Which best explains what determines whether a number is irrational? a) a number that can be written as a decimal that repeats and does not terminate b) a number that can be written as a decimal that terminates and does not repeat c) a number that can be written as a square root that does not result in a whole number d) a number that can be writtten as a decimal that neither repeats nor terminates

Irrational number can be written as decimal number that, neither a terminating decimal or repeating decimal. Thus, the option D is the correct option, which is a number that can be written as a decimal that neither repeats nor terminates.

Irrational numbers are the number which is the real number but not the rational number(a/b).The irrational numbers can not be represents in the fractional form.

Irrational numbers are written in the form of root of a number such as,

,   ,     etc.

Irrational number can be written as decimal number that, neither a terminating decimal or repeating decimal.

Lets check all the given options as,

Hence, A number that can be written as a decimal that neither repeats nor terminates the option D is the correct option.

Learn more about the irrational number here;

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Option: D is the correct answer.

D) a number that can be written as a decimal that neither repeats nor terminates

We know that real numbers are  divided into two categories:

1)

  Rational Number--

A number that can be expressed in the form of p/q i.e. a fraction where p belongs to integers and q belongs to natural numbers and also the decimals which are terminating and  repeating.

2)

   Irrational Number--

A number that cannot be expressed in the form of p/q are irrational also the non-repeating and non-terminating decimals are considered as irrational.

         Hence, the answer is:

            Option: D

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!