Answer:
The equivalent expression is 6x+8.
Step-by-step explanation:
Given expression is:
1.5(3x + 4) + 0.25(6x + 8)
We will solve the expression and combine alike terms.
4.5x + 6 + 1.5x + 2
6x + 8
Therefore,
The equivalent expression is 6x+8.
Let s = the smaller one of the two.
Since they are consecutive, the second one is (s + 1)
Since they are natural numbers, they cannot be negative.
We know that s(s + 1) = s + (s + 1) + 155
So:
s(s + 1) = 2s + 156
s^2 + s = 2s + 156
s^2 - s - 156 = 0
(s - 13)(s + 12) = 0
From this, it looks like s can be either 13 or -12. But since it's a natural number, it cannot be negative. So, it is 13.
s was the smaller one. The larger one is s + 1 = 14
Check: 13*14=182=13+14+155
Answer:
- Transitive Property of Equality
- Alternate Interior Angles Theorem
Step-by-step explanation:
a) You're trying to justify that two sums equal to 180° are equal to each other. The <em>Transitive Property of Equality</em> is that justification.
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b) You're trying to justify that angles 3 and 6 are congruent. These are between the parallel lines, so are "interior" angles. They are on opposite sides of the transversal, so are "alternate" angles. They do not share a vertex, so cannot be vertical angles. The applicable theorem is the <em>Alternate Interior Angles Theorem</em>.
