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:
Step-by-step explanation:
First you add 4 on both sides
X^2=0
Then you take square on both sides
X=+- the square root of 4
Simplify that
X=plus or minus 2
The answer can be either -2 or +2 (which is just 2)
Ratios are the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
Equivalent ratios are like equivalent fractions, if they are the same value they are equivalent.
For example, to find two ratios that are equal to 1:7, first write 1:7 as the fraction 1/7.
Answer:
15 units.
Step-by-step explanation:
The distance between the points (x1, y1) and (x2, y2) is
√(x1-y1)^2 + (y1-y2)^2))
So here it is:
√(10- -2)^2 + (6- -3)^2)
= √(144+81)
= √225
= 15.
Answer:
70
Step-by-step explanation:
7^2 - ( 6-3^3)
PEMDAS
Parentheses first
7^2 - ( 6-3^3)
The exponent in the parentheses first
7^2 - ( 6-27)
7^2 - ( -21)
Now the exponent
49 - (-21)
Now subtract
49 +21
70
