The letters from the word "alert" are used to form a password into a school computer system. How many 5-letter passowrds can be
1 answer:
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9514 1404 393
Answer:
y = 3/2x -10
Step-by-step explanation:
The point-slope equation can be written ...
y = m(x -h) +k . . . . . for a line with slope m through point (h, k)
Using the given values, this is ...
y = (3/2)(x -6) -1 = 3/2x -9 -1
y = 3/2x -10 . . . . . slope-intercept equation
Answer:
a) 388.03
b) 148.49
c) π/8
Step-by-step explanation:
Find the diagram attached
Let the opposite side be y
Given
a) Hypotenuse = 420
theta = 3π/8 rad
theta = 3(180)/8
theta = 67.5degrees
Using the SOH CAH TOA identity
sin theta = opposite/hypotenuse
sin 67.5 = y/420
x = 420sin67.5
x = 420(0.9238)
x = 388.03
Hence the length of the side opposite to the given angle is 388.03
b) Hypotenuse = 420
theta = 3π/8 rad
theta = 3(180)/8
theta = 67.5degrees
Using the SOH CAH TOA identity
cos theta = adjacent/hypotenuse
cos 67.5 = x/420
x = 420cos67.5
x = 420(0.3827)
x = 148.49
Hence the length of the side adjacent to the given angle is 148.49
c) The sum of angle in the triangle is π
Let the measure of the unknown angle be z
z + 3π/8 + π/2 = π
z + 3π+4π/8 = π
z + 7π/8 = π
z = π - 7π/8
z = (8π-7π)/8
z = π/8
Hence the measure of the other acute angle is π/8
