39. Physics If two forces pull at right angles to each other, the resultant force can be represented by the diagonal of a rectangle, as shown below. This diagonal is a hypotenuse of a right triangle. A 50-lb force and a 120-lb force combine for a resultant force of 130 lb. Are the forces pulling at right angles to each other? Explain.

    

40. A rectangular box is 4 cm wide, 4 cm tall, and 10 cm long. What is the diameter of the smallest circular opening through which the box will fit? Round to the nearest tenth of a centimeter.

C Challenge

41. Reasoning Use the diagram below.

    
    Image Long Description

    1. Find the area of the larger square. Write your answer as a trinomial.
    2. Find the area of the smaller square.
    3. Find the area of each triangle in terms of a and b.
    4. The area of the larger square equals the sum of the area of the smaller square and the areas of the four triangles. Write this equation and simplify. What do you notice?
42. Geometry The lengths of the sides of a right triangle are three consecutive integers. Write and solve an equation to find the three integers.

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

43. A park has two walking paths shaped like right triangles. The first path has legs 75 yd and 100 yd long. The second path has legs 50 yd and 240 yd long. What is the total length of the shorter path, in yards?

44. Joe plants a rectangular garden in the corner of his field, as shown. The area of the garden is 60% of the area of the field. What is the longest side length of Joe's field, in feet?

    

45. What is the slope of the graph of the equation y = 1 2 x + 7 ? y equals , 1 half , x plus 7 question mark
46. What is the positive solution of the equation − 3.2 | t | = − 17.28 ? negative 3.2 vertical line t vertical line equals negative , 17.28 , question mark
47. A candidate in an election received 72.5% of the vote. What decimal represents the portion of the voters who did NOT vote for the candidate?

Mixed Review

See Lesson 9-1.

Graph each function.

48. y =   x 2 − 1 y equals , x squared , minus 1
49. y = 2 x 2 − 8 y equals 2 , x squared , minus 8
50. y = − x 2 + 13 y equals negative , x squared , plus 13

Get Ready! To prepare for Lesson 10-2, do Exercises 51–54.

See Lesson 8-2.

Simplify each product.

51. 9 a ( 5 a − 3 ) 9 eh open 5 eh minus 3 close
52. 4 x ( 3 x 2 − 6 x ) 4 x open 3 , x squared , minus 6 x close
53. 4 d ( 4 d 2 + 7 d 3 ) 4 d open 4 , d squared , plus 7 , d cubed , close
54. ( 6 m + 3 m 3 ) ( − 2 m ) open 6 m plus 3 , m cubed , close open negative 2 m close

Table of Contents