university math english 1 ppt

55. Choice e is correct. Three of the answer choices can be immediately eliminated because the length of

the height cannot be negative. Answer choices b, c, and d all have negative lengths.

Call the height h and the base h + 5. The area of a triangle is

b

2

h

. Substitute in h and h + 5 for the base

and height, and set the area equal to 80 since the are of the given triangle is 80;

h(h

2

+ 5)

= 80

Solve for h. The equation is quadratic, so the quadratic formula will be used;

h2 +

2

5h = 80

h2 + 5h = 160

h2 + 5h − 160 = h

Use the quadratic formula to solve.

The negative value is eliminated from the answer because it does not make sense. The answer is

.

56. Choice i is correct. The easiest way to find the length of one side is to draw the square on the coordi￾nate plane and count the spaces. There are 7 spaces between (−2, 3) and (5, 3). Therefore, the length of

a side is 7.

The distance formula can also be used. First, you must decide which points are consecutive vertices of

the square. Let’s use (−2, 3) and (5, 3). The distance formula is then:

d = (5 − (−2))2 + (3 − 3)2

d = 72+ 0

d = 49

d = 7

(−2,3) (5,3)

(−2,−4) (5,−4)

7

−5 + 665

2

−5 ± 665

2

−5 ± 25 + 6 40

2

−5 ± (5)2

− 4(1)( −160)

2(1)

–ACT MATH TEST PRACTICE–

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