Answer:
sec A = 5/4
Step-by-step explanation:
Sec of an angle is hypotenuse/adjacent side
In your problem, sec A = 25/20 = 5/4
It helps if you can draw a figure of the problem. Make sure you memorize the definition of each trig function
Answer: -1
Step-by-step explanation:
− 0.25(−8+12) = -0.25 x 4 =-1
Answer:
a) SPAZ is equilateral.
b) Diagonals SA and PZ are perpendicular to each other.
c) Diagonals SA and PZ bisect each other.
Step-by-step explanation:
At first we form the triangle with the help of a graphing tool and whose result is attached below. It seems to be a paralellogram.
a) If figure is equilateral, then SP = PA = AZ = ZS:
![SP = \sqrt{[4-(-4)]^{2}+[(-2)-(-4)]^{2}}](https://tex.z-dn.net/?f=SP%20%3D%20%5Csqrt%7B%5B4-%28-4%29%5D%5E%7B2%7D%2B%5B%28-2%29-%28-4%29%5D%5E%7B2%7D%7D)

![PA = \sqrt{(6-4)^{2}+[6-(-2)]^{2}}](https://tex.z-dn.net/?f=PA%20%3D%20%5Csqrt%7B%286-4%29%5E%7B2%7D%2B%5B6-%28-2%29%5D%5E%7B2%7D%7D)



![ZS = \sqrt{[-4-(-2)]^{2}+(-4-4)^{2}}](https://tex.z-dn.net/?f=ZS%20%3D%20%5Csqrt%7B%5B-4-%28-2%29%5D%5E%7B2%7D%2B%28-4-4%29%5E%7B2%7D%7D)

Therefore, SPAZ is equilateral.
b) We use the slope formula to determine the inclination of diagonals SA and PZ:




Since
, diagonals SA and PZ are perpendicular to each other.
c) The diagonals bisect each other if and only if both have the same midpoint. Now we proceed to determine the midpoints of each diagonal:








Then, the diagonals SA and PZ bisect each other.
Answer:
Step-by-step explanation:
There is a 1/12 probability that volume 1 will be correctly put in position 1.
If we assume that volume 1 is right, then since there are then only 11 books left to choose from, there is then a 1/11 prob that volume 2 will be in position 2. And so on. By the same reasoning there is 1/10 prob that volume 3 is then right, 1/9 prob for volume 4, 1/8 prob for volume 5, and 1/7 prob for volume 6,
and 1/6 prob for volume 7,and 1/5 prob for volume 8,and 1/4 prob for volume 9,and 1/3 prob for volume 10,and 1/2 prob for volume 11,and 1/1 prob for volume 12.
So the probability is 1 /(12*11*10*9*8*7*6*5*4*3*2*1) = 1 / 479,001,600 ....