Which of the following statements is true if p is an internet and q is a nonzero integer? a. an irrational number can be written as a fraction p/q. b. a rational number can not be written as a fraction p/q. c. all numbers can be written as a fraction p/q. d. a rational number can be written as a fraction p/q.

D. A rational number can be written as a fraction p/q

Step-by-step explanation:

All real numbers are classified into two major categories namely rational and irrational numbers.

A number which can be written in the form , p and q are integers and q ≠ 0 is called a rational number.

Ex:

is a rational number

5 is a rational number since 5 can be written as and clearly, 1 ≠ 0

0 is also rational since 0 can be written as .

A number which cannot be written in the form is called an irrational number.

Ex:

is an irrational number since it cannot be written in form,

Hence, the correct option is D.

last option

step-by-step explanation:

given that δdef is right and isoceles,

assuming that side df is the hypotenuse means that de an ef are the other 2 sides that intersect at 90° and are of equal length.

because they are of equal length, we can say that they are congruent

because they intersect at 90°, their slopes must be opposite reciprocals.

only the last option satisfies these conditions.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204