Is every linear equation a quadratic equation?.

The central angle states the property of the center of the circle, So It is called the central angle.

What is a Central Angle?

The central angle is the angle that a circle's arc occupies in its center. The arms of the central angle are formed by the radius vectors. In other words, it's an angle whose vertex is the center of a circle and whose arms, which have the circle's two radii as their arms, cross at two separate positions. These two points make an arc when they are combined. The angle that this arc at the circle's center subtends is known as the central angle.

An arc's angle at the circle's center is twice as large as its angle at any other point along the circle's circumference. the angle subtended by the arc in the opposite segment of the circle is twice as large as the angle at the center of the circle.

Hence,

The central angle states the property of the center of the circle, So It is called the central angle.

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The standard form polynomial representing the volume of this shipping container is expressed as V = 24x⁵+78x⁴-147x³-624x²-360x

Volume of the shipping container = Lengt * Breadth * Height

Given

Length = 4x² + 3x

Breadth = x² – 8

Height = 6x +15

Volume of the container = ( 4x² + 3x)( x² - 8)(6x+15)

( 4x² + 3x)( x² - 8)  = 4x⁴-32x²+3x³-24x

( 4x² + 3x)( x² - 8) = 4x⁴+3x³-32x²-24x

(4x⁴+3x³-32x²-24x)(6x+15) = 24x⁵+60x⁴+18x⁴+45x³-192x³-480x²-144x²-360x

Collect like terms

( 4x² + 3x)( x² - 8)(6x+15) = 24x⁵+78x⁴-147x³-624x²-360x

Hence the standard form polynomial representing the volume of this shipping container is expressed as V = 24x⁵+78x⁴-147x³-624x²-360x

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The length of Stan's movie is 2 hours 25 minutes

The length of Talia's movie is 2 hours 55 minutes.

In order to determine the length of the movies, subtract the end time of the movie from the time the movie started.

Subtraction is the mathematical operation that is used to calculate the difference between two or more numbers. The sign that is used to represent subtraction is -.

Length of the movie = time the movie ended - time the movie started

Length of Stan's movie = 9:40 - 7:15 = 2 : 25 hours

Length of the Talia's movie = 10 : 10 - 7 : 15 = 2 : 55 hours

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Answer: 8/7y - 56

Step-by-step explanation: To find the equivalent expression, we multiply 8 by both of the values in the parenthesis.

8 × 1/7y = 8/7y

8 × (-7) = -56

8/7y - 56 is our final answer.

The point, M, that is midway between P=(5,−8,−6) and Q=(-7,-2,-8) is

In geometry, the midpoint formula is an equation that determines the separation between two known coordinate locations at their halfway point.

The midway between the points P and Q is calculated using the method

Mid point = ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2)

Applying the method to the given points gives

P = (5, −8, −6) and Q = (-7, -2, -8)

M = ((5 + -7)/2, (-8 + -2)/2, (-6 + -8)/2)

M = (-1, -5, -7)

The coordinates of point M (-1, -5, -7) is the mid way between point  P=(5,−8,−6) and Q=(-7,-2,-8).

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To prove that all positive integers less than 4 are prime numbers, we will use the method of exhaustive proof.

Proof by contradiction is a method that establishes the the validity of a proposition, by assuming the proposition to be false leads to a contradiction.

Trivial Proof implies that if q is true then p → q is true regardless of the

truth value of p.

Proof by Induction is a method for proving that a statement P(n) is true for every natural number n

Finally, Proof by exhaustion, also known as proof by cases, is a method of proof in which the statement to be proved is split into a finite number of cases, and each type is then checked to see if the proposition in question holds.

Here, as we can see, by definition, exhaustive proof will be most appropriate as we can easily split the statement into 3 cases, taking the integers 1, 2 and 3 in each.

Thus, we will use Exhaustive Proof.

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The value of the unknown is 6

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

the expression -1 1/8 - 3/4 = -1 1/8 - ?/8 shows that

-3/4=-?/8

the LCM of the denominator of two fractions is 8

multiply both sides by 8

-3/4×8=-?/8×8

therefore,. -? = -3×2

?= 6

Therefore the value if the unknown is 6

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The fraction is expressed with a common denominator as - 15/ 8

A fraction is simply described as the part of a whole, element or number.

There are several types of fractions, which includes;

From the information given, we have  the fractions;

-1 1/8 - 3/4.

Convert the mixed fraction to improper fraction

- 9/ 8 - 3/4

Find the Lowest common multiple

-9 - 6  /8

Subtract the numerators

-15/ 8

Hence, the value of the expression is -15/8

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The values of r for which the shaded region will be greater than or equal to 12 square units is r ≥ 8

Given that,

We have to find the darkened region's area will be more than or equal to 12 square units for what values of r.

We can see a rectangle and a triangle in the given image.

The triangle is the part of the rectangle that is not coloured.

Thus;

Area of rectangle minus area of rectangle gives the area of the shaded area.

We know that formula for area of rectangle is;

Ar = length × width

Thus; Ar = 3 × r

Ar = 3r

Area of a triangle is;

At = ½ × base × height

At = ½ × r × 3

At = ½(3r)

Thus;

Area of shaded region = 3r - 1/2(3r)

Area of unshaded portion = 1.5r

We are informed that the unshaded area must have a minimum area of 12 and a maximum area of 12. Thus;

1.5r ≥ 12

r ≥ 12/1.5

r ≥ 8

Therefore, The values of r for which the shaded region will be greater than or equal to 12 square units is r ≥ 8

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Answer:

13: 22 < x < 74

14: Side DF, Side DE, side EF

Step-by-step explanation:

So for the first one, you add 26 + 48 which equals 74. Then, you subtract 48 - 26 which equals 22. So the range is 22 < x < 74.

For the second one, the angle corresponds to the side across from it. The smallest side will be across from the smallest angle. So, the order is side DF, side DE , and then side EF.

Hope this helps!!! :)

Answer:

V=HWL

54cm³

Step-by-step explanation:

V=HWL

∴V=9*2*3

V=54cm³

The required five equation of linear equation are given below.

A linear equation is a mathematical condition of the structure y=mx+b. including just a steady and a first-request (straight) term, where m is the incline and b is the y-catch. At times, the above is known as a "direct condition of two factors," where y and x are the factors.

Five examples of linear equation,

1) 2x – 3 = 0

2) 2y = 8

3) m + 1 = 0

4) x/2 = 3

5) x + y = 2

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Answer:

u + v = < - 9, - 7 >

Step-by-step explanation:

to sum u and v add the corresponding x and y components of the 2 vectors

u + v

= < - 8, - 5 > + < - 1, - 2 >

= < - 8 - 1, - 5 - 2 >

= < - 9, - 7 >

Answer:

£10

Step-by-step explanation:

3:4 is equal to 3/4 (three-quarters)

Paul gets 75%, and Brian gets 25%.

Paul gets £30.  30 is 3/4 of what number?

75/100 × x = 30

Multiply both sides by 100 and divide both sides by 75

x = 30 × 100/75

x = 30 x 1.33333333333

x= 40

£30 is 75% of £40

30/40 x 100 = 75%

10/40 x 100 = 25%

Brian gets £10

The critical point of the function f(x, y) = x^2 + y^2 + 3xy - 7.5x is (0, 0) because the partial derivatives of f with respect to x and y are both equal to 0 at this point.

In mathematics, a critical point is a location along a function or curve where the derivative of the function is either equal to 0 or undefined. Accordingly, a critical point occurs where the slope of the function is either 0 or not specified, producing a flat or vertical tangent line. Critical points are significant because they frequently point to locations where the function changes course or exhibits a local extreme value, such as a maximum or minimum. Taking the function's derivative and then solving for the values of x where the derivative equals zero or is undefined will help you locate key spots. The critical points of the function are at these values of x.

How to solve?

To use the Second Derivative Test, we need to calculate the Hessian matrix of the function at the point (0, 0).

The Hessian matrix for f(x, y) at (0, 0) is given by:

H = [2 3]

[3 2]

λ1 = 5, λ2 = -1

Since the Hessian matrix has one positive and one negative eigenvalue, the point (0, 0) is a saddle point.

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The coordinates of point $p$ along the directed line segment $ab$ is at the point (2.8, -1).

Step 1

To find the coordinates of P so that AP to PB is the given ratio, first look for the slope in rise over run form.

Then, determine the ratio by thinking of it as dividing into segments.

After, add the ratio (in fraction or in decimal) of the run to the x-coordinate and add the ratio (in fraction or in decimal) of the rise to the y-coordinate of the first point in the line segment.

Step 2

First, let us find the slope of the line through rise over run and do not simplify the slope:

[tex]m = \frac{rise}{run}\\ \\m = \frac{1-(-4)}{6-(-2)} \\\\= \frac{5}{8}[/tex]

Since the ratio is 3:2, we want to partition the entire segment into 5 parts with P located at 3\5 of the segment from point A. Therefore, we add 0.6 of the run to the x−coordinate and of the rise to the

y−coordinate:

rise=5⋅0.6=3               y=−4+3=−1

run=8⋅0.6=4.8             x=−2+4.8=2.8

Therefore, the point is at (2.8,−1).

Hence the answer is  the coordinates of point $p$ along the directed line segment $ab$ is at the point (2.8, -1).

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Random residual plots are not make sense because it should have a non linear curve, as the scatter plot is negative.

A chart that displays the values ​​of two variables along two axes. Each correlation is indicated by the placement of the resulting points.

A series of points plotted on the horizontal and vertical axes is called a scatterplot. Statistical scatterplots (called variables) are very important because they can show the extent, if any, of relationships between the values ​​of observed quantities or events. You can see that the scatterplot is a non-linear curve with negative points.

Therefore, since the scatterplot is negative, the residual plot is meaningless as it must have a non-linear curve.

your question is incomplete, but most probably your full question was

The relationship of miles per gallon of SUVs to weight is represented by the following scatter plot:

Brian created the following residual plot:

Does her residual plot make sense based on the scatter plot? Explain.

The random residual plot makes sense because the scatter plot appears to have a negative relationship.

The random residual plot does not make sense because it should have a linear relationship like the scatter plot.

The random residusl plot does not make sense because it should have a noninar curve, as the scatter plot is negative.

The random residual plot makes sense because the scatter plot appears to have a lines relationship.

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a. The equation for the line of best-fit is:

y = 8.52x + 11.7.

b. The correlation coefficient is of: 0.9987, hence there is a strong positive correlation between the variables.

To obtain the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.

The points in this problem are given on the table as follows:

(0, 12.2), (1, 19.1), (2, 29.4), (3, 37.3), (4, 45.7).

As we consider the input x as the number of years since 2011.

Then, using the calculator, the equation is given as follows:

y = 8.52x + 11.7.

Using a correlation coefficient calculator, the numeric value of the coefficient is of:

r = 0.9987.

Hence the correlation between the variables is classified as follows:

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Chemical reactions such as photosynthesis explains the manner in which green plants manufacture their own food using the energy derived from sunlight.

What is photosynthesis?

Photosynthesis is the process in which green plants prepare their own food in the presence of sunlight and light energy is converted into chemical energy by the process of cellular respiration.

The process of photosynthesis takes place in green plants only due to presence of chlorophyll and materials such as sunlight, water, carbon dioxide is required for the process of photosynthesis.

The equation of photosynthesis is represented below:

6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂.

The process of food manufacturing in plant is done through photosynthesis and the plants are known as autotrophs as they are the producers.

In the process of photosynthesis the reactant have 6 carbon dioxide molecules and six water molecules, and light energy converted into chemical energy due to presence of chlorophyll.

Therefore, Chemical reactions such as photosynthesis explains the manner in which green plants manufacture their own food using the energy derived from sunlight.

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Answer:

One side length is 17. Because you square root 289 to figure out the side length.

Step-by-step explanation:

The area of a square is a side length * a side length

or l^2 = 289

sqrt or 289 = 17

Reject the null hypothesis, because the P-value is small (it's less than 1%) then confront Bill about his cheating play with someone else.

Fail to reject the null hypotheses, because the P-value is not small (it's more them 10%).

One of the most generally utilized p-values is 0.05. If the determined p-values end up being under 0.05, the invalid speculation is viewed as bogus, or invalidated (subsequently the name invalid theory). What's more, on the off chance that the worth is more prominent than 0.05, the invalid speculation is viewed as obvious.

That p-value is the likelihood that we'll obtain similar outcomes as the invalid speculation, and in our model, the edge for that likelihood is 0.05. So if the determined p-value is under 0.05, it really intends that there's exceptionally less probability that we'll come by similar outcomes as the invalid speculation. Also, in the event that the p-value is more than 0.05, the likelihood of obtaining similar outcomes as invalid speculation is exceptionally high, so we can believe the invalid speculation to be valid.

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The value of y - intercept is: -5

It is distance between point on Y axis where graph cuts it and origin generally denoted by c.

Here in this question initially f(x) was = x

later we took new function g(x) = f(x-5) = x-5

therefore we call g(x) = x - 5now we need to find y intercept and we know that on y axis (x - coordinate = 0)

just put x=0 in above equation g(0) = -5

which is value of y intercept

y = -5

because one point is origin(0,0) and other is this one(0,-5)we need to calculate distance between these 2 that after finding from distance formula we get answer as 5 but here intercept is negative so, our final answer is -5

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Applying the equation of the model, y = 123.1(1.069)^x:

a. 150.4 thousand students

b. 467.5 thousand students

In the above problem given, we are told that the equation that models the the number of college students who studied abroad each year is: y = 123.1(1.069)^x, where:

The number of students from a country in thousands is represented as y

The number of years after 1998 is represented as x in the equation.

We can apply the equation for this model to solve the given problem as explained below:

a. 1998 to 2001 is 3 years. x = 3. Therefore, substitute x = 3 into y = 123.1(1.069)^x:

y = 123.1(1.069)^3

y = 150.4

Therefore, the number of students that are studying abroad in 2001 is about: 150.4 thousand.

b. 1998 to 2018 is 20 years. x = 20, therefore, substitute x = 20 into y = 123.1(1.069)^x:

y = 123.1(1.069)^20

y = 467.5

Number of students studying abroad in 2018 (y) is therefore about 467.5 thousand.

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There are 35 experimental units are in the experiment.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given there are 2 types of paints, and 3 types of metal, Thirty sheets of metal were used in the experiment.

We have to apply the addition operation in order to find the number of experimental units.

The number of experimental units in the experiment is found as,

=2+3+30

=5+30

=35

Thus, there are 35 experimental units are in the experiment.

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A rational root is such a number that makes any polynomial function equal to zero.

let us consider a general polynomial equation-

P(x) = anxn + an− 1xn − 1 + … + a1x1 + a0

hence, the rational roots must be of the form = [tex]\pm[/tex] (factors of a0) / (factors of an).

let us now take an example,

[tex]F(x) = 4x^3 - 6x^2 + 9x + 10[/tex]

here ao = 10, and factors of 10: 1,2,5,

an = 4 and the factors of 4: 1,2,4

Hence, we have Possible Rational Roots:

[tex]$$\pm\left\{1, 2, 5, 10,\frac{1}{2}, \frac{1}{4}, \frac{5}{2}, \frac{5}{4}\right\}$$[/tex]

In this way, we have the rational numbers which can be possible solutions for our function f(x).

Now we substitute each of these rational numbers one by one to check if it satisfies the equation as follows.

[tex]F(1) = 4(1)^3 - 6(1)^2 + 9(1) + 10=17\neq 0[/tex]

Hence, it doesn't satisfy the equation, it means it's not the root of the equation.

Similarly, we can check for the rest of the numbers.

we will get f(-1/2)=0, f(5)=0, f(5/4)=0 and f(-2)=0

Hence, x=5,5/4,-1/2 or -2 are the solutions for the equation F(x).

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The 3 phases of the agile life cycle:

The Continuous Delivery: Lean Life Cycle.

The Exploratory (Lean Startup) Life Cycle.

The Program Life Cycle for a Team of Teams.

What is the Agile cycle?

The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.

The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.

The project management approach a team decides on will have a small impact on the Agile life cycle. For instance, Scrum teams work in sprints, which are brief timeframes akin to iterations. They also have responsibilities that are precisely defined, like Scrum master. Kanban teams, on the other hand, operate more continuously and don't have set roles. Another illustration is Extreme Programming, where teams frequently work in shorter iterations and give engineering practices more attention.

Hence,

The 3 phases of the agile life cycle:

The Continuous Delivery: Lean Life Cycle.

The Exploratory (Lean Startup) Life Cycle.

The Program Life Cycle for a Team of Teams.

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To find the roots and multiplicity of a polynomial, we first need to find its factors.

To do this, we use the factoring method of our choice (such as the quadratic formula, factoring by grouping, etc.), and then we determine how many times each factor occurs. The roots of the polynomial are the factors that have a multiplicity of 1, and the multiplicity of a root is the number of times that it occurs as a factor.

A polynomial is an equation that can be written in the form:

ax² + bx + c = 0

where a, b, and c are real numbers and x is a variable. The roots of a polynomial are the values of x that make the equation true. The multiplicity of a root is the number of times that the root appears as a solution to the equation.

To find the roots of a polynomial, you can use the Quadratic Formula:

x = (-b +/- sqrt(b² - 4ac)) / (2a)

where a, b, and c are the coefficients of the equation. The +/- sign indicates that there are two roots, one with a positive sign and one with a negative sign.

The multiplicity of a root can be found by counting how many times the root appears as a solution to the equation. For example, if the root x = 2 appears twice as a solution, then the multiplicity of the root is 2.

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Answer:

......................................................d

There are two outliers in the given data and they are 3 and 30. Hence, option C is correct.

Two definitions are given for an arithmetic sequence. A "series where the variances in between every two succeeding terms are the same" is what it is. Each term in an algebraic expression is created by multiplying its previous term by a specified integer (either positive, negative, or zero).

As per the given information in the question,

The length of dolphins is given as:

3, 15, 30, 19, 11, 18, 17, 12

As we can see in this data every length is somewhere close to 20 but lengths 3 and 30 are not similar to others.

So, these two are outliers.

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The first statement is always true.

If m ∠m = 64° then m ∠F = 64°.

What is isomorphic triangles?

If there is an isomorphism connecting the vertices of P and Q, and that isomorphism has the property that three vertices of P form a triangle in Tp if and only if the mapping of the three vertices in Q, then the triangulations of two simple polygons, Tp and Tq, are said to be isomorphic (or occasionally compatible).

Given: ΔDEF ≅ ΔJAM

As the triangles are isomorphic that means that each angle of the triangle are same.

⇒ ∠D = ∠J

∠E = ∠A

∠F = ∠M

Hence, If m ∠m = 64° then m ∠F = 64° is true.

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A program that reads a list of scores and then assigns grades based on the following scheme is listed below.

Python 2.6 version

def grade(score, best):

   if score >= best -10:

       return 'A'

   if score >= best -20:

       return 'B'

   if score >= best -30:

       return 'C'

   if score >= best -40:

       return 'D'

   return 'F'

score = raw_input("Enter scores: ")

scores = [ int(s) for s in score.split()]

best = scores[0]

for i in range(len(scores)):

   if scores[i] > best:

       best = scores[i]

for i in range(len(scores)):

   print "Student", i, "score is", scores[i], "and grade is", grade(scores[i], best)

# Copy pastable link: https://paste.ee/p/qA5RQ

def grade(score, best):

if score >= best -10:

return 'A'

if score >= best -20:

return 'B'

if score >= best -30:

return 'C'

if score >= best -40:

return 'D'

return 'F'

score = input("Enter scores: ")

scores = [ int(s) for s in score.split()]

best = scores[0]

for i in range(len(scores)):

if scores[i] > best:

best = scores[i]

for i in range(len(scores)):

print("Student", i, "score is", scores[i], "and grade is", grade(scores[i], best))

Sample execution:

Enter scores: 40 55 70 58 Student 0 score is 40 and grade is C Student 1 score is 55 and grade is B Student 2 score is 70 and grade is A Student 3 score is 58 and grade is B

# copy pastable code link: https://paste.ee/p/UVTbP

Hence the answer is a program that reads a list of scores and then assigns grades based on the following scheme is listed above.

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