Answer:
Here
Step-by-step explanation:
Answer:
Below in bold.
Step-by-step explanation:
Nth term an = a1 + d(n - 1) where a1 = term 1 and d = common difference.
Here a1 = 5 and d = 8-5 = 3.
So an = 5 + 3(n - 1)
15th term a15
= 5 + 3(15 - 1)
= 5 + 42
= 47.
3/5 x 10= 6 miles because coach runs 10 times what you run
<h2>
Explanation:</h2>
In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.
So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.
So let's name the vertices as:
![A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)](https://tex.z-dn.net/?f=A%28-1%2C3%29%20%5C%5C%20%5C%5C%20B%281%2C5%29%20%5C%5C%20%5C%5C%20C%285%2C1%29%20%5C%5C%20%5C%5C%20D%283%2C-1%29)
First pair of opposite sides:
<u>Slope:</u>
![\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}](https://tex.z-dn.net/?f=%5Ctext%7BFor%20AB%7D%3A%20%5C%5C%20%5C%5C%20m%3D%5Cfrac%7B5-3%7D%7B1-%28-1%29%7D%3D1%20%5C%5C%20%5C%5C%20%5C%5C%20%5Ctext%7BFor%20CD%7D%3A%20%5C%5C%20%5C%5C%20m%3D%5Cfrac%7B1-%28-1%29%7D%7B5-3%7D%3D1%20%5C%5C%20%5C%5C%20%5C%5C%20%5Ctext%7BSo%20AB%20and%20CD%20are%20parallel%7D)
Second pair of opposite sides:
<u>Slope:</u>
![\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}](https://tex.z-dn.net/?f=%5Ctext%7BFor%20BC%7D%3A%20%5C%5C%20%5C%5C%20m%3D%5Cfrac%7B1-5%7D%7B5-1%7D%3D-1%20%5C%5C%20%5C%5C%20%5C%5C%20%5Ctext%7BFor%20AD%7D%3A%20%5C%5C%20%5C%5C%20m%3D%5Cfrac%7B-1-3%7D%7B3-%28-1%29%7D%3D-1%20%5C%5C%20%5C%5C%20%5C%5C%20%5Ctext%7BSo%20BC%20and%20AD%20are%20parallel%7D)
So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:
![d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28y_%7B2%7D-y_%7B1%7D%29%5E2%2B%28x_%7B2%7D-x_%7B1%7D%29%5E2%7D%20%5C%5C%20%5C%5C%20%5C%5C%20Diagonal%20%5C%20BD%3A%20%5C%5C%20%5C%5C%20d%3D%5Csqrt%7B%285-%28-1%29%29%5E2%2B%281-3%29%5E2%7D%3D2%5Csqrt%7B10%7D%20%5C%5C%20%5C%5C%20%5C%5C%20Diagonal%20%5C%20AC%3A%20%5C%5C%20%5C%5C%20d%3D%5Csqrt%7B%283-1%29%5E2%2B%28-5-1%29%5E2%7D%3D2%5Csqrt%7B10%7D%20%5C%5C%20%5C%5C%20%5C%5C)
So the diagonals measure the same, therefore this is a rectangle.
(-4) to the power of 4 is equal to 256