1. find the value of x. round the length to the nearest tenth.
(picture 1)

a. 6.9 cm
b. 9.8 cm
c. 8.4 cm
d. 17.1 cm

2. a conveyor belt carries supplies from the first floor to the second floor, which is 26 feet higher. the belt makes a 60° angle with the ground. how far do the supplies travel from one end of the conveyor belt to the other? round your answer to the nearest foot. if the belt moves at 75 ft/min, how long, to the nearest tenth of a minute, does it take the supplies to move to the second floor?

a. 45 ft; 37 min
b. 37 ft; 22.5 min
c. 30 ft; 0.4 min
d. 15 ft; 1.1 min

3.for each triangle shown below, determine whether you would use the law of sines or law of cosines to find angle x. then find angle x to the nearest tenth.
(picture 2)

a. 8.8 by the law of sines (ssa)
b. 22.9 by the law of cosines (sas)
c. 10.7 by the law of sines (sas)
d. 68.3 by the law of cosines (sss)

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages

step-by-step explanation:

assume that you have 3 different side lengths.   apply the pythagorean theorem here:   square each of the two shortest sides; call them a and b, so that their squares are a² and b².   also square the longest side, calling the result c².

now, if a² + b² = c² is true, the triangle is a right triangle; otherwise it is not a right triangle.