Answer:
Step-by-step explanation:
Height doubles at every 30 seconds, so let's call n how many times it happens, and the t the total time:
n = t/30
If the height doubles one time, it is multiplied by 2, if it doubles 2 times, it's multiplied by 2², for n times, it is multiplied by 2ⁿ, so for an initial height equal to 3:
Answer:
The least common denominator is (b-8)(b+8)(b-1)
Step-by-step explanation:
We are given expression as
Firstly, we will factor both denominators
so, we can plug it back
First term denominator is
(b-8)(b+8)
Second term denominator is
(b+8)(b-1)
So,
Least common denominator will be
(b-8)(b+8)(b-1)
So, we get
The vector AB is not related with the vector CD as k is not the same for each pair of components.
<h3>Are two vectors similar?</h3>
In this question we must prove if the vector AB is a multiple of the vector CD, that is:
![\vec B - \vec A = k \cdot [\vec D - \vec C]](https://tex.z-dn.net/?f=%5Cvec%20B%20-%20%5Cvec%20A%20%3D%20k%20%5Ccdot%20%5B%5Cvec%20D%20-%20%5Cvec%20C%5D)
(1, 4) - (2, 3) = k · [(- 2, 2) - (1, 3)]
(- 1, 1) = k · (- 3, - 1)
Hence, the vector AB is not related with the vector CD as k is not the same for each pair of components.
To learn more on vectors: brainly.com/question/13322477
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Part A;
There are many system of inequalities that can be created such that only contain points C and F in the overlapping shaded regions.
Any system of inequalities which is satisfied by (2, 2) and (3, 4) but is not stisfied by <span>(-3, -4), (-4, 3), (1, -2) and (5, -4) can serve.
An example of such system of equation is
x > 0
y > 0
The system of equation above represent all the points in the first quadrant of the coordinate system.
The area above the x-axis and to the right of the y-axis is shaded.
Part 2:
It can be verified that points C and F are solutions to the system of inequalities above by substituting the coordinates of points C and F into the system of equations and see whether they are true.
Substituting C(2, 2) into the system we have:
2 > 0
2 > 0
as can be seen the two inequalities above are true, hence point C is a solution to the set of inequalities.
Part C:
Given that </span><span>Natalie
can only attend a school in her designated zone and that Natalie's zone is
defined by y < −2x + 2.
To identify the schools that
Natalie is allowed to attend, we substitute the coordinates of the points A to F into the inequality defining Natalie's zone.
For point A(-3, -4): -4 < -2(-3) + 2; -4 < 6 + 2; -4 < 8 which is true
For point B(-4, 3): 3 < -2(-4) + 2; 3 < 8 + 2; 3 < 10 which is true
For point C(2, 2): 2 < -2(2) + 2; 2 < -4 + 2; 2 < -2 which is false
For point D(1, -2): -2 < -2(1) + 2; -2 < -2 + 2; -2 < 0 which is true
For point E(5, -4): -4 < -2(5) + 2; -4 < -10 + 2; -4 < -8 which is false
For point F(3, 4): 4 < -2(3) + 2; 4 < -6 + 2; 4 < -4 which is false
Therefore, the schools that Natalie is allowed to attend are the schools at point A, B and D.
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