The sum of the first n odd numbers is n squared! So, the short answer is that the sum of the first 70 odd numbers is 70 squared, i.e. 4900.
Allow me to prove the result: odd numbers come in the form 2n-1, because 2n is always even, and the number immediately before an even number is always odd.
So, if we sum the first N odd numbers, we have
The first sum is the sum of all integers from 1 to N, which is N(N+1)/2. We want twice this sum, so we have
The second sum is simply the sum of N ones:
So, the final result is
which ends the proof.
Answer:
1. 1,605
2. -605
3. 21,575
Step-by-step explanation:
Answer:
Dimensions → (5 inches × 4 inches)
Step-by-step explanation:
Scale factor used for the drawing by Steffie = 
Since, scale factor = 
For Steffie,
Actual length of the crate = 
= 
= 45 inches
Actual width of the crate = 
= 36 inches
Since Brian used the scale factor = 
Length of the drawing = Actual length × Scale factor
= 45 ×
= 5 inches
Width of the drawing = Actual width × Scale factor
= 36 ×
= 4 inches
Therefore, dimensions of the drawing made by Brian are (5 inches × 4 inches)
Answer:
x⁵ + 5x³ + 7x² + 35
Step-by-step explanation:
(x² + 5) (x³ + 7)
To distribute binomials (expressions with two terms), you can use the FOIL method (First, Outer, Inner, Last):
x⁵ + 7x² + 5x³ + 35
To put into standard form, rearrange from highest power to lowest power:
x⁵ + 5x³ + 7x² + 35
