A16 inch candle is lit and burns at a constant rate of 1.1 inches per hour. let t represent the never of hours that have elapsed since the candle was lit.

a) write an expression in terms of t that represents the number of incrhs that have burned from the candle since it was lit.
b) write an expression in terms of t that represents the remaining length of the candle (in inches).

(a) Number of inches that have burned from the candle since it was lit is (1.1t) inches

(b) The remaining length of the candle is (16 - 1.1t) inches

Step-by-step explanation:

(a). Length of candle before it was lit = 16 inches

Constant rate at which at which candle burns = 1.1 inches per hour

Let t represent the number of hours that have elapsed since the candle was lit

In 1 hour, 1.1 inches of the candle burned

Therefore, in t hours, (1.1t) inches of the candle would have burned since the candle was lit

(b) Remaining length of candle = length of candle before it was lit - length of candle that have burned = 16 inches - 1.1t inches = (16 - 1.1t) inches

We require the congruence between another pair of corresponding angles to say that those triangles are similar by the Angle-Angle Postulate.

Step-by-step explanation:

To prove that the two triangles similar we can use these postulates:

Angle-Angle Postulate: if two pairs of corresponding angles between two triangles are congruent, then, those triangles are similar.Side-Side-Side Postulate: if all corresponding sides between two triangles are proportional, or they are in a same proportion, then, those triangles are similar.Side-Angle-Side Postulate: If two pairs of corresponding angles are proportional, and one pair of corresponding angles (which are formed by the proportional sides) are congruent, then, those triangles are similar.

So, in the problem, we know that one pair of corresponding triangles are congruent. Now, we require the congruence between another pair of corresponding angles to say that those triangles are similar by the Angle-Angle Postulate. That's the shortest way.