I drew a graph and plotted the coordinates. a hexagon is the shape u will get
Answer:
Diameter = 19.33
Step-by-step explanation:
Imaging a radius line from O to the endpoints of the 7. call this line R.
Label the part of the vertical line from O to the 90 degree intersection y.
Now you have a right triangle.
Using the Pythagorean theorem:
R² = 7² + y²
also
y = R - 3
substitute for y:
R² = 49 + (R-3)²
R² = 49 + R² - 6R + 9
simplify:
0 = 58 - 6R
6R = 58
R = 9.6667
Diameter = 2(9.6667) = 19.33
Answer:
smallest integer=9,
total number of integers are in the sequence = 19.
Step-by-step explanation:
- let a be the first term and the number of terms be n. as they are consecutive,the common difference will be 1. these will form Arithmetic Progression series.
- the sum of n terms in AP series is :
![\frac{n}{2} (a+l)](https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7B2%7D%20%28a%2Bl%29)
[ where, l: last term]
- or, sum of n terms in AP series is :
![\frac{n}{2}(2a+[n-1]d)](https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7B2%7D%282a%2B%5Bn-1%5Dd%29)
[where, d: common difference]
using the first formula,
342 = ![\frac{n}{2} (a+3a)](https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7B2%7D%20%28a%2B3a%29)
342= ![\frac{n}{2} (4a)](https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7B2%7D%20%284a%29)
342=2an .......equation 1.
using the second formula,
342=![\frac{n}{2} (2a+{n-1}l)](https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7B2%7D%20%282a%2B%7Bn-1%7Dl%29)
684=n[2a+n-1]
684=2an+n^2-n
from equation 1,
342=n^2-n .......equation 1
-n-342=0
after solving, the solution to the above equation is 19.
substituting this in equation 2,
171=a[19]
a=9
so, smallest integer= a = 9,
total number of integers are in the sequence = n = 19.
Answer:
x = - 7 and y = 30
Step-by-step explanation:
2x - y = -9
subtract 2x from either side
-y = -9 - 2x
divide either side by -1
y = 9 + 2x
Plug in 9 + 2x for y
9 + 2x = -5 - 5x
Add 5 to either side and subtract 2x from either side
14 = -2x
divide either side by -2
-7 = x
plug in -7 for x in one of the equations
y = -5 - ( 5 x -7 )
y = -5 - ( - 35)
y = -5 + 35
y = 30
plug in x and y
30 = -5 - ( 5 x -7)
30 = -5 - (-35)
30 = -5 + 35
30 = 30