Answer:
Step-by-step explanation:
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Answer:
The distance A’C’ is 4.47 units
Step-by-step explanation:
Before we go on, we need to get the appropriate transformation
Mathematically, we have a 90 degrees clockwise rotation yielding the following;
(x,y) to (-y,x)
A is (-4,1)
C is (-2,5)
By transforming, we have
A’( -1,-4)
C’ (-5,-2)
To get the magnitude of the line segment, we are going to use the distance formula between points
We have this as;
D = √(x2-x1)^2 + (y2-y1)^2
D = √(-5-(-1))^2 + (-2-(-4))^2
D = √(-4)^2 + (2)^2
D = √(16 + 4)
D = √20
D = 4.47 units
Answer:
Step-by-step explanation:
Using the given expressions, we can write the area as ...
A = BH
42 = (2x +1)(x +3) = 2x^2 +7x +3
2x ^2 +7x -39 = 0
(x -3)(2x +13) = 0
x = 3 or -6.5 . . . . . these values make the factors be zero
In order for the parallelogram to have positive dimensions, the value of x must be 3. So, the base and height are ...
base = 2(3) +1 = 7
height = 3 +3 = 6
For #32,
P=2L+2W
Subtract 2W from both sides, and swap left and right
2L = P-2W
Divide by 2
2L/2=(P-2W)/2
L = P/2 - 2W/2
L=P/2 - W
For #35
Most of the expenses are in fractions (of the original amount, A), so they can be added:
A/4 + A/5 + 2A/5 + 750 = A
add the fractions, with a common denominator of 20,
5A/20 + 4A/20 + 8A/20 +750 = A
(5A+4A+8A)/20 +750 = A
17A/20 + 750 = A
Now subtract 17A/20 from both sides and swap left and right
A - 17A/20 = 750
(3/20)A = 750
Multiply both sides by 20/3 (to make one unit of A on the left)
(3/20)*(20/3) A = 750*20/3
A =250*20=5000
