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goldfiish [28.3K]
3 years ago
13

Which expression is equivalent to square root -108 - square root -3?

Mathematics
1 answer:
horsena [70]3 years ago
4 0

Answer:

A) 5 square root 3i

Step-by-step explanation:

Simplify each term.

6i√3−i√3

Subtract 1i√3 from 6i√3.

5i√3

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The U.S.A. Olympic Synchronized Swimming Team is designing a routine for their upcoming competition. From the center of the pool
Mama L [17]

Answer:

The equation of the circle is;

(x - 2)² + (y - 4)² = 5²  

Step-by-step explanation:

We note that the general equation of a circle is given as follows;

(x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The radius of the circle

The given parameters are;

The location of the center of the pool to the center of their formation = 2 feet to the right and 4 feet up from the center of the pool

The point through which the circle which they form goes through = A point 3 feet to the left and 4 feet up from the center of their formation

Taking the center of the pool as the origin of the coordinate plane system, we have;

The coordinate of the center of the circle = The coordinate of their motion from the center of the circle

∴ The coordinate of the center of the circle = (2, 4)

∴ (h, k) = (2, 4)

h = 2, k = 4

The coordinate of the point through which the circle passes = (2 - 3, 4 + 4) = (-1, 8)

∴ The length of the radius, 'r', can be found as, r = √((-3)² + 4²) = 5 or r = √((-1 - 2)² + (8 - 4)²) = 5

r = 5

The equation of the circle is therefore presented by substituting the values of 'h', 'k', and 'r', as follows;

(x - 2)² + (y - 4)² = 5².

4 0
3 years ago
What is the Factor 4m^3-32n^3
Klio2033 [76]

Answer:

2(47m^3-16n^3)

Step-by-step explanation:

7 0
3 years ago
A medical company tested a new drug for possible side effects. The table
Lelu [443]
The correct answer is b
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What are the solutions to the equation 2(x-3)^2=54 ?
erastova [34]

Answer:

      x =(6-√108)/2=3-3√ 3 = -2.196

 x =(6+√108)/2=3+3√ 3 = 8.196

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

2 • (x - 3)2 - 54 = 0

Step  2  :

 2.1    Evaluate :  (x-3)2   =  x2-6x+9 

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   2x2 - 12x - 36  =   2 • (x2 - 6x - 18) 

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

   x2-6x+9  =

   (x-3) • (x-3)  =

  (x-3)2  (x-3)1 =

   x-3

Now, applying the Square Root Principle to  Eq. #4.3.1  we get:

   x-3 = √ 27

Add  3  to both sides to obtain:

   x = 3 + √ 27

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

   x2 - 6x - 18 = 0

   has two solutions:

  x = 3 + √ 27

   or

  x = 3 - √ 27

Solve Quadratic Equation using the Quadratic Formula

 4.4     Solving    x2-6x-18 = 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   =    -6

                      C   =  -18

Accordingly,  B2  -  4AC   =

                     36 - (-72) =

                     108

Applying the quadratic formula :

               6 ± √ 108

   x  =    —————

                    2

Can  √ 108 be simplified ?

Yes!   The prime factorization of  108   is

   2•2•3•3•3 

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

√ 108   =  √ 2•2•3•3•3   =2•3•√ 3   =

                ±  6 • √ 3

  √ 3   , rounded to 4 decimal digits, is   1.7321

 So now we are looking at:

           x  =  ( 6 ± 6 •  1.732 ) / 2

Two real solutions:

 x =(6+√108)/2=3+3√ 3 = 8.196

or:

 x =(6-√108)/2=3-3√ 3 = -2.196

7 0
3 years ago
Evaluate: a-2b/c : if a = -8, b = 6.5, and c = -2.<br><br> -1.5<br><br> 10.5<br><br> -9
Mkey [24]
The answer to ur equation is  -1.5
3 0
3 years ago
Read 2 more answers
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