > 0; an equation with a = 0 is thought to be degenerate because they become linear or even simpler.
Solution Explained:
Lets assume, length = x and width = y
So we know, the area and perimeter is supposed to be 8500 and 440 respectively
we form the equations,
1) 8500 = xy , and [Area = length*width]
2) 440 = 2(x + y) [ Perimeter = 2(length +width)]
220 = x + y
So, x = 8500/y (from equation 1) and put the value of x in 2
220 = x + (8500/x)
After solving this we get the quadratic equation,
x^2 - 220x + 8500 = 0
Solving the equation, we get
x = 170 or, x = 50 which are the two possible lengths of the region.
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The most intense rainfall on record was 75 mm in 2 min at Barst, Guadeloupe. At this rate, how much rain would you expect to fall in 1 h?
The amount of rainfall in 1 hour at Barst , Guadeloupe is 2250 mm
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the amount of rainfall in 2 minutes = 75 mm
So , the amount of rainfall in 1 minute = amount of rainfall in 2 minutes / 2
= 75 / 2
= 37.5 mm
And , 1 hour = 60 min
So ,
The amount of rainfall in 1 hour = amount of rainfall in 1 minute x 60
= 37.5 mm x 60
= 2250 mm
Hence , the amount of rainfall in 1 hour at Barst , Guadeloupe is 2250 mm
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each side of a square is increased 3 inches. when this happens, the area is multiplied by 4. what is the side length of the original square?
The side length of the original square is 3.
Let s = side length of the original square
s + 3 = side length of the new square
Area of a square = s²
A = s²
A = (s+3)²
A = s² + 6s + 9
Area multiplied by 4 = 4 × s²
So,
s² + 6s + 9 = 4s²
4s² - s² - 6s - 9 = 0
3s² - 6s - 9 = 0
s² - 2s - 3 = 0
a = 1
b = -2
c = -3
s = -b ± √b² - 4ac / 2a
= -(-2) ± √(-2)² - 4(1)(-3) / 2(1)
= 2 ± √4+12/2
= 2± √16/2
= 2 ± 4/2
= 2+4/2 or 2-4/2
= 6/2 or -2/2
= 3 or -1
side length can not be negative
Therefore, s = 3
A = s²
A = (3)²
= 9
A = (s+3)²
= (3+3)²
= 36
Hence the side length of the original square is 3.
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The two triangles are similar, solve for x.
There are two triangles and both of them are similar, then the value of x will be equal to 4.5.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the given diagram shown in the question,
Δ JKL is similar to Δ ABC.
Then,
10x + 9 = 54
Solve the equation for x,
10x = 54 - 9
10x = 45
x = 45/10
x = 4.5
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Is the following statement bicondional? A quadrilateral is a square if and only if it has four congruent sides and four right angles.
A) True b) False c) not enough information
The statement is true.
The quadrilateral is a square if and only if it has four congruent sides and four right angles.
Quadrilateral:
A closed quadrilateral has four sides, four vertices, and four angles. It is a type of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total interior angle of 360 degrees. The Latin words quadra, which means four, and latus, which means sides, are combined to form the English word quadrilateral. A quadrilateral does not necessarily have to have equal lengths on each of its four sides. As a result, depending on the sides and angles, we can have different types of quadrilaterals.
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A flight from Baltimore to San Joe took 5 hour and covered 3,010 mile. What wa the plane’ average peed?
The plane's average speed is 602 miles/hour.
What is the average speed?
The overall distance the object covers in a given amount of time is its average speed. It can be calculated by:
Average Speed = (Total distance)/(Total Time)
Given, Total distance traveled = 3010 miles
Total time taken = 5 hours
Now, the average speed is given by:
average speed = (3010/5) miles/hour
= 602 miles/hour
Hence, the plane's average speed is 602 miles/hour.
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the attention span of a two-year-old is exponentially distributed with a mean of about 8 minutes. suppose we randomly survey 60 two-year-olds.
The mean has a value of 8 minutes and a standard deviation of 0.9736.
What is mean?The sum of a set of numbers divided by the total number of numbers in the set is known as the arithmetic mean or arithmetic average in mathematics and statistics. The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including basic arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
Here,
X= attention span of the 2 year old
μ=8
σ=8
m=1/8
X=exp(1/8)
mean=N(8,8/√60)
Mean is normally distributed with value about 8 minutes and difference being 0.9736.
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andre lives with his wife and three children. approximately how many pounds of municipal solid waste does andre and his family generate each day?
If andre lives with his wife and three children. 22 pounds of municipal solid waste his family generates each day.
What is population density?It is defined as the ratio of the population to the total area. The population density represents the average number of people living in each square unit.
It is given that and lives with his wife and three children.
We have to find the mass of municipal solid waste Andre and his family generate each day.
From the data research 22 pounds of municipal solid waste, his family generates each day.
Thus, if Andre lives with his wife and three children. 22 pounds of municipal solid waste his family generates each day.
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In rhombus ABCD , DB = 16 and AC = 12 What is the perimeter of rhombus ABCD
Answer:
40
Step-by-step explanation:
You can always look it up but that is the answer
factory costs $460,000. You forecast that it will produce cash inflows of $150,000 in year 1, $210,000 in year 2, and $360,000 in year 3. The discount rate is 12%. a. What is the value of the factory? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
The worth of the factory is $97580.17.
Given data;
Cost of $460,000 for the factory. You project that it will bring in $150,000 in the first year, $210,000 in the second, and $360,000 in the third. The 12% discount rate applies.
To know the factory's worth;
Let,
[tex]NPV = \frac{C_0}{(1 + r)^0} + \frac{C_1}{(1 + r)^1} + \frac{C_2}{(1 + r)^2} + \frac{C_3}{(1 + r)^3}[/tex]
Here,
C₀ = -460,000, C₁ = 150,000, C₂ = 210,000, C₃ = 360,000
[tex]NPV = \frac{-460,000}{(1 + 0.12)^0} + \frac{150,000}{(1 + 0.12)^1} + \frac{210,000}{(1 + 0.12)^2} + \frac{360,000}{(1 + 0.12)^3}[/tex]
NPV = $97,580.17
Therefore, the factory's worth is $97580.17.
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What would be an appropriate way to assign digits in order to simulate flipping an unfair coin with P(H) = 0.3? *
Assign digits 1,2,3 to be a head. Assign 4 - 9 to be a tail.
Assign digits 0,1,2,3 to be a head. Assign 4 - 9 to be a tail.
Assign digits 0,1,2,3 to be a tail. Assign 4 - 9 to be a head.
Assign digits 0,1,2 to be a tail. Assign 3 - 9 to be a head.
Assign digits 0,1,2 to be a head. Assign 3 - 9 to be a tail
Assign digits 1,2,3 to be a head. Assigning 4 - 9 to be a tail would be the most appropriate way.
Option (A) is correct.
What is probability?
Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.
There are 10 chances to flip the coin.
If we assign digits 1, 2, and 3 to be as a head and if we assign 4 - 9 as a tail,
then we can get the probability of getting head
P(H) = 3/ 10 = 0.3.
Hence, Assign digits 1,2,3 to be a head. Assigning 4 - 9 to be a tail would be the most appropriate way.
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Why we Cannot construct a triangle of given sides as 5 cm 5 cm and 10 cm?.
Answer:
Because the sum of the length of any two sides of a triangle is greater than the length of the third side
Step-by-step explanation:
Why we Cannot construct a triangle of given sides as 5 cm 5 cm and 10 cm?.
5+5=10 (not possible)
using traditional methods it takes 11.111.1 hours to receive a basic driving license. a new license training method using computer aided instruction (cai) has been proposed. a researcher used the technique on 2626 students and observed that they had a mean of 10.910.9 hours with a variance of 1.441.44. is there evidence at the 0.0250.025 level that the technique reduces the training time? assume the population distribution is approximately normal. step 4 of 5 : determine the decision rule for rejecting the null hypothesis. round your answer to three decimal places.
The technique reduces at the training time t = 0.709.
The decision rule is a statement that tells under what circumstances to reject the null hypothesis. The decision rule is based on specific values of the test statistic.
Given that,
Population mean = 11.1 hrs
Sample mean = 10.9 hrs
Sample size , n = 26
α = 0.025
Sample standard deviation = 1.44
Therefore the null and alternate hypothesis will become,
H₀ : μ = 11.1 hrs
Hₐ : μ ≠ 11.1 hrs
here we have to use two tailed test to [perform above hypothesis,
t = (x - μ)/ (s/[tex]\sqrt{n}[/tex])
= (10.9 - 11.1) /(1.44/[tex]\sqrt{26}[/tex] )
= - 0.2/ 0.282
t = 0.709.
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. the 49th parallel that separates the united states and canada is an example of what type of border?
The 49th parallel that separates the united states and Canada is an example of Antecedent border.
An antecedent border is one that existed before to the development of the cultural landscape and persisted even after inhabitants came in to occupy the surrounding region.A political border that existed before the area was occupied by the existing residents is known as an antecedent boundary. For instance, the colonists drew the border between the USA and Canada before they settled North America.Relict boundaries are historical boundaries that have been removed for political reasons but are still visible in the cultural environment. The majority of European borders are afterwards drawn, and we can see how well each one complies with major or minor divisions of natural and cultural areas.Thus this is the meaning Antecedent border.
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the probability distribution shows the weights x, in kilograms, of boxes being shipped from a certain factory. a shipped box is randomly chosen. what is the probability that it weighs less than 29 kilograms? a probability distribution histogram. the vertical axis has no scale. horizontal axis is labeled x and extends from 24 to 32 with an interval of 1. the bars in all intervals are equal in height. responses 0.75 0.75 0.625 0.625 0.5 0.5 0.375
The probability that it weighs less than 29 kilograms is 0.625.
How likely is it that a box will weigh less than 29 kilograms?
according to the histogram( image attached )
A box could weigh any one of 8 different amounts, all of which have the same chance of happening.
thus, the equal probability is:
= 1/8
= 0.125
According to the probability distribution, The probability that a box weighs less than 29 kilograms is represented by the probability below 27. There are 5 weights below 29 which makes the probability :
= 5 × 0.125
= 0.625
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a farmer plans to enclose a rectangular pasture adjacent to a river (see figure). the pasture must contain 5,000 square meters in order to provide enough grass for the herd. no fencing is needed along the river. what dimensions will require the least amount of fencing?
50 m is dimensions will require the least amount of fencing .
What is rectangle?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. It is also known as an equiangular quadrilateral for this reason.
Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.
Let x = length of the side parallel to the river
y = length of each of the other two sides
Then xy = 5,000, so y = 5,000/x
Minimize: L = length of the fence
L = x + 2y
= x + 10,000/x, where x > 0
L' = 1 - 10,000/x2 = (x2 - 10,000)/x2
L' = 0 when x = 100 or -100
Since x can't be negative, x must be 100.
When 0 < x < 100, L' < 0. So, L is decreasing.
When x > 100, L' > 0. So L is increasing.
Therefore, L has a relative and absolute minimum when x = 100 m
y = 5,000/x = 50 m
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Given m n, find the value of x.
(x+20)°
(4x-5)°
∠(x+20)° and ∠(4x-5)° are the same side interior angles or supplementary angles thus x will be 33.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
As per the given angles,
∠(x+20)° and ∠(4x-5)° are supplementary angles.
∠(x+20)° + ∠(4x-5)° = 180°
x + 20 + 4x - 5 = 180
5x + 15 = 180
5x = 165
x = 33
Hence "∠(x+20)° and ∠(4x-5)° are the same side interior angles or supplementary angles thus x will be 33".
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Find the Slope and Y-intercept of each line
Slope of graph is -4 and y- intercept is -8.
What is slope of graph?
In math, slope is employed to explain the gradient and direction of lines.
Main Body:
The slope of a line is the ratio of rise to run. Hence, here are the steps to find slope from a graph.
Select any two random points on the graph of the line (preferably with integer coordinates).Label them as A and B (in any order).Calculate the "rise" from A to B. While going vertically from A to B, if we have to go"up", then the rise is positive;
"down", then the rise is negative.
Calculate the "run" from A to B. While going horizontally from A to B, if we have to go"right", then the run is positive;
"left", then the run is negative.
Now, use the formula: slope = rise/run.hence slope of graph = -8/2 = 4.
And y intercept is point cutting y-axis , so it is -8.
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Is a quadratic function linear or nonlinear?.
A Quadratic function is non-Linear.
Answer:
nonlinear
Step-by-step explanation:
Quadratic functions are non-linear. A linear function produces a straight line while a quadratic function produces a parabola
