The total cost of the least expensive fence would be $800.
To minimize perimeter and maximize area we take factors that are as close to equal as possible. In this case, the closest whole number factors are 200 and 100. Since the north and south faces cost less, we will make those 100 ft and make the more expensive east and west faces 200 ft.
100 ft × $2/ft = $200 per side × 2 sides = $400 for the north and south facing sides.
200 ft × $1/ft = $200 per side × 2 sides = $400 for the east and west facing sides
$400 + $400 = $800
Answer: q=31
Step-by-step explanation:
q -8 = 23 Add 8 to both sides
+8 +8
q = 31
/ = divided -1/3(1) = -3 + 5 = 2 (g = 1)
Answer: The HL Theorem can be used to prove ABR ≅ RCA because both triangles share the same hypotenuse and a leg. The HL theorem states that If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
a.
By Fermat's little theorem, we have
5 and 7 are both prime, so 
and 
. By Euler's theorem, we get
Now we can use the Chinese remainder theorem to solve for 
. Start with
- Taken mod 5, the second term vanishes and
. Multiply by the inverse of 4 mod 5 (4), then by 2.
- Taken mod 7, the first term vanishes and
. Multiply by the inverse of 2 mod 7 (4), then by 6.
b.
We have 
, so by Euler's theorem,
Now, raising both sides of the original congruence to the power of 6 gives
Then multiplying both sides by 
gives
so that is the inverse of 25 mod 64. To find this inverse, solve for 
in 
. Using the Euclidean algorithm, we have
64 = 2*25 + 14
25 = 1*14 + 11
14 = 1*11 + 3
11 = 3*3 + 2
3 = 1*2 + 1
=> 1 = 9*64 - 23*25
so that 
.
So we know
Squaring both sides of this gives
and multiplying both sides by tells us
Use the Euclidean algorithm to solve for .
64 = 3*17 + 13
17 = 1*13 + 4
13 = 3*4 + 1
=> 1 = 4*64 - 15*17
so that 
, and so 
