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Ilia_Sergeevich [38]
2 years ago
9

Compleete the equation of the line whose y-intercept 0-,1 and slope is 4

Mathematics
1 answer:
siniylev [52]2 years ago
7 0

Answer:

y = 4x - 1

Step-by-step explanation:

y = mx + b, m is the slope, b is the y intercept or -1

You might be interested in
Solve 3k^2=8k+8,using completing the square method ​
GenaCL600 [577]

Answer:

3k2=8k+8 

Two solutions were found :

 k =(8-√160)/6=(4-2√ 10 )/3= -0.775

 k =(8+√160)/6=(4+2√ 10 )/3= 3.442

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "k2"   was replaced by   "k^2". 

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

                     3*k^2-(8*k+8)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

3k2 - (8k + 8) = 0

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3k2-8k-8 

The first term is,  3k2  its coefficient is  3 .

The middle term is,  -8k  its coefficient is  -8 .

The last term, "the constant", is  -8 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -8 = -24 

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   -8 .

     -24   +   1   =   -23     -12   +   2   =   -10     -8   +   3   =   -5     -6   +   4   =   -2     -4   +   6   =   2     -3   +   8   =   5     -2   +   12   =   10     -1   +   24   =   23

Observation : No two such factors can be found !! 

Conclusion : Trinomial can not be factored

Equation at the end of step  2  :

3k2 - 8k - 8 = 0

Step  3  :

Parabola, Finding the Vertex :

 3.1      Find the Vertex of   y = 3k2-8k-8

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, 3 , 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,Ak2+Bk+C,the  k -coordinate of the vertex is given by  -B/(2A) . In our case the  k  coordinate is   1.3333  

 Plugging into the parabola formula   1.3333  for  k  we can calculate the  y -coordinate : 

  y = 3.0 * 1.33 * 1.33 - 8.0 * 1.33 - 8.0 

or   y = -13.333

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = 3k2-8k-8

Axis of Symmetry (dashed)  {k}={ 1.33} 

Vertex at  {k,y} = { 1.33,-13.33}  

 k -Intercepts (Roots) :

Root 1 at  {k,y} = {-0.77, 0.00} 

Root 2 at  {k,y} = { 3.44, 0.00} 

Solve Quadratic Equation by Completing The Square

 3.2     Solving   3k2-8k-8 = 0 by Completing The Square .

 Divide both sides of the equation by  3  to have 1 as the coefficient of the first term :

   k2-(8/3)k-(8/3) = 0

Add  8/3  to both side of the equation : 

   k2-(8/3)k = 8/3

Now the clever bit: Take the coefficient of  k , which is  8/3 , divide by two, giving  4/3 , and finally square it giving  16/9 

Add  16/9  to both sides of the equation :

  On the right hand side we have :

   8/3  +  16/9   The common denominator of the two fractions is  9   Adding  (24/9)+(16/9)  gives  40/9 

  So adding to both sides we finally get :

   k2-(8/3)k+(16/9) = 40/9

Adding  16/9  has completed the left hand side into a perfect square :

   k2-(8/3)k+(16/9)  =

   (k-(4/3)) • (k-(4/3))  =

  (k-(4/3))2 

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

   k2-(8/3)k+(16/9) = 40/9 and

   k2-(8/3)k+(16/9) = (k-(4/3))2 

then, according to the law of transitivity,

   (k-(4/3))2 = 40/9

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

   (k-(4/3))2   is

   (k-(4/3))2/2 =

  (k-(4/3))1 =

   k-(4/3)

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

   k-(4/3) = √ 40/9 

Add  4/3  to both sides to obtain:

   k = 4/3 + √ 40/9 

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

   k2 - (8/3)k - (8/3) = 0

   has two solutions:

  k = 4/3 + √ 40/9 

   or

  k = 4/3 - √ 40/9 

Note that  √ 40/9 can be written as

  √ 40  / √ 9   which is √ 40  / 3 

Solve Quadratic Equation using the Quadratic Formula

 3.3     Solving    3k2-8k-8 = 0 by the Quadratic Formula .

 According to the Quadratic Formula,  k  , the solution for   Ak2+Bk+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

                                     

            - B  ±  √ B2-4AC

  k =   ————————

                      2A 

  In our case,  A   =     3

                      B   =    -8

                      C   =   -8 

Accordingly,  B2  -  4AC   =

                     64 - (-96) =

                     160

Applying the quadratic formula :

               8 ± √ 160 

   k  =    —————

                    6

Can  √ 160 be simplified ?

Yes!   The prime factorization of  160   is

   2•2•2•2•2•5  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a squarei.e. second root).

√ 160   =  √ 2•2•2•2•2•5   =2•2•√ 10   =

                ±  4 • √ 10 

  √ 10   , rounded to 4 decimal digits, is   3.1623

 So now we are looking at:

           k  =  ( 8 ± 4 •  3.162 ) / 6

Two real solutions:

 k =(8+√160)/6=(4+2√ 10 )/3= 3.442 

or:

 k =(8-√160)/6=(4-2√ 10 )/3= -0.775 

Two solutions were found :

 k =(8-√160)/6=(4-2√ 10 )/3= -0.775

 k =(8+√160)/6=(4+2√ 10 )/3= 3.442

5 0
2 years ago
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Find the side of a square with area of 25 sq. ft
zheka24 [161]
The side of a square would be 5 because the square root of 25 is 5.
7 0
2 years ago
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Suppose that a number written as a decimal has an infinite number of non-repeating digits after the decimal point. What is this
enyata [817]

Answer:

irrational numbers

Step-by-step explanation:

These types of numbers are known in mathematics as irrational numbers. This is because there is no way to truly rationalize these numbers as we cannot truly rationalize the meaning of infinity. These numbers keep going endlessly and there doesn't exist an end. One example of an irrational number is the value of Pi which we know as a simplified 3.14 but in reality, the value of Pi is endless. The first thousand places of Pi can be seen below

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989

4 0
3 years ago
Pls help!!!!!!!!!!!!!!!!!
vazorg [7]

Answer:

19 for each one

Step-by-step explanation:

Divide 57 by 3

3 0
3 years ago
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A tunnel is 300 feet deep and makes an angle of 30 with the ground .
Goshia [24]

Answer:

\boxed{C.\:\: 600\:feet}

Step-by-step explanation:


The tunnel, the ground and the depth of the tunnel form a right angle triangle.

The length of the tunnel is the hypotenuse of the right triangle that has been formed.


Let the length of the tunnel be m\: feet.


Using the sine ratio, we obtain;


\sin(30\degree)=\frac{Opposite}{Hypotenuse}


The length of the opposite side is 300\:feet


We substitute the given values to obtain;


\sin(30\degree)=\frac{300}{m}


\Rightarrow \frac{1}{2}=\frac{300}{m}


We cross multiply to obtain;


m=300\times2


m=600\:feet


Therefore the correct answer is C.


4 0
3 years ago
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