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slamgirl [31]
3 years ago
15

If f(x) = x^2 - 2x+3 then what is f(-3)?

Mathematics
2 answers:
leva [86]3 years ago
6 0

Answer:

f(-3)=18

Step-by-step explanation:

(-3)*2-2*(-3)+3

9+6+3

18

galben [10]3 years ago
5 0

Answer:

f(- 3) = 18

Step-by-step explanation:

To evaluate f(- 3) substitute x = - 3 into f(x)

f(- 3) = (- 3)² - 2(- 3) + 3 = 9 + 6 + 3 = 18

You might be interested in
Sarah, Natasha and Richard share some sweets in the ratio 4:2:3. Sarah gets 13 more sweets than Richard. How many sweets are the
gayaneshka [121]

Answer:

117 sweets

Step-by-step explanation:

Please see attached picture for full solution. (model method)

S, N and R represents the number of sweets Sarah, Natasha and Richard have respectively.

Alternatively,

Let the number of sweets Sarah have be 4x.

Number of sweets Natasha have= 2x

Number of sweets Richard have= 3x

<em>Sarah gets 13 more sweets than Richard</em>

4x= 3x +13

4x -3x= 13

x= 13

Total number of sweets

= 4x +2x +3x

= 9x <em>(</em><em>simplify</em><em>)</em>

= 9(13) <em>(</em><em>subst</em><em>.</em><em> </em><em>x</em><em>=</em><em>1</em><em>3</em><em>)</em>

= 117 sweets

4 0
3 years ago
Read 2 more answers
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
3 years ago
Read 2 more answers
What type of graph is best to use to show data that are parts of a whole?
san4es73 [151]
A pie chart? i think
6 0
3 years ago
Can someone please help me
ss7ja [257]

Answer:

a.) 1/2

b.) 1/8

c.) 5/8

d.) 1/2

Step-by-step explanation:

for A it is asking for probability of 1 and is 1/2 of the circle

for B it is asking for  probability of 3 and it is 1/2 of and 1/4 of the circle so 1/8

for C it is asking for probability of the odd numbers and there is tow odd numbers 1 and 3 the probability of 1 is 1/2 and the probability of 3 is 1/8 adding them up will give you 5/8

for d it asks for the probability of at least 2 so therefor 2, 3, and 4 and they are 1/8 + 1/8 + for 1/4 = 1/2

6 0
3 years ago
Which of these are measures of central tendency that can be found for this list of heights recorded in the high-jump event at a
Gwar [14]
I believe the correct answer is a hope this helps if not then sorry
3 0
3 years ago
Read 2 more answers
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