Answer:
Step-by-step explanation:
a) We have 15! as the product of 1 to 15 natural numbers. Since 17 is prime there will be no factor common to these
By actual division we find
15! (mod 17) =16
From this we deduce
even 16! mod 17 = 16 = -1
According to Wilson theorem
(17-1)! = -1 mod 17
Thus verified 17 is prime
Hence 15! (mod 17) =-1=16
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b) 2(26!) is divided by 29
Since 29 is prime
(29-1)! = -1 mod 29
28! = -1 mod 29 = 28
When divided this gives 25 as remainder
Answer:
y = 2(x - 2)² + 3 vertex form
y = 2x² - 8x + 11 standard form
Step-by-step explanation:
Vertex form
y = a(x - h)² + k
(h, k) = (2, 3)
y = a(x - 2)² + 3
To find "a" plug in the y-intercept (0, 11)
11 = a(-2)² + 3
11 = 4a + 3
Subtract 3 from both sides
8 = 4a
a = 2
y = 2(x - 2)² + 3
Expand
y = 2(x² - 4x + 4) + 3
y = 2x² - 8x + 11
Step-by-step explanation:
tan30 = 14/x
x = 14tan30
x = -89.7
Because the two angles equal each other:
80=20x and solve for x
These are corresponding angles