can someone help me out with this?? I am God awful at basic math such as this...apologies if I sound absurdly stupid;;​

Answer:

Option 4:  (3,5)

Step-by-step explanation:

(x - 3)(x - 5) < 0

Therefore, the intervals that must be tested are x < 3 , 3<x<5  and  x>5

Test of the interval  x<3⇒ Let x = 0 ⇒ (-3)(-5) = 15 > 0

Test of the interval  3<x<5 ⇒ Let x = 4  ⇒ (4-3)(4-5) = (1)(-1) = -1 < 0

Test of the interval  x>5⇒ Let x = 6 ⇒ (6-3)(6-5) = (3)(1) = 3 > 0

So, the solution set for the quadratic inequality is the interval 3<x<5

Or x ∈ (3,5)

See the attached figure.

The answer is option 4

Answer:

1. (3,5)   2. b and c

Step-by-step explanation:

Just took it and got it correct

The shape that has three equal side lengths of 4 cm and has no right angle is an: equilateral triangle.

What is an Equilateral Triangle?

An equilateral triangle is a triangle that has equal angles and also has side length that are of equal measure.

The angles of an equilateral triangle each equals 60 degrees.

Therefore, the shape with three equal sides and no right angles is an: equilateral triangle.

Learn more about the equilateral triangle on:

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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.

To know more about quadratic equation click on,

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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