Answer:
You can prove this statement as follows:
Step-by-step explanation:
An odd integer is a number of the form
where
. Consider the following cases.
Case 1. If
is even we have:
.
If we denote by
we have that
.
Case 2. if
is odd we have:
.
If we denote by
we have that ![(2k+1)^{2}=8m+1](https://tex.z-dn.net/?f=%282k%2B1%29%5E%7B2%7D%3D8m%2B1)
This result says that the remainder when we divide the square of any odd integer by 8 is 1.
Answer:
30 m
Step-by-step explanation:
You simply add the lengths of all the sides. 3 m is not needed for this.
The line
is already written in the
form. This means that
is the slope. If two lines are perpendicular, their slopes are the anti-inverse of each other, i.e. their product is -1.
So, our perpendicular line has a slope of ![-\frac{1}{10}](https://tex.z-dn.net/?f=%20-%5Cfrac%7B1%7D%7B10%7D%20)
Finally, we want a line passing through (1,1) with slope
:
![y-1 = -\dfrac{1}{10}(x-1) \iff y = -\dfrac{x}{10} + \dfrac{1}{10}+1 = -\dfrac{x}{10} + \dfrac{11}{10}](https://tex.z-dn.net/?f=%20y-1%20%3D%20-%5Cdfrac%7B1%7D%7B10%7D%28x-1%29%20%5Ciff%20y%20%3D%20-%5Cdfrac%7Bx%7D%7B10%7D%20%2B%20%5Cdfrac%7B1%7D%7B10%7D%2B1%20%3D%20-%5Cdfrac%7Bx%7D%7B10%7D%20%2B%20%5Cdfrac%7B11%7D%7B10%7D%20)
Answer:
Total cost is $100.41 ( $93.84 + $6.57)
Step-by-step explanation:
Thinking Point: The total cost is the cost of the items PLUS the tax. 93.84 ∙ 0.07 = 6.5688 (round to “cents”) = $6.57
Hope this helped!