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>
9x + 26 + 7x - 17 = 2x + (-3x) + 5x =
16x + 9 = 2x - 3x + 5x =
16x + 9 = 4x
9 = 4x - 16x
9 = - 12x
-9/12 = x
- 3/4 = x
Answer:
C. 6x + 9 - 3x^2
Step-by-step explanation:
We have 4 expressions and are being asked which has 3 terms.
When it comes to terms, terms are numbers that are different, it could be separated through a variable, square root, symbol, e.t.c.
So when looking for an answer, we need 3 numbers with different variables or symbols, let's look
A. only has two, 10x and 8. Therefore it is wrong.
B. has 4 terms, 3x^3, 6x^2, 9x, and 12. Therefore it is wrong.
<u>C. is correct because it has 3 terms, 6</u><u>x</u><u>, </u><u>9</u><u>, and 3x</u><u>^2</u><u>.</u>
D. has 2 terms, 833 and 12x, though 16 is there, it is the same as 833, therefore not counting it as its own term.
Hi,
First we must go back to the formula of the Area of a 2d figure which is L*W or Length times the Width. So, we could divide 64 by 16.
64/16 = 4
The answer is 4.
