Use the Pythagorean theorem, which says that in a right triangle, the square of the hypotenuse is equal to the sum of the
squares of the legs. If the hypotenuse has length c and the legs have lengths a and b, then c^2 = a^2 + b^2. Let leg EF be called b.
Substitute 6 for c and 4 for a and solve for b. Then 62 = 4^2 + b^2. So 36 = 16 + b^2. Subtract 16 from both sides, and you get 20
= b^2.
B
Be sure to read the definition of > x >. Because −2 is an even number, the value of > −2 > equals 3 x = 3(−2) = −6.
77.
F
Substitute the values given for a and b into the expression: [−(−2)(3)] × (−2) = (2)(3)(−2) = −12.
78.
C
Use the formula for circumference of a circle: C = 2πr. Here 10 π = 2πr. Divide both sides by π and you have 10 = 2r. Hence
r = 5. Next, use the formula for the area of a circle, which is A = πr^2. Here A = π(5^2 ) = π(25) = 25π.
79.
J
Substitute the value of 4 for y in the expression and evaluate: 7 + |3(4)| + 7 + |−2(4)| = 7 + |12| +7 + |−8| = 7 + 12 + 7 + 8 = 34.
Remember that any values within absolute value symbols, whether positive or negative, become positive when the symbols
are removed.
80.
C
This triangle has a height of 8 (each box counts as 4) and a base of 12. The area of a triangle is
81.
J
In order to avoid a messy denominator, begin by cross multiplying the equation given: xy = 12. Next substitute for
Solve for y by multiplying both sides by 2. We are left with y = 24, choice (K).
82.
C
The figure given is a square. All the points on segment BC have an x-coordinate of 2, so DC = AB = 4, and because it is a
square, all 4 sides must have a length of 4. Thus, the area is 42 = 4 × 4 = 16.
83.
F
You must calculate the total cost first: Then 7% of $9 is or $0.63, so the total is $9.63.
84.
85. B
