List four rational number between -4/5 and -2/3

-31/45, -32/45, -33/45, -34/45, and -35/45

Step-by-step explanation:

Rational numbers are any number that can be written as a ratio of two integers.

First, find the common denominator using the least common multiple (LCM).

The LCM of 3 and 5 is 15.  So the fractions can be written as:

-12/15 and -10/15

If we keep the denominator 15, then only one rational number can be written between these two: -11/15.  We need to find four rational numbers.  So instead, let's use a denominator of 45.  The fractions become:

-36/45 and -30/45

Now we can write five rational numbers between those:

-31/45, -32/45, -33/45, -34/45, and -35/45.

Choose any 4 that you like.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)