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Otrada [13]
3 years ago
6

Which relation is a function?

Mathematics
1 answer:
sergejj [24]3 years ago
7 0

To determine which relation is a function, we can perform something called the vertical line test. We cover the graph in repeating vertical lines and if one vertical line connects with more than one point of the relation, the relation is not a function.

The relation in the bottom right corner is the only relation that passes the vertical line test.

You might be interested in
What is the solution set of (x-2)(x-3)=3
natali 33 [55]

Answer:

x =(5-√13)/2= 0.697

x =(5+√13)/2= 4.303

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

 (x - 2) • (x - 3) -  3  = 0  

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  x2-5x+3  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -5x  its coefficient is  -5 .

The last term, "the constant", is  +3  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 3 = 3  

Step-2 : Find two factors of  3  whose sum equals the coefficient of the middle term, which is   -5 .

     -3    +    -1    =    -4  

     -1    +    -3    =    -4  

     1    +    3    =    4  

     3    +    1    =    4  

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step  2  :

 x2 - 5x + 3  = 0  

Step  3  :

Parabola, Finding the Vertex :

3.1      Find the Vertex of   y = x2-5x+3

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).  

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.  

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.  

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   2.5000  

Plugging into the parabola formula   2.5000  for  x  we can calculate the  y -coordinate :  

 y = 1.0 * 2.50 * 2.50 - 5.0 * 2.50 + 3.0

or   y = -3.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-5x+3

Axis of Symmetry (dashed)  {x}={ 2.50}  

Vertex at  {x,y} = { 2.50,-3.25}  

x -Intercepts (Roots) :

Root 1 at  {x,y} = { 0.70, 0.00}  

Root 2 at  {x,y} = { 4.30, 0.00}  

Solve Quadratic Equation by Completing The Square

3.2     Solving   x2-5x+3 = 0 by Completing The Square .

Subtract  3  from both side of the equation :

  x2-5x = -3

Now the clever bit: Take the coefficient of  x , which is  5 , divide by two, giving  5/2 , and finally square it giving  25/4  

Add  25/4  to both sides of the equation :

 On the right hand side we have :

  -3  +  25/4    or,  (-3/1)+(25/4)  

 The common denominator of the two fractions is  4   Adding  (-12/4)+(25/4)  gives  13/4  

 So adding to both sides we finally get :

  x2-5x+(25/4) = 13/4

Adding  25/4  has completed the left hand side into a perfect square :

  x2-5x+(25/4)  =

  (x-(5/2)) • (x-(5/2))  =

 (x-(5/2))2

Things which are equal to the same thing are also equal to one another. Since

  x2-5x+(25/4) = 13/4 and

  x2-5x+(25/4) = (x-(5/2))2

then, according to the law of transitivity,

  (x-(5/2))2 = 13/4

We'll refer to this Equation as  Eq. #3.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-(5/2))2   is

  (x-(5/2))2/2 =

 (x-(5/2))1 =

  x-(5/2)

Now, applying the Square Root Principle to  Eq. #3.2.1  we get:

  x-(5/2) = √ 13/4

Add  5/2  to both sides to obtain:

  x = 5/2 + √ 13/4

Since a square root has two values, one positive and the other negative

  x2 - 5x + 3 = 0

  has two solutions:

 x = 5/2 + √ 13/4

  or

 x = 5/2 - √ 13/4

Note that  √ 13/4 can be written as

 √ 13  / √ 4   which is √ 13  / 2

Solve Quadratic Equation using the Quadratic Formula

3.3     Solving    x2-5x+3 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

                                     

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     1

                     B   =    -5

                     C   =   3

Accordingly,  B2  -  4AC   =

                    25 - 12 =

                    13

Applying the quadratic formula :

              5 ± √ 13

  x  =    —————

                   2

 √ 13   , rounded to 4 decimal digits, is   3.6056

So now we are looking at:

          x  =  ( 5 ±  3.606 ) / 2

Two real solutions:

x =(5+√13)/2= 4.303

or:

x =(5-√13)/2= 0.697

4 0
3 years ago
Read 2 more answers
Which value of x makes the inequality true?
grigory [225]

The answer is A.

AKA 1.6

5 0
2 years ago
75 points. Will give certified if work is shown and the answer is correct.
Svetach [21]
Volume of the first dwarf planet (r₁ = 832 mi):

V_1=\dfrac{4}{3}\cdot\pi\cdot r_1^3=\dfrac{4}{3}\cdot\pi\cdot 832^3=\dfrac{2303721472}{3}\pi\approx7.679\cdot10^8\pi\,\text{mi}^3

Volume of the second dwarf planet (r₂ = 829 mi):

V_2=\dfrac{4}{3}\cdot\pi\cdot r_2^3=\dfrac{4}{3}\cdot\pi\cdot 829^3=\dfrac{2278891156}{3}\pi\approx7.5963\cdot10^8\pi\,\text{mi}^3

So difference between the volumes is:

V_1-V_2\approx7.679\cdot10^8\pi-7.5963\cdot10^8\pi=0.0827\cdot10^8\pi=\boxed{8270000\pi\,\text{mi}^3}

or if we want exact value (we use (a³-b³) = (a-b)(a²+ab+b²) ):

V_1-V_2=\dfrac{4}{3}\cdot\pi\cdot r_1^3-\dfrac{4}{3}\cdot\pi\cdot r_2^3=\dfrac{4}{3}\pi(r_1^3-r_2^3)=\dfrac{4}{3}\pi(832^3-829^3)=\\\\\\=\dfrac{4}{3}\pi(832-829)(832^2+832\cdot829+829^2)=\\\\\\=\dfrac{4}{3}\pi\cdot3(692224+689728+687241)=4\pi\cdot2069193=\boxed{8276772\pi\,\text{mi}^3}
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2 years ago
Which of the following represents A U B?
algol [13]

Answer:

Step-by-step explanation:

7 0
3 years ago
find the mean of the data set. if necessary, round to the nearest tenth. 15.8, 14.9, 16.7, 17.6, 13.4 15 points
lana [24]
I believe that answer is 15.7.
6 0
2 years ago
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