Find the coordinates of the vertices of the figure formed by each system of inequalities.
1 answer:
Answer:
D(1, –5), (7, 1), (–11, 7)
Step-by-step explanation:
The given inequalities are:
y + x ≥ –4
y ≥ x – 6
3y + x ≤ 10
We graph the inequalities as shown in the attachment.
The coordinates of the vertices of the figure formed by the given system of inequalities are:
(1, –5), (7, 1), (–11, 7)
The correct choice is D.
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Answer:
1400ft²
Step-by-step explanation:
Given
Room Dimension: 20 ft by 25 ft by 10 ft
Where Length = 20 ft
Width = 25 ft
Height = 10 ft
Required
Surface area of painted walls and ceiling
We'll assume that the room is rectangular in shape and all 4 sides are covered.
<em>This means that Mickey will paint 4 walls and 1 ceiling.</em>
The dimension of the 2 of the 4 walls is as follows;
20ft by 10ft, 25ft by 10ft,
Because opposite sides of a rectangle are equal, the dimension of the remaining 2 walls is: 20ft by 10ft, 25ft by 10ft
Calculating the area of the 4 walls;
The dimension of the ceiling is as follows:
20ft by 25ft
Calculating the area of the ceiling
So, the area Micky will cover = Area of 4 walls + Area of ceiling
Total Surface Area
Total Surface Area =
Hence, Micky will cover 1400ft²
Answer:
x = √2 + 2, -√2 + 2
Step-by-step explanation:
y = -2(x-2)² + 4
-2(x-2)² + 4 = 0 --- replace y with 0
-2(x - 2)² = -4 --- subtract 4 from both sides
(x - 2)² = --- divide both sides by -2
(x - 2)² = 2 --- simplify
x - 2 = +-√2 --- square root both sides
x - 2 = √2 --- split into 2 equations
x - 2 = -√2
x = √2 + 2 --- solve first equation
x = -√2 + 2 --- solve second equation
x = √2 + 2, -√2 + 2