Algebra

The sum of an infinite geometric progression is calculated using the formula S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio. Substituting the given values yields 4 / (1 - 0.5) = 8. Option A (6) is incorrect because it fails to apply the correct division by the remaining fractional part.

Factoring the quadratic equation yields (x - 5)(x + 1) = 0, which gives the roots x = 5 and x = -1. Option C is incorrect because it reverses the signs, which would result from factoring the equation as (x + 5)(x - 1) = 0 instead of the given expression

Factoring the quadratic equation yields (x - 3)(x - 4) = 0, which gives the roots x = 3 and x = 4. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !Option D is incorrect because using negative roots -3 and -4 would result in a positive middle coefficient of +7x instead of -7x.
• !An answer of 5 is incorrect because 2 raised to the 5th power is only 32, while choosing 7 would overestimate the value at 128.
• !Option C is incorrect because it reverses the signs, which would result from factoring the equation as (x + 5)(x - 1) = 0 instead of the given expression
• !The sum of an infinite geometric progression is calculated using the formula S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio.

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