Ratios and proportions... 7/9 and 140/180

The solutions obtained by using quadratic formula are given as -4 + 2√2 and -4 - 2√2 respectively.

What is a quadratic equation?

The general form of a quadratic equation is given as ax^2 + bx + c = 0.

Here, a ≠ 0 and b and c are integers.

The degree of a quadratic equation is 2.

The given quadratic equation is   x² + 8x - 6 = 0.

The quadratic formula for a quadratic equation ax² + bx + c  is given as,

x = (-b ± √(b² - 4ac))/2a

Substitute the values of corresponding coefficients to get,

x = (-8 ± √(8² - 4 × 1 × -6))/2 × 1

  = (-8 ± √32)/2

  = -4 ± 2√2

Hence, the solution of the given quadratic equation is given as -4 + 2√2 and -4 - 2√2 respectively.

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Answer:

Two solutions were found :

x =(8-√88)/2=4-√ 22 = -0.690  

x =(8+√88)/2=4+√ 22 = 8.690

Step-by-step explanation:

olving    x2-8x-6 = 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   =    -8

                     C   =   -6  

Accordingly,  B2  -  4AC   =

                    64 - (-24) =

                    88

Applying the quadratic formula :

              8 ± √ 88  

  x  =    —————

                   2

Can  √ 88 be simplified ?

Yes!   The prime factorization of  88   is

  2•2•2•11  

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).

√ 88   =  √ 2•2•2•11   =

               ±  2 • √ 22  

 √ 22   , rounded to 4 decimal digits, is   4.6904

So now we are looking at:

          x  =  ( 8 ± 2 •  4.690 ) / 2

Two real solutions:

x =(8+√88)/2=4+√ 22 = 8.690  

or:

x =(8-√88)/2=4-√ 22 = -0.690  

Two solutions were found :

x =(8-√88)/2=4-√ 22 = -0.690  

x =(8+√88)/2=4+√ 22 = 8.690

Answer: 1 = 69°, 2 = 69°, 3 = 111°

Step-by-step explanation:

The image is that of an isosceles trapezoid.  Which means:

1. The base angles (1 & 2) are congruent (equal)
2. which results in the other set of base angles (3 and 111°) being congruent.  
3. Since it is a quadrilateral (4 sides), the sum of the angles is 360°

∠3 = 111°   →  refer to #2 above.

Let ∠1 =x, then ∠2 = x  → refer to #1 above

2(111) + 2(x) = 360    →    refer to #3 above

222 + 2x = 360

          2x = 138

            x = 69

The amount of soil dug out of well is 63.585 .

How to calculate the volume of cylinder?

Volume of Cylinder=

Given values: =3.14

                      r=0.9 m (d/2)

                      h=25 m

Volume:

=63.585

Therefore 63.585 cubic meters of soil was dug out.

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The answer is c hopes this helps.

Answer:

Assuming the function is f(x) = 5(2)^x, then the answer is the graph with the point (2,20) on the curve. Plugging in x = 2 leads to y = 20 y = 5(2)^x

Step-by-step explanation: