Answer: Two solutions
Step-by-step explanation:
1. x =(-2-√-76)/-8=(1+i√ 19 )/4= 0.2500-1.0897i
2. x =(-2+√-76)/-8=(1-i√ 19 )/4= 0.2500+1.0897i
Answer:
The dimensions are:
Length = 5m and Width = 4m
Or
Length = 4m and Width = 5m
Step-by-step explanation:
A rectangular dining room has an area of 20 square meters. It's perimeter is 18 meters. What are the dimensions of the dining room?
Area of a rectangle = Length × Width
= LW = 20 m²
Perimeter of a rectangle =
2L + 2W = 18 m
Hence:
LW = 20...... Equation 1
L = 20/W
2L + 2W = 18 ...... Equation 2
We substitute
20/W for L in Equation 2
2(20/W) + 2W = 18
40/W + 2W = 18
Multiply through by W
40 + 2W² = 18W
2W² - 18W + 40 = 0
2W² - 10W - 8W + 40 = 0
(2W - 8 )(W - 5) = 0
2W - 8 = 0
2W = 8 , W = 8/2 = 4m
W - 5 = 0
W = 5m
W = 4m or 5 m
Solving for L
When W = 5 m
L = 20/W
L = 20/5
L = 4m
When W = 4m
L = 20/W
L = 20/4
L = 5m
Therefore, the dimensions are:
Length = 5m and Width = 4m
Or
Length = 4m and Width = 5m
If f = {(4, 2), (6, 1), (8, 4), (10, 2), (12, 5)}, what is the range
UNO [17]
Answer:
Range = {2,1,4,5}
Step-by-step explanation:
When a function is given in the form if a relation. i.e. ordered pairs.
When the function is given in the form of ordered pairs then the set of first elements i.e. x-coordinates of all ordered pairs forms domain while the set of second elements i.e. y-coordinate of all ordered pair is called range.
So in the given function:
Range = {2,1,4,5}
The repeating values are only written once..
F(x) is a parabola opening upward, while g(x) is a parabola facing downward.
So there needs to be a negative out front of the f(x) term. The negative will flip the parabola. That means the answer is either A or B
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After we flip the parabola, we need to translate the vertex (0,0) to the point (2,1) so that it matches up with the vertex of g(x)
To move from (0,0) to (2,1) we shift 2 units to the right and 1 unit up.
To move 2 units to the right, replace 'x' with 'x-2'
To move 1 unit up, you tack on a "+1"
So f(x) turns into -f(x) and then we replace the x with x-2 to get -f(x-2). Finally we tack on a "+1" to get -f(x-2)+1
The g(x) function is g(x) = -f(x-2)+1
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Therefore the final answer is choice B
Answer:
OPTION C: 300 cm³
Step-by-step explanation:
Volume of a cylinder =
where, - is the radius of the cylinder;
and - is the height.
Given: and
⇒ V = (5)² (12) = (25) (12)
⇒ V = 300
Therefore, the volume of the cylinder, V = 300 cm³.