The answer is 24 feet because segment DE’ is equal to segment DE
Answer:
- The sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is <u>translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis</u>.
Explanation:
By inspection (watching the figure), you can tell that to transform the triangle XY onto triangle X"Y"Z", you must slide the former 5 units to the left, 1 unit down, and, finally, reflect it across the x-axys.
You can check that analitically
Departing from the triangle: XYZ
- <u>Translation 5 units to the left</u>: (x,y) → (x - 5, y)
- Vertex X: (-6,2) → (-6 - 5, 2) = (-11,2)
- Vertex Y: (-4, 7) → (-4 - 5, 7) = (-9,7)
- Vertex Z: (-2, 2) → (-2 -5, 2) = (-7, 2)
- <u>Translation 1 unit down</u>: (x,y) → (x, y-1)
- (-11,2) → (-11, 2 - 1) = (-11, 1)
- (-9,7) → (-9, 7 - 1) = (-9, 6)
- (-7, 2) → (-7, 2 - 1) = (-7, 1)
- <u>Reflextion accross the x-axis</u>: (x,y) → (x, -y)
- (-11, 1) → (-11, -1), which are the coordinates of vertex X"
- (-9, 6) → (-9, -6), which are the coordinates of vertex Y""
- (-7, 1) → (-7, -1), which are the coordinates of vertex Z"
Thus, in conclusion, it is proved that the sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis.
Lets compare both equations so we can explain the reason for it, and see it clearly:
<span>y1 = 5x + 1
</span><span>y2 = 4x + 2
y1 > y2
</span>5x + 1 > 4x + <span>2
</span>To see why that happens we need to solve for x:
5x - 4x > 2 - 1
x > 1
Therefore, the first equation is greater than the second for values of x > 1
1. linear equation
2. rearrange the equation so 4y = 12 - 3× and then divide both sides by 4 to get:
y = 3 - 3/4×
3. equation of a straight line / linear equation
4. gradient is + 3
5. not sure sorry
6. 3x = 12 - 4y. Divide each side by 3 to get:
x = 4 - 4/3y
7. use y = 3 - 3/4x by doing and x and y table. So when x = 1, y = 3 - 3/4 (1) (replace the x which the x value you've chosen). Then plot.
8. Make up any problem such as weather, food, etc.
Hope that helps !
The approximate volume is 33.5103217
The exact volume is 32/3cm
so the answers would be 32/3 or 33.49
