check the picture below, that's pretty much the same block, or "rectangular prism", with a width of 10, length of 5 and height of 1.
so anyhow, is really 6 rectangles stacked up to each other at the edges, so, we can simply get the area of each of those rectangles, add them up and that's the surface area.
front and back, two rectangles of 5x1
left and right, two rectangles of 1x10
top and bottom, two rectangles of 10x5
Answer:
a) 5+13k where k is integer
b) 20+13k where k is integer
c)12+13k where k is integer
Step-by-step explanation:
(a)
.
8x-1=13k
Subtract 13k on both sides:
8x-13k-1=0
Add 1 on both sides:
8x-13k=1
I'm going to use Euclidean Algorithm.
13=8(1)+5
8=5(1)+3
5=3(1)+2
3=2(1)+1
Now backwards through the equations:
3-2=1
3-(5-3)=1
3-5+3=1
(8-5)-5+(8-5)=1
2(8)-3(5)=1
2(8)-3(13-8)=1
5(8)-3(13)=1
So compare this to:
8x-13k=1
We see that x is 5 while k is 3.
Anyways 5 is a solution or 5+13k is a solution where k is an integer.
b)
8x-4=13k
Subtract 13k on both sides:
8x-13k-4=0
Add 4 on both sides:
8x-13k=4
We got this from above:
5(8)-3(13)=1
If we multiply both sides by 4 we get:
8(20)-13(12)=4
So x=20 and 20+13k is also a solution where k is an integer.
c)
[tex]99x \equiv 5 (mod 13)[/tex
99x-5=13k
Subtract 13k on both sides:
99x-13k-5=0
Add 5 on both sides:
99x-13k=5
Using Euclidean Algorithm:
99=13(7)+8
13=8(1)+5
Go back through the equations:
13-8=5
13-(99-13(7))=5
8(13)-99=5
99(-1)+8(13)=5
Compare this to 99x-13k=5 and see that x=-1 or -1+13=12 or 12+13k is a solution where k is an integer.
Answer: 2
Step-by-step explanation: To find the greatest common factor or GCF of 8 and 18, we begin by finding all of the factors of each number.
To find the factors of 8, we know that 8 ÷ 1 is 8 so 1 and 8 are factors.
8 ÷ 2 is 4 so 2 and 4 are factors.
However, if we continue to divide 8 by 3, 4, 5, and so on, we won't find any new factors. So the factors of 8 are 1, 2, 4, and 8.
Now let's find the factors of 18.
18 ÷ 1 is 18 so 1 and 18 are factors.
18 ÷ 2 is 9 so 2 and 9 are factors.
18 ÷ 3 is 6 so 3 and 6 are factors.
However, if we continue to divide by 4, 5, 6, and so on, we won't find any new factors. So the factors of 18 are 1, 2, 3, 6, 9, and 18.
Now that we have our list of factors, to find the greatest common factor, we simply find the largest number that is shared by the two lists.
Notice that our lists share a 1 but the largest number they share is a <em>2</em><em>.</em>
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So the greatest common factor or <em>gcf</em> of 8 and 18 is 2.
I have also shown my work on the whiteboard.
