Mathematics: Pls someone help me with this question pls

Pls someone help me with this question pls

vperez719

01.05.2021

$p =\frac{1}{6}$

Step-by-step explanation:

Given

$Polygons =\{Quadrilateral, Pentagon, Hexagon, Octagon, Nonagon, Decagon\}$

Required

Probability of assigning a nonagon

From the given set of polygons, there are 6 polygons in the set and 1 one of them is a nonagon

This means that:

n = 6 --- Total

Nonagons = 1

So, the probability, p is:

$p =\frac{Nonagons}{n}$

$p =\frac{1}{6}$

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gracye

26.09.2021

Area = $3x^{4} - 4x^{3} - 8x^{2} -35x -10$ .

Step-by-step explanation:

Given : Vanessa uses the expressions (3x² + 5x + 10) and (x² – 3x – 1) to represent the length and width of her patio.

To find : Which expression represents the area (lw) of Vanessa’s patio?

Solution : We have given

Length = (3x² + 5x + 10)

Width = (x² – 3x – 1)

Area= length * width .

Area = (3x² + 5x + 10) * (x² – 3x – 1).

Area = 3x² (x² – 3x – 1) + 5x (x² – 3x – 1) + 10 (x² – 3x – 1).

Area = $3x^{4} - 9x^{3} - 3x^{2} + 5x^{3} - 15x^{2} -5x + 10x^{2} -30x -10$ .

Combine like terms

Area = $3x^{4} - 9x^{3} + 5x^{3} - 3x^{2} - 15x^{2} + 10x^{2} -5x -30x -10$ .

Area = $3x^{4} - 4x^{3} - 18x^{2} + 10x^{2} -35x -10$ .

Area = $3x^{4} - 4x^{3} - 8x^{2} -35x -10$ .

Therefore, Area = $3x^{4} - 4x^{3} - 8x^{2} -35x -10$ .

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