Part A;
There are many system of inequalities that can be created such that only contain points D and E in the overlapping shaded regions.
Any system of inequalities which is satisfied by (-4, 2) and (-1, 5) but is not satisfied by (1, 3), (3, 1), (3, -3) and (-3, -3) 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 second quadrant of the coordinate system.The area above the x-axis and to the left of the y-axis is shaded.
Part B:It can be verified that points D and E are solutions to the system of inequalities above by substituting the coordinates of points D and E into the system of equations and see whether they are true.
Substituting D(-4, 2) into the system
we have:
-4 < 0
2 > 0
as can be seen the two inequalities above are true, hence point D is a solution to the set of inequalities.
Also, substituting E(-1, 5) into the system we have:
-1 < 0
5 > 0
as can be seen the two inequalities above are true, hence point E is a solution to the set of inequalities.
Part C:Given that chicken can only be raised in the area defined by y > 3x - 4.
To identify the farms in which chicken can be raised, we substitute the coordinates of the points A to F into the inequality defining chicken's area.
For point A(1, 3): 3 > 3(1) - 4 ⇒ 3 > 3 - 4 ⇒ 3 > -1 which is true
For point B(3, 1): 1 > 3(3) - 4 ⇒ 1 > 9 - 4 ⇒ 1 > 5 which is false
For point C(3, -3): -3 > 3(3) - 4 ⇒ -3 > 9 - 4 ⇒ -3 > 5 which is false
For point D(-4, 2): 2 > 3(-4) - 4; 2 > -12 - 4 ⇒ 2 > -16 which is true
For point E(-1, 5): 5 > 3(-1) - 4 ⇒ 5 > -3 - 4 ⇒ 5 > -7 which is true
For point F(-3, -3): -3 > 3(-3) - 4 ⇒ -3 > -9 - 4 ⇒ -3 > -13 which is true
Therefore, the farms in which chicken can be raised are the farms at point A, D, E and F.
Answer:
The two numbers are - 12 and - 12 .
Step-by-step explanation:
Let the two numbers be x and y then
By the question
x * y = 144
or x = 144 / y ....... I)
Again
x + y = - 24
Or 144/y + y = - 24
or, ( 144 + y²) / y = - 24
or, 144 + y² = - 24y
y² + 24y + 144 = 0
y² + ( 12 + 12 ) y + 144 =0
y² + 12y + 12y + 144 = 0
y(y + 12 ) + 12 ( y + 14) = 0
( y + 12 ) ( y + 12 ) = 0
Either
y + 12 =0
y = - 12
Now
x = 144 / - 12 = - 12
Therefore the two numbers are - 12 and - 12 .
Hope it will help :)❤
Here we have a geometric progression!
Data:
n (Number of terms) = 8
(e<span>ighth term)</span>
<span>r (common ratio) = ?<span>
a1 (first term)</span><span> = - 1
a2 second term) = - 4
If: </span></span>
<span>Now, find the geometric progression
</span>Formula:
Solving:
The answer is 25 feet because there are 3 feet in a yard.
Answer: D. $10 per hour.
Explanation: Multiply 3 shifts with 8 hours, so that’s 24 hours he worked. Then divide 240/24 and your answer is 10.
Hope this helps you! ^^
