Answer:
Vertex is (-4, -18)
Step-by-step explanation:
f(x) = 
Let (h, k) be the vertex
An easy way to find h is to use the formula h = -b/2a
In your case where f(x) = 
a = 2 and b = 8
So, h = -8/2(1) = -8/2 = -4
Substitue -4 in for x to find k
k = (
) + 8(-4) - 2
= (16) - 32 - 2
= 16 - 32 - 2
= -18
Vertex is (-4, -18)
Note: Another way to find the vertex is to complete the square, but this can really be difficult in some cases
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 = 1 +√5
Step-by-step explanation:
There are different formulas for the area of a triangle available, depending on the given information.
<h3>Formulas</h3>
When two sides and the angle between them are given, the relevant area formula is ...
Area = 1/2(ab)sin(C)
When the base and height of a triangle are given, the relevant area formula is ...
Area = 1/2bh
<h3>Equal Areas</h3>
The problem statement tells us the two triangles shown have equal areas. That means the two formulas will give the same result.
Area from angle = Area from base/height
1/2(x·x)sin(30°) = 1/2(x-2)(x+1)
x² = 2(x² -x -2) . . . . . . . . . . . use sin(30°) = 1/2, multiply by 4
x² -2x -4 = 0 . . . . . . . . subtract x², eliminate parentheses
(x -1)² = 5 . . . . . . . . . add 4+1 to complete the square
<h3>Value of x</h3>
x = 1 ± √5 . . . . . . take the square root, add 1
The value of x must be greater than 2 in order for the triangle side lengths to be positive. (x-2 > 0) This means x = 1-√5 is an extraneous solution.
The value of x is 1 +√5.
Answer: 2.18
Step-by-step explanation:
Angle B= 180- (Angle A + Angle C)
= 180- (70+90)
= 180-160=20
((sin A)/BC)=((sin B)/AC)
((sin 70)/6)=((sin 20)/AC)
(0.9/6)=(0.3/AC)
AC= (6*0.3)/0.9
AC= 2.18
Answer:
7x+9
Step-by-step explanation:
6x+4+x+5
6x+x+4+5
7x+9
