# Tutor profile: Grace L.

## Questions

### Subject: SAT

The following question is modified from SAT(Math) Sample Question online: Abby is staying at a hotel that charges $100 per night plus tax for a room. A tax of 5% is applied to the room rate, and an additional onetime untaxed fee of $5.00 is charged by the hotel. Which of the following represents Abby's total charge, in dollars, for staying x nights?

From the question, we learnt that the fee for Abby to stay in the hotel per night is Hotel Fee+Tax+Additional onetime untaxed fee Since the number of nights she stays is x, we have: 100x+5%*100x+5.00 To rewrite it, we have 1.05(100x)+5

### Subject: Geometry

In Triangle ABC, ∠ABC=30º, ∠ACB=60º, AC=1. Draw a graph and calculate the length of AB and BC.

By knowing ∠ABC=30º, ∠ACB=60º, we can figure out that ∠CAB=90º we know Triangle ABC is a right triangle which follows the 30-60-90 triangle rule, which means the ratio between lengths is 1:2:√3. The length of AC is 1, and it is the shortest side. By following the ratio rule, we know the longest side BC=2, and AB=√3. The length of AB=√3, BC=2.

### Subject: Algebra

f(x)=x-5 g(x)=|x+5| What is f(g(-3))?

f(g(x))=|x+5|-5 f(g(-3))=|-3+5|-5 f(g(-3))=-3

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