Problem 1) Line n is the line of symmetry (not line o) because we can fold the lower half to match up with the upper half. The folding line is over line n.
Problem 2) I agree. Nice work on getting the correct answer. The folding line is a vertical line through the center
Problem 3) It's hard to say for sure, but I think the top left corner is NOT reflective over any line of symmetry no matter how you rotate it. So I would uncheck that box. I agree with your other choices though. Great job with those.
D. (y-3)
I'm assuming that they want you to find the factors of the quadratic expression, which are (y-5)(y-3). (y-5) isn't up there, so (y-3) is the only solution that's really possible.
Consider rectangular box with
- length x units (x≥0);
- width 3 units;
- height (8-x) units (8-x≥0, then x≤8).
The volume of the rectangular box can be calculated as
In your case,
Note that maximal possible value of the height can be 8 units (when x=0 - minimal possible length) and the minimal possible height can be 0 units (when x=8 - maximal possible length).
From the attached graph you can see that the greatest x-intercept is x=8, then the height will be minimal and lenght will be maximal.
Then the volume will be V=0 (minimal).
Answer: correct choices are B (the maximum possible length), C (the minimum possible height)
I think it’s A sorry if it’s wrong!
The cross product of the normal vectors of two planes result in a vector parallel to the line of intersection of the two planes.
Corresponding normal vectors of the planes are
<5,-1,-6> and <1,1,1>
We calculate the cross product as a determinant of (i,j,k) and the normal products
i j k
5 -1 -6
1 1 1
=(-1*1-(-6)*1)i -(5*1-(-6)1)j+(5*1-(-1*1))k
=5i-11j+6k
=<5,-11,6>
Check orthogonality with normal vectors using scalar products
(should equal zero if orthogonal)
<5,-11,6>.<5,-1,-6>=25+11-36=0
<5,-11,6>.<1,1,1>=5-11+6=0
Therefore <5,-11,6> is a vector parallel to the line of intersection of the two given planes.
