Answer:
The range of z-score is given below as
Answer:
tHE ANSWER IS 10X15
Step-by-step explanation:
10X15=150
9.
By the Segment Addition Postulate, SAP, we have
XY + YZ = XZ
so
YZ = XZ - XY = 5 cm - 2 cm = 3 cm
10.
M is the midpoint of XZ=5 cm so
XM = 5 cm / 2 = 2.5 cm
11.
XY + YM = XM
YM = XM - XY = 2.5 cm - 2 cm = 0.5 cm
12.
The midpoint is just the average of the coordinate A(-3,2), B(5,-4)
![M = (A+B)/2 = \left( \dfrac{-3 + 5}{2}, \dfrac{2 + -4}{2} \right)](https://tex.z-dn.net/?f=M%20%3D%20%28A%2BB%29%2F2%20%3D%20%5Cleft%28%20%5Cdfrac%7B-3%20%2B%205%7D%7B2%7D%2C%20%5Cdfrac%7B2%20%2B%20-4%7D%7B2%7D%20%5Cright%29)
Answer: M is (1,-1)
You'll have to plot it yourself.
13.
For distances we calculate hypotenuses of a right triangle using the distnace formula or the Pythagorean Theorem.
![AB^2 =(5 - -3)^2 + (-4 - 2)^2 = 8^2 + 6^2 = 100](https://tex.z-dn.net/?f=AB%5E2%20%3D%285%20-%20-3%29%5E2%20%2B%20%28-4%20-%202%29%5E2%20%3D%208%5E2%20%2B%206%5E2%20%3D%20100)
Answer: AB=10
M is the midpoint of AB so
Answer: AM=MB=5
14.
B is the midpoint of AC. We have A(-3,2), B(5,-4)
B = (A+C)/2
2B = A + C
C = 2B - A
C = ( 2(5) - -3, 2(-4) - 2 ) = (13, -10)
Check the midpoint of AC:
(A+C)/2 = ( (-3 + 13)/2, (2 + -10)/2 ) = (5, -4) = B, good
Answer: C is (13, -10)
Again I'll leave the plotting to you.
Answer:
Step-by-step explanation:
By Pythagoras Theorem:
![{y}^{2} = {(9 + 3)}^{2} - {(6)}^{2} \\ \\ {y}^{2} = {(12)}^{2} - {(6)}^{2} \\ \\ {y}^{2} = 144 - 36 \\ \\ {y}^{2} = 108 \\ \\ {y} = \sqrt{108} \\ \\ {y} = \sqrt{36 \times 3} \\ \\ {y} = \sqrt{ {6}^{2} \times 3} \\ \\ {y} = 6\sqrt{3}\:units](https://tex.z-dn.net/?f=%20%7By%7D%5E%7B2%7D%20%20%3D%20%20%7B%289%20%2B%203%29%7D%5E%7B2%7D%20%20-%20%20%7B%286%29%7D%5E%7B2%7D%20%5C%5C%20%20%5C%5C%20%20%20%7By%7D%5E%7B2%7D%20%20%3D%20%20%7B%2812%29%7D%5E%7B2%7D%20%20-%20%20%7B%286%29%7D%5E%7B2%7D%20%5C%5C%20%20%5C%5C%20%20%20%7By%7D%5E%7B2%7D%20%20%3D%20144%20-%20%2036%20%5C%5C%20%20%5C%5C%20%20%7By%7D%5E%7B2%7D%20%20%3D%20108%20%5C%5C%20%20%5C%5C%20%20%7By%7D%20%20%3D%20%20%5Csqrt%7B108%7D%20%20%5C%5C%20%20%5C%5C%20%20%7By%7D%20%20%3D%20%20%5Csqrt%7B36%20%5Ctimes%203%7D%20%20%5C%5C%20%20%5C%5C%20%7By%7D%20%20%3D%20%20%5Csqrt%7B%20%7B6%7D%5E%7B2%7D%20%20%5Ctimes%203%7D%20%20%5C%5C%20%20%5C%5C%20%7By%7D%20%20%3D%20%206%5Csqrt%7B3%7D%5C%3Aunits%20)
Answer:
20 ft
Step-by-step explanation:
The formula for the surface area of a pyramid is often written in terms of the base dimensions and the slant height. We can solve that formula for the slant height.
SA = base area + lateral area
SA = b² + 2bs . . . . . where b is the base dimension, and s is the slant height
SA -b² = 2bs . . . . . subtract the base area
s = (SA -b²)/(2b) . . . . divide by the coefficient of s
Using the given values for surface area and base length, we find ...
s = (896 -16²)/(2·16) = 640/32 = 20 . . . feet
The slant height of the pyramid is 20 feet.