Answer:
D
Step-by-step explanation:
If you look at the right side of each piecewise function, you will see the x-values. That is what we will be focusing on in this explanation. All four equations have x <u>></u> 4, and we know that to be true. If you look at the equation on the graph going South West, you will see that the endpoint is at x=1. Only 1 equation, D, has this in the piecewise function. To confirm it is D, you can see that 1<x<4 is also in the piecewise function, and all the values line up with their corresponding y-values.
Hope this helps! :)
Given that the octagon rotates 360 degrees, it is a given that for every regular division of the polygon (360/8 = 45 degrees), the image would coincide with the pre-image during the rotation. Therefore, the octagon would coincide a total of 8 times as it rotates 360 degrees about its center.
Answer:
a) 820
b)450
c) -540
d) -294
e) 1440
f) 1425
Step-by-step explanation:
a) it is an arithmetic progression with ratio=4
a1=3,
a2=3+r=3+4=7.....
a20=a1+19r
so a20=3+19*4=3+76=79
S=(a1+an)*n/2 where n=20
so S=(3+79)*20/2=820
b) a15=a1+14*r=2+14*4=2+56=58
S=(a1+a15)*15/2=(2+58)*15/2=60*15/2=30*15=450
It is the same formula for all the exercises
S=(a1+an)*n/2 , where n is the number of terms
c) a40=30+39*(-3)=30-87=-57
So S=(30-57)*40/2=-540
d) a14=5+13*(-4)=5-52=-47
S=(5-47)*14/2=-42*14/2=-42*7=-294
e) it is 5+7+9+......+75
nr of terms = (an-a1) :r+1=(75-5):2+1=36
S=(5+75)*36/2=36*40=1440
f) ratio=7-4=3
the same formula for n= (91-4):3+1=87:3+1=29+1=30
S=(4+91)*30/2=95*30/2=2850/2=1425
Answer:
1.25 cups
Step-by-step explanation:
Since you have 5 5/8 cups = 4 1/2 water bottles
you can make it
5.625 cups = 4.5 water bottles
Then, all you have to do is divide both sides of this equation by 4.5, so
5.625 / 4.5 = 1 water bottle
1.25 cups = 1 water bottle
Answer:
Begin by factoring 2 out of 2x^2 - 2x - 12 equals 0:
2(x^2 - x - 6) = 0
2(x - 3)(x + 2) = 0. 2 is never zero, but x-3 and x+2 can each be set = to 0:
This results in x = 3 and x = -2. The equation is true for these two x-values.
Hope this helped :3
-Jazzy <3
