Lesson 7 We All Scream for Ice Cream Practice Understanding

Ready

1.

The side lengths of right triangle $A B C$ are $13$ , $5$ , and $12$ . If $5$ is the numerator of $\cos A$ in the triangle, what is the trigonometric ratio for $\sin A$ ?

2.

The side lengths of right triangle $E F G$ are $20, 29$ , and $21$ . If $20$ is the numerator of $\cos E$ in the triangle, what is the trigonometric ratio for $\tan E$ ?

3.

The side lengths of a right triangle $J M S$ are $16, 63$ , and $65$ . If $16$ is the numerator of $\sin J$ in the triangle, what is the trigonometric ratio for $\cos J$ ?

4.

The side lengths of right triangle $P Q R$ are $35, 37$ , and $12$ . If $12$ is the numerator of $\cos P$ in the triangle, what is the trigonometric ratio for $\sin P$ ?

5.

The side lengths of right triangle $X Y Z$ are $33, 56$ , and $65$ . If $56$ is the numerator of $\sin Y$ in the triangle, what is the trigonometric ratio for $\cos X$ ?

6.

The side lengths of right triangle $L M N$ are $39, 80$ , and $89$ . If $80$ is the numerator of $\sin M$ in the triangle, what is the trigonometric ratio for $\cos L$ ?

Set

Solve each equation. Identify extraneous solutions.

7.

$x + \frac{2}{x} = 3$

8.

$\frac{x}{2} - \frac{1}{3 x} = \frac{1}{6}$

9.

$2 x + \frac{3}{x + 2} = 1$

10.

$\frac{2}{x^{2} - 2 x} - \frac{1}{x - 2} = 1$

11.

$3 x - \frac{1}{2 x - 1} = 4$

12.

$\frac{2 x}{x^{2} + 3 x} - \frac{2}{x + 3} = \frac{2}{x}$

13.

Channing takes twice as long as Dakota to complete a school project. It takes them 15 hours to complete the project together. How long would it take each student to complete the project if he works alone?

14.

A print shop can print an Algebra 2 book in $24$ minutes if both of their print machines are working together to do the job. If a print machine is working alone, the job takes longer. Machine A can print the book $20$ minutes faster than machine B. How long does it take each machine to print the entire book?

15.

The scenario in problem 14 generates an extraneous solution. Neither solution makes a denominator equal zero. Why can we not use both solutions?

Go

Perform the indicated operations.

(Assume all denominators ≠ 0)

16.

Rewrite by dividing out all common factors.

$\frac{x^{2} + 8 x + 12}{x^{2} + 3 x - 18}$

17.

Rewrite by dividing out all common factors.

$\frac{x^{2} - 3 x - 40}{x^{2} - 11 x + 24}$

18.

Add.

$\frac{x^{2} + 8 x + 12}{x^{2} + 3 x - 18} + \frac{x^{2} - 3 x - 40}{x^{2} - 11 x + 24}$

19.

Multiply.

$\frac{x^{2} + 5 x - 36}{(x - 4)} \cdot \frac{3 (x + 2)}{x + 9}$

20.

Subtract.

$\frac{4}{x^{2} - 4} - \frac{1}{x - 2}$

21.

Divide.

$\frac{x^{2} - 2 x - 3}{x + 1} \div \frac{x - 3}{5}$