If you can divide 81 by 4 and end up with a remainder of 1, then yes, 81 is a part of your sequence.
To justify that, it helps to think about ways we can represent numbers in terms of quotients and remainders. For example, if we take 10/3, we’ll obtain the quotient 3 with a remainder of 1, so another way of writing 10 would be 3(3)+1. If we replace that second three with any integer n, 3n+1 represents *every number* that leaves us with a remainder of 1 when we divide it by 3.
By the same logic, 4n+1 represents every number that leaves a remainder of 1 when we divide it by 4. 81 indeed meets this requirement, since can be written as 4(20)+1, so it would be a part of the sequence.
A rotation would also give you this transformation.
You could do a 90 degree counter-clockwise or a 270 degree clockwise
Answer:
ab = 1/2.
Step-by-step explanation:
The sides of the large square have length √5 while the sides of the small one have sides of length 2.
Each corner has a right triangle with legs of length a and b and hypotenuse 2.
So we have the system
a + b = √5
a^2 + b^2 = 2^2 = 4
Using the identity a^2 + b^2 = (a + b)^2 - 2ab:
4 = (√5)^2 - 2ab
4 = 5 - 2ab
2ab = 5 - 4 = 1
ab = 1/2.
2 1/2 pounds of apple makes serve 6
(2 1/2 x 24)/6 = 10 pounds of apple will make serve 24.
Therefore, she will use 10 pounds of apples.
The right answer for the question that is being asked and shown above is that: "D. a rectangle with a length of 20 units and a width of 11 units." This is the statement that <span>best describes the resulting cross-section of the prism</span>
