Answer:
The image of the point (1, -2) under a dilation of 3 is (3, -6).
Step-by-step explanation:
Correct statement is:
<em>What are the coordinates of the image of the point (1, -2) under a dilation of 3 with the origin.</em>
From Linear Algebra we get that dilation of a point with respect to another point is represented by:
(Eq. 1)
Where:
- Reference point with respect to origin, dimensionless.
- Original point with respect to origin, dimensionless.
- Dilation factor, dimensionless.
If we know that 
, 
and 
, then the coordinates of the image of the original point is:
![\vec P' = (0,0) +3\cdot [(1,-2)-(0,0)]](https://tex.z-dn.net/?f=%5Cvec%20P%27%20%3D%20%280%2C0%29%20%2B3%5Ccdot%20%5B%281%2C-2%29-%280%2C0%29%5D)
The image of the point (1, -2) under a dilation of 3 is (3, -6).
Answer:
2 lessons per day for 27 days and 3 lessons a day for 4 days.
Step-by-step explanation:
66/31 = 2 4/31
Since 66 divided by 31 is 2 with remainder 4, you need to do 31 days of 2 lessons per day. To do the extra 4 lessons, do one more lesson per day for 4 of those days.
That results in:
2 lessons per day for 27 days and 3 lessons a day for 4 days.
Check:
2 lessons a day for 27 days = 2 * 27 = 54
3 lessons a day for 4 days = 3 * 4 = 12
54 + 12 = 66
If you do 2 lessons a day for 27 days and 3 lessons a day for 4 days, you will do the 66 lessons.
Answer:
54
Step-by-step explanation:
Multiply:
<em>37x37=72</em>
<em>Subtract:</em>
<em>180-72=108</em>
<em>Divide:</em>
<em>108/2=54</em>
<span>1800 mi / 30 hr = 60 mi/hr
hope that helped</span>
D = rt. The first car's rate is r, and the other one, going faster, is r + 12. The time they travel is 2 hours. Since one is going faster than the other, he has gotten farther. But, regardless of that, the distance between them is 232. So the distance the first one travels, r*t, which 2r, plus the distance the second one travels, 2(r+12) = 232. 2r + 2r + 24 = 232. Solve for r. 4r = 208 and r = 52. The slower one goes 52 and the faster one goes 64
