Place value of whole numbers 301,256,878
1 answer:
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Answer:
The ratio of perimeter of ABCD to perimeter of WXYZ =
Step-by-step explanation:
First, we have to determine the multiplicative factor of the dimensions for both figures.
Considering sides AB and WX,
multiplicative factor =
= 1.5
So that:
XY = 6 x 1.5 = 9
YZ = 7 x 1.5 = 10.5
ZW = 7 x 1.5 = 10.5
Perimeter of ABCD = 6 + 7 + 7 + 8
= 28
Perimeter of WXYZ = 9 + 10.5 + 10.5 + 12
= 42
The ratio of the perimeters of the two quadrilaterals can be determined as;
ratio =
=
=
The ratio of the perimeter of ABCD to perimeter of WXYZ is .
Answer:
(x, y) = (1/2, -1)
Step-by-step explanation:
Subtracting twice the first equation from the second gives ...
(2/x +1/y) -2(1/x -5/y) = (3) -2(7)
11/y = -11 . . . . simplify
y = -1 . . . . . . . multiply by y/-11
Using the second equation, we can find x:
2/x +1/-1 = 3
2/x = 4 . . . . . . . add 1
x = 1/2 . . . . . . . multiply by x/4
The solution is (x, y) = (1/2, -1).
_____
<em>Additional comment</em>
If you clear fractions by multiplying each equation by xy, the problem becomes one of solving simultaneous 2nd-degree equations. It is much easier to consider this a system of linear equations, where the variable is 1/x or 1/y. Solving for the values of those gives you the values of x and y.
A graph of the original equations gives you an extraneous solution of (x, y) = (0, 0) along with the real solution (x, y) = (0.5, -1).
Questions (contd)
(a) For what amount of driving do the two plans cost the same?
(b) What is the cost when the two plans cost the same?
Answer:
(a) 100 miles
(b) $65
Step-by-step explanation:
Given
Plan 1:
per mile
Plan 2:
per mile
Solving (a): Number of miles when both plans are equal
Represent the distance with x and the cost with y
So:
Plan 1:
Plan 2:
To solve (a), we equate both plans together; i.e.
Collect Like Terms
Solve for x
Hence, 100 mile would cost both plans the same
Solving (b): Cost when both plans are the same:
In this case, we simply substitute 100 for x in any of the y equation.
<em>Hence, the amount is $65</em>