Answer:
Given the coordinates of rectangle ABCD are;
A = (3, 5)
B = (5,5)
C = (5, 1) and
D = (3, 1)
The rule of rotation 90 degree counter-clockwise around the origin is given by;
Now, the coordinates of each vertex when rectangle ABCD is rotated 90 degree counter-clockwise around the origin are;
Answer:
Step-by-step explanation:
You are being asked to compare the value of a growing infinite geometric series to a fixed constant. Such a series will always eventually have a sum that exceeds any given fixed constant.
__
<h3>a)</h3>
Angelina will get more money from the Choice 1 method of payment. The sequence of payments is a (growing) geometric sequence, so the payments and their sum will eventually exceed the alternative.
__
<h3>c)</h3>
For a first term of 1 and a common ratio of 2, the sum of n terms of the geometric series is given by ...
Sn = a1×(r^n -1)/(r -1) . . . . . . . . . . series with first term a1, common ratio r
We want to find n such that ...
Sn ≥ 1,000,000
1 × (2^n -1)/(2 -1) ≥ 1,000,000
2^n ≥ 1,000,001 . . . . add 1
n ≥ log(1,000,001)/log(2) . . . . . take the base-2 logarithm
n ≥ 19.93
The total Angelina receives from Choice 1 will exceed $1,000,000 after 20 days.
Black 20% 1/5
navy 25% 1/4
Brown 35% 7/20
other 20% 1/5
hope it helps!!
Answer:0.015625
Step-by-step explanation:
Let x be the numbers. The union between the conditions, x < - 3 or greater than or equal to 5 is,
-3 > x ≥ 5
The numbers do not have the intersection. Thus, the answer to this item is all number that fall into the conditions, -3 > x ≥ 5.
