0.777... is rational, because it is a number with infinite but repeating decimal part.
1/3 is rational, because it's the division between two integers
$-\sqrt{16}=-4$ , so this is rational as well.

Since the product of two rational numbers is always rational, we have that

$0.\bar{7}\cdot \dfrac{1}{3},\quad \dfrac{1}{3}\cdot \dfrac{1}{3},\quad -4\cdot \dfrac{1}{3}$

are all rationals, since they are the product of two rationals.

On the other hand, we have

$\sqrt{27}=\sqrt{9\cdot 3}=3\sqrt{3}$

and thus

$3\sqrt{3}\cdot \dfrac{1}{3}=\sqrt{3}$

which is irrational.

3 0

2 years ago

What is the area of triangle ABC

deff fn [24]

$\text{Area of triangle} = \dfrac{1}{2} ab \sin c$

$\text{Area of triangle} = \dfrac{1}{2} (40)(25) \sin(80)$

$\text{Area of triangle} = 492.4 \ m^2$

6 0

3 years ago

Read 2 more answers

Which polynomial is a product of (3x+2) and (x-7)

pogonyaev

(3x+2) (x-7)

FOIL

first 3x*x = 3x^2

outer 3x*-7 = -21x

inner = 2*x = 2x

last 2*-7 = -14

add them together = 3x^2 -21x+2x -14