Letters a, b, c, and d are angles measures. Which equation is enough information to prove that lines m and n are parallel lines
cut by transversal p? Select three options. a = c a = d c = d b + c = 180° b + d = 180°
1 answer:
Response:
b + d = 180°, a = d, and a = c
Detailed explanation:
In the diagram, we observe that the only condition for the lines to be parallel is that the angles correspond with their counterparts, for instance, a must equal d. The equation a = c indicates that all angles must be equal for lines m and n to remain parallel. Finally, the equation b + d = 180° confirms that this holds true only if lines m and n are parallel.
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Answer:
The universal formula applicable for determining the necessary combinations of n ice cream flavors.
For 10 flavors of ice cream
Step-by-step explanation:
Let's denote V = Vanilla, C = Chocolate, S = Strawberry, P = Pineapple, B = Berry
For 2 flavors of ice cream:
V, C
{V/V, V/C, C/C}
3 possible combinations
For 3 flavors of ice cream:
V, C, S
{V/V, V/C, V/S, C/S, C/C, S/S}
6 possible combinations
For 4 flavors of ice cream:
V, C, S, P
{V/V, V/C, V/S, V/P, C/S, C/P, S/P, C/C, S/S, P/P}
10 possible combinations
For 5 flavors of ice cream:
V, C, S, P, B
{V/V, V/C, V/S, V/P, V/B, C/S, C/P, C/B, S/P, S/B, P/B, C/C, S/S, P/P, B/B }
15 possible combinations
Thus, we derive a sequence of
3, 6, 10, 15...This sequence is recognized as the Triangular number series1 + 2 = 3
1 + 2 + 3 = 61 + 2 + 3 + 4 = 10
1 + 2 + 3 + 4 + 5 = 15The general formula for this sequence isUtilizing this formula allows us to predict the number of 2-scoop combinations from 10 flavors.Consequently, there are 55 varying combinations for a 2-scoop cone when selecting from 10 flavors.
The mistake is present in step 3. According to the product rule, we find
(meaning that a factor of is overlooked)
Then