Answer: 1. {-2, -3} 2. {-5, 5} 3. {-3, 5}
<u>Step-by-step explanation:</u>
1) First, factor the equation by finding two numbers whose product is 6 and sum is 5. Then apply the Zero Product Property by setting each product equal to zero and solving for m.
m² + 5m + 6 = 0
∧
1 + 6 = 7
2 + 3 = 5 This works!
(x + 2)(x + 3) = 0
x + 2 = 0 x + 3 = 0
x = -2 x = -3
2) Factor out the GCF of 5. Notice the remaining factor is the difference of squares (because the middle term is missing and the first and last terms are perfect squares. Then apply the Zero Product Property by setting each product equal to zero and solving for p.
5p² - 125 = 0
5(p² - 25) = 0
5(p +5)(p - 5) = 0
5 ≠ 0 p+ 5 = 0 p - 5 = 0
p = -5 p = 5
3) Factor out the GCF of 2. Factor the equation by finding two numbers whose product is -15 and sum is -2. Then apply the Zero Product Property by setting each product equal to zero and solving for x.
2x² - 4x - 30 = 0
2(x² - 2 - 15) = 0
∧
1 - 15 = -14
3 - 5 = -2 This works!
(x + 3)(x - 5) = 0
x + 3 = 0 x - 5 = 0
x = -3 x = 5
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The shape with 9 sides is a Nonagon the prefix non means 9 and the word agon means shape so the word nonagon means 9 sides <span />
The slope is negative one half because perpendicular lines always have slopes that are opposite reciprocals
meaning not only are they reciprocals meaning 1 over the number (or flipping the numerator and the denominator of a fraction) you also change the sign