a.
The polynomial w^2+18w+84 cannot be factored
The perfect square trinomial is w^2+18w + 81
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The reason the original can't be factored is that solving w^2+18w+84=0 leads to no real solutions. Use the quadratic formula to see this. The graph of y = x^2+18x+84 shows there are no x intercepts. A solution and an x intercept are basically the same. The x intercept visually represents the solution.
w^2+18w+81 factors to (w+9)^2 which is the same as (w+9)(w+9). We can note that w^2+18w+81 is in the form a^2+2ab+b^2 with a = w and b = 9
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b.
The polynomial y^2-10y+23 cannot be factored
The perfect square trinomial is y^2-10y + 25
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Using the quadratic formula, y^2-10y+23 = 0 has no rational solutions. The two irrational solutions mean that we can't factor over the rationals. Put another way, there are no two whole numbers such that they multiply to 23 and add to -10 at the same time.
If we want to complete the square for y^2-10y, we take half of the -10 to get -5, then square this to get 25. Therefore, y^2-10y+25 is a perfect square and it factors to (y-5)^2 or (y-5)(y-5)
4,700 is one of the correct answers to this question.
The amount of radioactive material remaining after 24 hours is 92.15 kg.
<h3>
Exponential function</h3>
An exponential function is in the form:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplier.
Let y represent the amount of the substance after t hours.
From the equation, a = 100 mg
Also, after 6 hours:
After 24 hours:
y = 100(0.9966)²⁴ = 92.15 kg
The amount of radioactive material remaining after 24 hours is 92.15 kg.
Find out more on Exponential function at: brainly.com/question/12940982
