Answer:
Range: y ≥ 4
Step-by-step explanation:
Range is the y value
y = (x-2)^2 +4
The smallest the squared term can be is zero
y = 0 +4
The smallest y can be is 4
y ≥ 4
Answer:
88 degree
Step-by-step explanation:
We assume the measure of MN is x degree.
As the measure of LP is 30 degree more than that of MN, so that the measure of LP is: x + 30 degree
In the circle, as 4 points M,N,P,L are on the circle, we have:
+) ∡MPN = 1/2 * (measure of ∡MPQMN) = x/2 = ∡MPQ
+) ∡LMP =1/2 * (measure of LP) = (x+30)/2 = ∡QMP
We have ∡NQM and ∡MQP are complementary angles, so that:
∡MQP + ∡NQM = 180
=> ∡MQP = 180 - ∡NQM = 180 -103 = 77
In the triangle QMP, total measure of 3 internal angles are 180 degree, so that:
∡MQP + ∡QMP + ∡MPQ = 180
=> 77 + (x + 30)/2 + x/2 = 180
=> 77 + x/2 + 15 + x/2 = 180
=> x = 180 -77-15= 88
So that the measure of MN is 88 degree
We can see this is a summation of multiples of 8 plus 1, which starts at 1.
This can be written in the following way:
Lets verify the summation expression by doing the sequence for the first 4 elements (hence
, as it starts from 0):
![\Sigma_{m=0}^{3}(8m+1)=[8(0)+1]+[8(1)+1]+[8(2)+1]+[8(3)+1]=](https://tex.z-dn.net/?f=%5CSigma_%7Bm%3D0%7D%5E%7B3%7D%288m%2B1%29%3D%5B8%280%29%2B1%5D%2B%5B8%281%29%2B1%5D%2B%5B8%282%29%2B1%5D%2B%5B8%283%29%2B1%5D%3D)
As you can see, the generalization is correct.
52.4/2= 26.2
26.2-3= 23.2
So the original number = 23.2
Answer:
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