1² + 3² + 4² + 4(n - 1)² = ¹/₃n(2n - 1)(2n + 1)
1² + 3² + 4² + (2n - 2)² = ¹/₃n(2n - 1)(2n + 1)
1 + 9 + 16 + (2n - 2)(2n - 2) = ¹/₃n(2n(2n + 1) - 1(2n + 1))
10 + 16 + (2n(2n - 2) - 2(2n - 2)) = ¹/₃n(2n(2n) + 2n(1) - 1(2n) - 1(1) 16 + (2n(2n) - 2n(2) - 2(2n) + 2(2)) = ¹/₃n(4n² + 2n - 2n - 1)
26 + (4n² - 4n - 4n + 4) = ¹/₃n(4n² - 1)
26 + (4n² - 8n + 4) = ¹/₃n(4n² - 1)
26 + 4n² - 8n + 4 = ¹/₃n(4n²) - ¹/₃n(1)
4n² - 8n + 4 + 26 = 1¹/₃n³ - ¹/₃n
4n² - 8n + 30 = 1¹/₃n³ - ¹/₃n
+ ¹/₃n + ¹/₃n
4n² - 7²/₃n + 30 = 1¹/₃n³
-1¹/₃n³ + 4n² - 7²/₃n + 30 = 0
-3(-1¹/₃n³ + 4n² - 7²/₃n + 30) = -3(0)
-3(-1¹/₃n³) - 3(4n²) - 3(-7²/₃n) - 3(30) = 0
4n³ - 12n² + 23n - 90 = 0
Answer:
Step-by-step explanation:
Answer = 0.5
hope this helps
y=ax+b
->a= positive (the line is going up)
->to find a, we move one unit horizontally and look over how many units you meet the graph (1 to right, 4 up) so the a= 4
-> to find b, we look for the y-coordinate of the point where the graph and the y-axis cross. they cross in (0,1) so b is 1
when we take this all together we get y=4x+1
Answer:
a) 1.8 
b) 3.6 
Step-by-step explanation:
Conversion and calculation of areas
The area of a rectangle is A=wh, where w is the width and h is the height. There are 3 feet in one yard
a)
We are told Kalie put 6 stickers, each one of 1/2 centimeters (0.5 cm) wide by 3/5 (0.6 cm) centimeter long. The area of one sticker is
A=(0.5)(0.6)=0.3
Assuming there is no overlapping, the 6 stickers have a total area
6*0.3 =1.8
b)
Each of Elana's wrapping papers measures 2/5 yards long and 1/4 yard wide. Converting them to feet we have
long=2/5*3=1.2 feet
wide=1/4*3=0.75 feet
Area of each paper=1.2 feet*0.75 feet=0.9
Area of the entire board, assuming no overlapping and no space left uncovered=4*0.9
Area of board=3.6
