You can turn 5 into 10/2 and add to x/2
then you need to use simple algebra to left the x alone in the equation so you need to multiply both sides by 2 so you get
2y=10+x
then you need to subtract both sides a 10 so
2y-10=x
now change the x to f'(x) and y to x so:
f'(x)=2x-10
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.
</span>
Answer: 2/6 or 33%
Step-by-step explanation: Hope this helps <3
5x²+y²=3
by implicit differentiation we shall have:
10x+2yy'=0
the second derivative will be:
10+2y"=0
2y"=-10
y"=-5
Answer:
Step-by-step explanation:
Remark
Anything multiplied by 0 = 0. So the whole right side is 0.
(6x - 9)*3 - 1 = 0 Add 1 to both sides.
(6x - 9)*3 - 1 + 1 = 0 + 1 Combine
(6x - 9)*3 = 1 Divide both sides by 3
(6x - 9)*3/3 = 1/3 Simplify
(6x - 9) = 1/3 Remove brackets. Add 9 to both sides
6x - 9+9 = 9 1/3 Combine
6x = 9 1/3
6x = 28/3 Divide both sides by 6
6x / 6 = 28/3 // 6 Invert the 6 and multiply.
x = 28/3 * 1/6
x = 28/18
Answer
x = 14/9
