Answer:
Given: ABCD is a parallelogram,
In which E ∈ BC and F lies on the extension of DC,
Such that line segment EF goes through the vertex A.
To prove:
Proof:
Since, By the definition of parallelogram,
By the Alternative interior angle theorem,
Also, ( vertically opposite angles )
Thus, By AA similarity postulate,
Hence proved.
Answer:
Step-by-step explanation:
Given
Required
Determine the probability of selecting the oldest 3
First, we need to determine the total possible selection.
Since it's a selection, we make use of combination as follows:
In this case:
So:
In the combination, there can be only 1 set of oldest people.
So:
Answer:
see below
Step-by-step explanation:
Since 2x appears on the left side of both equations, that term can be eliminated by subtraction, which is what the first choice suggests.
The result will be ...
3y = 7 -4y +5 . . . . . . . . . second equation subtracted from the first
7y = 12 . . . . . . add 4y
y = 12/7 . . . . . . divide by 7
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However, the fact that 2x is by itself on the left side of the second equation suggest that <em>substitution</em> may also be a good option. Perhaps an equally good first step is to use the expression in the second equation to substitute for 2x in the first:
(4y -5) +3y = 7
Either way, the resulting equation is 2-step.
7y = 12 . . . add 5
y = 12/7 . . . divide by 7
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The other suggested "first steps" do nothing useful.
Perimeter = 2x length + 2x width.
2(2x+3) + 2(x-5) = 44
Simplify:
4x + 6 +2x -10 = 44
Combine like terms:
6x -4 = 44
Add 4 to both sides:
6x = 48
Divide both sides by 6:
X = 8
Now replace x with 8 in the equation for length:
2x + 3 = 2(8) +3 = 16 + 3 = 19 cm
Length = 19 cm
Answer:
.9167 miles per lap
Step-by-step explanation:
3.6 miles total-1.2 miles walked= 4.4 miles in laps
4.4 miles=4.8 laps
we are solving for miles per lap, so we divide 4.4m/4.8l