## Answers to sample gateway

For each problem on the sample gateway, the correct answer is listed,
followed by a brief description of the solution and suggested reading
if you got the problem wrong.
- (d) Plug in
*m=-2v*; simplify. **Read:**
1.2.
- (c) Intersections have same
*y* value; solve for *x*
by putting everything on one side; *Q* has *x>0*.
**Read:** 1.8.
- (b)
*y*-intercept is where *x=0*; then solve for
*y*. **Read:** 1.8, 1.10, 2.2, 2.3.
- (c) Take reciprocal of fraction; then use
*1/x*^{-2}=x^{2}. **Read:** 1.2.
- (b) Distribute.
**Read:** 1.2, 1.3.
- (d) Move everything over to one side, solve.
**Read:** 1.5.
- (b)
*(ab)*^{r}=a^{r}b^{r}.
**Read:** 1.2.
- (a) Solve simultaneously. One method: 2nd equation implies
*x=-7y-2*, eliminate *x*, solve for *y*.
- (d) Solution means if you plug in
*x* and *y*,
equation works. Then solve for *&phi*. **Read:**
1.8, 2.2, 2.3. AKA: **Hsu's favorite question**.
- (a) Other answers ignore -8.5, ignore positive numbers, or make
no sense.
**Read:** 1.7.
- (c) Common denominator.
**Read:** 1.4.
- (e) Expand
*(g+4)(g+5)*, move everything to one side, and
solve for *g*. Alt: Try all answers. **Read:**
1.3, 1.5.

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