Answer:
The given expanded sum of the series is ![\sum\limits_{n=5}^{9}3n+2=115](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bn%3D5%7D%5E%7B9%7D3n%2B2%3D115)
Step-by-step explanation:
Given problem can be written as
![\sum\limits_{n=5}^{9}3n+2](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bn%3D5%7D%5E%7B9%7D3n%2B2)
To find their sums:
Now expanding the series
That is put n=5,6,7,8,9 in the given summation
![\sum\limits_{n=5}^{9}3n+2=[3(5)+2]+[3(6)+2]+[3(7)+2]+[3(8)+2]+[3(9)+2]](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bn%3D5%7D%5E%7B9%7D3n%2B2%3D%5B3%285%29%2B2%5D%2B%5B3%286%29%2B2%5D%2B%5B3%287%29%2B2%5D%2B%5B3%288%29%2B2%5D%2B%5B3%289%29%2B2%5D)
![=[15+2]+[18+2]+[21+2]+[24+2]+[27+2]](https://tex.z-dn.net/?f=%3D%5B15%2B2%5D%2B%5B18%2B2%5D%2B%5B21%2B2%5D%2B%5B24%2B2%5D%2B%5B27%2B2%5D)
(adding the terms)
![=115](https://tex.z-dn.net/?f=%3D115)
Therefore ![\sum\limits_{n=5}^{9}3n+2=115](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bn%3D5%7D%5E%7B9%7D3n%2B2%3D115)
Therefore the given sum of the series is ![\sum\limits_{n=5}^{9}3n+2=115](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bn%3D5%7D%5E%7B9%7D3n%2B2%3D115)
The given expanded sum of the series is ![\sum\limits_{n=5}^{9}3n+2=115](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bn%3D5%7D%5E%7B9%7D3n%2B2%3D115)
Answer:
distance was 35 units and the average speed was 5 units per minute
Step-by-step explanation:
-47--12=-35
the absolute value of -35 is 35
35 units took 7 minutes
so 1 unit takes 35/7 minutes= 5 minutes
Plug 4 in for every x
(3*4)-4=8
(4^2)-1=15 [(4^2) is 4*4]
(2*(4^2))-15= 15 [because of PEMDAS the exponent comes first and then multiply by 2 then subtract]
Perimeter is the sum of the lengths so add up all the sides from above
8+15+15=38
Gradient:
Find two points on the line and with those two points, calculate the difference in height(y coordinates) divided by the difference in width(x coordinates). If you get a positive value, then your line will be uphill.
Y-intercept:
Use y=mx+b
Find the slope first using the slope formula which is y2-y1 OVER x2-x1. Once you have that, take a point from the line and substitute the x and y coordinates along with the slope into y=mx+b.
So if your slope was 2/1 and your point was (4,8), it would be:
8=2(4)+b
8=6+b
*subtract 6 from both sides*
b=2
Answer:
Answers are below
Step-by-step explanation:
-3x > 9 Divide both sides by -3
x < -3 When you divide by a negative number, flip the inequality sign
3x > 9 Divide both sides by 3
x > -3
When you divide by a negative number, flip the inequality sign. This affects your answer because the first inequality means any number less than -3, while the second inequality means and number above -3