1.If two different lines are perpendicular to the same plane, they are:
a. Collinear
b. Coplanar
c. Congruent
d. Consecutive
I think the answer is B, is that correct?
Also, this:
2. Express 3 radical 75 plus radical 27 all over3 in radical form.
I simplified it to 18 radical 3 over 3, is there anything else I can do with it?
Thanks!
1. The correct answer is b. Coplanar.
To understand why, let's first clarify the terms:
- Perpendicular lines are lines that intersect at a right angle (90 degrees).
- A plane is a flat surface that extends infinitely in all directions.
When two different lines are perpendicular to the same plane, it means that both lines intersect the plane at a right angle. This implies that the lines must lie within the same plane, making them coplanar.
2. To express (3√75 + √27) / 3 in radical form, you are on the right track but there is still further simplification that can be done.
Let's break it down step-by-step:
First, simplify the expression under each radical:
- √75 can be simplified as √(25 * 3) = 5√3.
- √27 can be simplified as √(9 * 3) = 3√3.
Next, substitute the simplified values back into the original expression:
(3√75 + √27) / 3 becomes (3 * 5√3 + 3√3) / 3.
Now, let's simplify it further:
Using the distributive property, you can factor out the common factor of √3:
(3 * 5√3 + 3√3) / 3 = (15√3 + 3√3) / 3.
Combining like terms, you get:
(15√3 + 3√3) / 3 = 18√3 / 3.
Finally, simplify the fraction by dividing the numerator and denominator by 3:
18√3 / 3 = 6√3.
So, the simplified radical form for (3√75 + √27) / 3 is 6√3.