Answer:
D.(2, 2)
Step-by-step explanation:
- Staring point = (2, -4)
- Since he moved 6 units up, so, there will be change in only y-coordinate of the starting point and x-coordinate will remain unchanged.
- End point of the segment = (2, - 4 + 6) = (2, 2)
Initial coordinates:
A (0,0,0)
B (0,5,0)
C (3,5,0)
D (3,0,0)
E (3,0,4)
F (0,0,4)
G (0,5,4)
H (3,5,4)
<span>a.) The prism is reflected over the xz-plane.
Reflection Point P(x,y,z) over the xz-plane is P'(x,-y,z):
Reflection P(x,y,z) over the xz-plane → P'(x,-y,z)
Reflection A(0,0,0) over the xz-plane → A'(0,-0,0) = A'(0,0,0)
</span>Reflection B(0,5,0) over the xz-plane → B'(0,-5,0)
Reflection C(3,5,0) over the xz-plane → C'(3,-5,0)
Reflection D(3,0,0) over the xz-plane → D'(3,-0,0) = D'(3,0,0)
b.) <span>The reflected image is then translated 2 units back, 3 units left, and 1 unit up.
Translation P'(x,-y,z) 2 units back, 3 units left, and 1 unit up is P''(x-2,-y-3,z+1):
Translation P'(x,-y,z) → P''(x-2,-y-3,z+1)
Translation A'(0,0,0) →A''(0-2,0-3,0+1) = A''(-2,-3,1)
</span>Translation B'(0,-5,0) →B''(0-2,-5-3,0+1) = B''(-2,-8,1)
Translation C'(3,-5,0) →C''(3-2,-5-3,0+1) = C''(1,-8,1)
Translation D'(3,0,0) →D''(3-2,0-3,0+1) = D''(1,-3,1)<span>
</span>
<em><u>Question:</u></em>
As part of their government class, Maddie and Ryan had to log volunteer hours in their community. Ryan volunteered for one more than three times the numbers of hours that Maddie did. Altogether, they volunteered in their community for 45 hours. How many hours did Ryan volunteer?
<em><u>Answer:</u></em>
Ryan volunteered for 34 hours
<em><u>Solution:</u></em>
Let "x" be the number of hours Ryan volunteered
Let "y" be the number of hours Maddie volunteered
<em><u>Given that, Altogether, they volunteered in their community for 45 hours</u></em>
Therefore,
number of hours Ryan volunteered + number of hours Maddie volunteered = 45
x + y = 45 ------- eqn 1
<em><u>Ryan volunteered for one more than three times the number of hours that Maddie did</u></em>
number of hours Ryan = 1 + 3(number of hours Maddie)
x = 1 + 3y --------- eqn 2
<em><u>Substitute eqn 2 in eqn 1</u></em>
1 + 3y + y = 45
1 + 4y = 45
4y = 45 - 1
4y = 44
y = 11
<em><u>Substitute y = 11 in eqn 2</u></em>
x = 1 + 3(11) = 1 + 33
x = 34
Thus Ryan volunteered for 34 hours
Answer:
The median is 56
Step-by-step explanation:
50, 52, 52, 55, 56, 56, 56, 58, 58, 59, 60
Then you start eliminating
1. 52, 52, 55, 56, 56, 56, 58, 58, 59
2.52, 55, 56, 56, 56, 58, 58
3. 55, 56, 56, 56, 58
4. 56, 56, 56
5. 56
6. So, the median is 56.
Hope this helped!