Tue 05/28
11. find the common ratio of the sequence.
2, -10,50.-250,
0-5
.

-5

Step-by-step explanation:

Geometric sequences have common ratios.

You can see if a sequence is geometric by computing:

.

If you get the same result per consecutive pair, then there is a common ratio and the sequence is geometric.

Let's see:

So if this equations holds (if all 3 fractions equal the same thing), then is geometric and we have also have computed the common ratio.

The first fraction results in -250/50=-5.

The second fraction results in 50/-10=-5.

The third fraction results in -10/2=-5.

All three fractions are equal and so the equation holds so it is geometric and the common ratio is -5.

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)