Let x be the shortest shelf. The other shelves measures x + 2, x + 4, and x + 6. These lengths should add up to 5 ft or 60 inches
x + x + 2 + x + 4 + x + 6 = 5
The value of x is 12. Therefore, the shelves are 12, 14, 16, and 18 inches long. The longest shelf is x + 6. Thus, the answer is letter C.
Answer:
X=10, Y=20,Z=80
Step-by-step explanation:
We are given that the numbers X,Y and Z are in the ratio 1:2:8
Let the numbers be:
X=x
Y=2x
Z=8x
Now we are given that 40 is subtracted from Z such that the numbers X,Y,Z-40 form a geometric sequence.
that means x,2x,8x-40 forms a geometric sequence.
Also if a,b,c are in geometric progression then they have same common ratio.
i.e.
Hence, the number X =10
Y=2×10=20
Z=8×10=80
Answer:Hint:
the remainder is 2.
Step-by-step explanation:
23≡1 mod 7 and 33≡−1 mod 7.
Edit: The only thing you need from the modular arithmetic is that
a⋅b mod 7=(a mod 7)(b mod 7) mod 7,
meaning the remainder of a product is the remainder of the product of remainders. This is self-evident as a⋅b must have the same remainder as (a−7k)⋅(b−7l).
Since exponentiation is just repeated multiplication, we can write
230⋅320=(23)10⋅(33)6⋅32≡110⋅(−1)6⋅9=9
<h3>
Answer: D) Two</h3>
You need the starting point, and another point that helps direct where the ray is aimed. Call these two points A and B.
Saying "Ray AB" means we extend a line through AB such that the line goes forever through B and beyond B, but we do not do the same for point A. The point A is effectively a cliff where no road goes on the other side of it. Check out the diagram below to see what I mean. The arrow means the line goes on forever in that direction.
F(x) =2(5)x-1
f(3) =2(5)3-1
f(3) = 30-1
f(3) =29