Can you draw two quadrilaterals each having two $130^{\circ}$ angles and two $50^{\circ}$ angles that are not similar? Justify your answer.

The figures are similar. Find x.

A person of height is 6 feet standing 20 feet from a streetlight casts a shadow of 10 feet. How many times taller is the streetlight than the person? Assume the triangles are similar.

Are the following figures always, sometimes, or never similar? Explain. a. two triangles b. two squares c. two rectangles d. a square and a triangle.

The sail on a souvenir boat is similar in shape to the sail on a sailboat. The sail on the sailboat is in the shape of a right triangle with a base of 9 feet and a height of 24 feet. The height of the souvenir's sail is 3 inches. What is the base of the souvenir's sail?

A barrier in the shape of a rectangle is used to retain oil spills. On a blueprint, a similar barrier is 9 inches long and 2 inches wide. The width of the actual barrier is 1.2 miles. What is the length of the actual barrier?

A wide-screen television measures 36 inches by 54 inches. A movie theater screen measures 42 feet by 63 feet. Are the screens similar? Explain.

Identify the type of phrase italicized in each sentence. Write prep. for prepositional, part. for participial, G for gerund, and I for infinitive above each phrase. Fully one fourth of the school was absent during the flu epidemic.

22. Write the equation $y + 2 = \frac { 1 } { 4 } ( x + 3 )$ in the following forms: a. Slope-intercept form b. Standard form c. Standard form with a positive x-term d. Standard form with no fractions or decimals

Write one equation of the line through the given points in point-slope form and one in standard form using integers. (0, 1), (-3, 0)

Find the next two terms in the sequence.

$$12,4,1 \frac{1}{3}, \frac{4}{9}, \ldots$$

Underline the pronoun in parentheses that correctly completes each sentence. The tomato, because of (its, their) versatility, is found in cuisines from many different parts of the world.

Draw the figures with the given vertices in a coordinate plane. Which figures are similar? Explain your reasoning. Figure A: (-4, 2), (-2, 2), (-2, 0), (-4, 0) Figure B: (1, 4), (4, 4), (4, 1), (1, 1) Figure C: (2, -1), (5, -1), (5, -3), (2, -3)

A spur gearset has 17 teeth on the pinion and 51 teeth on the gear. The pressure angle is $20^{\circ}$ and the overload factor $K_{o}=1$. The diametral pitch is 6 teeth/in and the face width is 2 in. The pinion speed is 1120 rev/min and its cycle life is to be $10^{8}$ revolutions at a reliability R = 0.99. The quality number is 5. The material is a through-hardened steel, grade 1, with Brinell hardnesses of 232 core and case of both gears. For a design factor of 2, rate the gearset for these conditions using the AGMA method.