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:
C)
Step-by-step explanation:
Note that one of the lines is simply y=-1 for any x, so we can dismiss the only answer without y=-1. That rejected answer is A)
Now let's notice, that the other line is decreasing y when increasing x. That tells us that in the equation y = ax + b, a has to be negative. This brings us to reject option D).
What is the y of that line for x = 0? Because y = ax + b, for x = 0 we will get the value of b. This is called the intercept. The line is at y=4 for x=0, so we know that the b in the equation must be positive 4. This fits answer C, but rejects answer B). And so, we have found that C) is the only possible answer.
Answer
We have,
Volume of pyramid = 4834 in³
Base area of the pyramid = ?
Assuming height of the pyramid = 20 in
We know that
Volume of pyramid =
l w = 725.1 in²
Hence, area of the base of the pyramid is equal to 725.1 in².
From both sides of the equation, 4 should have been subtracted.
The solution should look like this:
X + 4 = 28
From each side, subtract 4 :
<em>X = 24</em>
I'd like to demonstrate more steps, but the answer has already popped up, so there aren't any more steps.
Answer:
The Great Ocean Conveyor Belt
Step-by-step explanation:
The ocean is not a still body of water. There is constant motion in the ocean in the form of a global ocean conveyor belt. This motion is caused by a combination of thermohaline currents (thermo = temperature; haline = salinity) in the deep ocean and wind-driven currents on the surface. Cold, salty water is dense and sinks to the bottom of the ocean while warm water is less dense and remains on the surface.
The ocean conveyor gets its “start” in the Norwegian Sea, where warm water from the Gulf Stream heats the atmosphere in the cold northern latitudes. This loss of heat to the atmosphere makes the water cooler and denser, causing it to sink to the bottom of the ocean. As more warm water is transported north, the cooler water sinks and moves south to make room for the incoming warm water. This cold bottom water flows south of the equator all the way down to Antarctica. Eventually, the cold bottom waters returns to the surface through mixing and wind-driven upwelling, continuing the conveyor belt that encircles the globe.
