Answer:
(1.13, 7.74) and (-4.13, 18.26)
Step-by-step explanation:
This can be solved in two ways: mathematically and graphically.
<u>Graphing</u>
Plot both lines and find where they intersect. See the attachment.
The intersection points are (1.13, 7.74) and (-4.13, 18.26)
<u>Mathematical</u>
y + 2x = 10
y = 10 - 2x
y = 3x² + 7x - 4
10 - 2x = 3x² + 7x - 4
3x² + 9x - 14 = 0
Solve this using the quadratic equation:
x = 1.13 and -4.13
Use these two values of x to find y:
y = 10 - 2x
y = 10 - 2(1.13)
y = 7.74
y = 10 -2x
y = 10 -2(-4.13)
y = 18.26
The two points are:
(1.13, 7.74) and (-4.13, 18.26)
Answer:
Number of points, x, Number of segments, y
x: 2, 3, 4, 5, ... N,. ...
y: 1, 3, 6, 10, ... (N-1)(N)/2, ...
Step-by-step explanation:
Adding Nth point, there are N-1 new segments,
and (sum over {i = 1 to N-1} of i) total segments. As Gauss knew when he was c.10 yo, the sum is (N-1)(N)/2.
Answer:
A) t = 1 second to reach the highest point
B) h = 96 feet
C) t = 3.449 seconds to hit the ground
Step-by-step explanation:
We notice that the equation that describes the position of the object in terms of the time, is a parabola (quadratic) with negative leading coefficient. therefore this is a parabola with arms pointing down, and with vertex at the top. It is at that top vertex that the maximum altitude of the object is reached.
We need therefore to find the position of the vertex (time "t" is the horizontal coordinate and height "h" is the vertical coordinate).
We know that the vertex (maximum of a parabola of this type - normally described by ) is given by
. Therefore in our case, understanding that time "t" is equivalent to the variable "x", and eight "h" is equivalent to the variable "y", that "-16" is
, and "32" is
, we have that the maximum occurs for:
which means at one second from the launching.
We then can find the answer to part B by replacing t with "1" second in the formula for the height "h":
That is : a height of 96 feet.
To find the answer for part C: the time to hit the ground, we solve for the variable "t" in the given expression for the height, by setting the height to zero (object touching the ground) and using the quadratic formula:
which gives us two solutions: t = -1.449 seconds, and t = 3.449 seconds
Since the negative time does not have physical meaning in our case (time before the object was launched), we adopt the second answer: t = 3.449 seconds
1. Angle addition postulate (this could be wrong)
2. Definition of bisect
3. Definition and postulate
4. Screenshot at the bottom
Last one I can't help, my bad.
There is a rumor that Daddy Warbucks is starting a new airline. He plans to serve six cities: San Francisco, Los Angeles, Dallas, Chicago, New York, and Miami. There will be direct flights between each pair of cities. How many different routes will this create?
Answer: There will be different routes.
The 15 different routes are:
1. San Francisco ------------ Los Angeles
2. San Francisco ------------ Dallas
3. San Francisco ------------ Chicago
4. San Francisco ------------ New York
5. San Francisco ------------ Miami
6. Los Angeles ------------ Dallas
7. Los Angeles ------------ Chicago
8. Los Angeles ------------ New York
9. Los Angeles ------------ Miami
10. Dallas ------------ Chicago
11. Dallas ------------ New York
12. Dallas ------------ Miami
13. Chicago ------------ New York
14. Chicago ------------ Miami
15. New York ------------ Miami
