Answer:
The difference between 19 and 8 is 11.
Step-by-step explanation:
Given:
The difference between a number and 8 is 11
Find the number.
Solution:
Let the unknown number be 
The difference between the unknown number can be written as:

We are given that the difference =11
So we can write the equation to find
as :

Using additive property to solve for 
Adding 8 to both sides to isolate
on one side.

∴ 
∴ The unknown number = 19
we know that
1 ft--------> is equals to 12 in
the ramp is 12 inches tall----------> 1 ft tall
A ramp measures------------------> 6 ft long
applying the Pythagorean theorem
c²=a²+b²
where
c-----> 6 ft long
a----> horizontal distance
b-----> 1 ft tall
a²=c²-b²------> a²=6²-1²-----> a²=35------> a=√35------> a=5.92 ft
the answer is
5.92 ft
(3,59)(5,87)
slope = (87 - 59) / (5 - 3) = 28/2 = 14 <== ur slope
y = mx + b
slope(m) = 14
use either of ur points...(3,59)...x = 3 and y = 59
now we sub and find b, the y int
59 = 14(3) + b
59 = 42 + b
59 - 42 = b
17 = b <=== ur y int (0,17)
Answer:
Proofs are in the explantion.
Step-by-step explanation:
We are given the following:
1)
for integer
.
1)
for integer
.
a)
Proof:
We want to show
.
So we have the two equations:
a-b=kn and c-d=mn and we want to show for some integer r that we have
(a+c)-(b+d)=rn. If we do that we would have shown that
.
kn+mn = (a-b)+(c-d)
(k+m)n = a-b+ c-d
(k+m)n = (a+c)+(-b-d)
(k+m)n = (a+c)-(b+d)
k+m is is just an integer
So we found integer r such that (a+c)-(b+d)=rn.
Therefore,
.
//
b) Proof:
We want to show
.
So we have the two equations:
a-b=kn and c-d=mn and we want to show for some integer r that we have
(ac)-(bd)=tn. If we do that we would have shown that
.
If a-b=kn, then a=b+kn.
If c-d=mn, then c=d+mn.
ac-bd = (b+kn)(d+mn)-bd
= bd+bmn+dkn+kmn^2-bd
= bmn+dkn+kmn^2
= n(bm+dk+kmn)
So the integer t such that (ac)-(bd)=tn is bm+dk+kmn.
Therefore,
.
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