Answer: (b) exactly one plane contains a given line and a point not on the line.
Step-by-step explanation: The basic postulates of geometry are very-well known to all of us. For example-
(i) The intersection of two lines determines a point,
(ii) Two parallel lines give result to a plane,
(iii) A line and a point not on the line determines a plane, etc...
Thus, with the help of the third point, we can easily arrive at the conclusion that a given line and a point not lying on the line is contained in a plane. For example- see the attached figure, AB is a line and P is any point not on the line. They both contained in the plane ABC.
Hence, the correct option is (b).
Answer:
I am stupid too, so forgive me if I am wrong.ಥ_ಥ
I am pretty sure the correct answer is D since 2 can be multiplied by 3 to get 6, and 3 can be multiplied by 3 to get 9. Thus, if the number of guitars is multiplied by 3, the number of amps will always be a multiple of 3.
Let's recall that in a parallelogram:
1. The opposite sides are paralell
In our exercise. sides CZ and KG are paralell. And so do sides KC and GZ.
2. Those opposite sides are equal in length.
3. The opposites angles are equal. In our exercise, angle C and G are equal and so do angles K and Z.
4. That also mean that the angles at the top of the figure are supplementary. It means they add up to 180 degrees. We have the same situation with the two angles at the bottom of the parallelogram.
In our case then:
Now, we can find the measure of angles K and Z, as follows:
Answer:
1 and 37/8 feet
Step-by-step explanation:
We set h(t) to 76 because we want to know when the ball will be at 76 feet high.
So, we have 76=-16t^2+90t+2. When we subtract 76 from both sides, we get -16t^2+90t-74=0, and when you mutiply the equation by -1 (so that x^2 has a positive coefficient, which makes things easier), we get 16t^2-90t+74=0.
We notice that each separate monomial has a common factor, 2, so we can take that out and make it 2(8t^2-45t+37) = 0. Factoring the quantity in the parentheses gives us 2(t-1)(8t-37) = 0.
Using Zero Product Property, we can set the two factors in parentheses to 0 (the 2 isn't really relevant so we don't need to worry about it). This gives us t-1=0 and 8t-37=0. Solving these two equations gives us t = 1 foot or t = 37/8 feet.
