The function ggg models the number of mosquitoes (in millions of mosquitoes) in a certain area as a function of rainfall (in centimeters) in that area. Which of these statements are true? Choose all answers that apply: Choose all answers that apply: (Choice A) A More rainfall relates to more mosquitoes as long as rainfall is less than 2\text{ cm}2 cm2, start text, space, c, m, end text. (Choice B) B More rainfall relates to more mosquitoes as long as rainfall is more than 2\text{ cm}2 cm2, start text, space, c, m, end text. (Choice C) C When there is no rainfall, there are about 111 million mosquitoes. (Choice D) D When there is no rainfall, there are about 222 million mosquitoes.

(Choice A) A More rainfall relates to more mosquitoes, as long as rainfall is less than 2 cm²

Step-by-step explanation:

The given function for the number of mosquitoes, (by analysis of the options) is, g(x) = 4·x - x²

Where;

x = The amount of rainfall

g(x) = The number of mosquitoes in millions

The given function can be expressed as follows;

g(x) = 4·x - x² + 0

The maximum point is given by g'(x) = d(4·x - x²)/dx = 4 - 2·x = 0

At the maximum (turning point), we have;

4 - 2·x = 0

4 = 2·x

x = 4/2 = 2

The level of rainfall that gives the maximum number of mosquitoes is, x = 2 cm²

The number of mosquitoes increases from zero rainfall up to the maximum number of 4 million mosquitoes at 2 cm² rainfall and then decreases to zero as the rainfall increases further more than 2 cm², as shown in the attached  graph of the function g(x) that models the number of mosquitoes created with MS Excel

Therefore, the true statement is (Choice A) more rainfall relates to more mosquitoes, as long as (the level of) rainfall is less than (the maximum) 2 cm².

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.