1. First transformation is rotation rotation of 180 about the origin. This transformation has a rule:
(x,y)→(-x,-y).
If points E(-2,-4), F(-1,-1), D(-2,-1) are vertices of triangle EFD, then
- E(-2,-4)→E''(2,4),
- F(-1,-1)→F''(1,1),
- D(-2,-1)→D''(2,1).
2. Second transformation is translation 1 unit left with a rule
(x,y)→(x-1,y).
Then
- E''(2,4)→E'(1,4),
- F''(1,1)→F'(0,1),
- D''(2,1)→D'(1,1).
Answer: 1st: rotation of 180 about the origin; 2nd: translation 1 unit left.
Answer:
5 : 2 : 3
Step-by-step explanation:
Total sweets = 50
Sweet types:
Jellies = 25
Fizzy cola = 10
Number of boiled sweets = 50 - (25 + 10) = 15
Ratio of :
Jellies : Fizzy cola : boiled sweets
25 : 10 : 15
Divide through by 5
Jellies : Fizzy cola : boiled sweets
5 : 2 : 3
Hey there! Let’s solve the question first.
(6^4)^-3= 4.593 or 4.6
The reason behind this, 6^4=1296^-3
And 1269^-3= 4.593 or 4.6
Hope this helps!
Consider any point P(x, y) in the coordinate axis.
The reflection of this point across the y-axis is the point P'(-x, y).
(x, y) and (-x, y) are the 'mirror' images of each other, with the y'axis as the 'mirror'.
For example the coordinates of the image of P(4, 13) after the reflection across the y-axis is P'(-4, 13)
or, if P(-5, -9), then P'(5, -9)
Answer: if coordinates of V are (h, k), coordinates of V' are (-h, k)
Answer:
a.
<u>Increasing:</u>
x < 0
x > 2
<u>Decreasing:</u>
0 < x < 2
b.
-1 < x < 2
x > 2
c.
x < -1
Step-by-step explanation:
a.
Function is increasing when it is going up as we go rightward
Function is decreasing when it is going down as we go rightward
We can see that as we move up (from negative infinity) until x = 0, the function is increasing. Also, as we go right from x = 2 towards positive infinity, the function is going up (increasing).
So,
<u>Increasing:</u>
x < 0
x > 2
The function is going down, or decreasing, at the in-between points of increasing, that is from 0 to 2, so that would be:
<u>Decreasing:</u>
0 < x < 2
b.
When we want where the function is greater than 0, we basically want the intervals at which the function is ABOVE the x-axis [ f(x) > 0 ].
Looking at the graph, it is
from -1 to 2 (x axis)
and 2 to positive infinity
We can write:
-1 < x < 2
x > 2
c.
Now we want when the function is less than 0, that is basically saying when the function is BELOW the x-axis.
This will be the other intervals than the ones we mentioned above in part (b).
Looking at the graph, we see that the graph is below the x-axis when it is less than -1, so we can write:
x < -1
