Answer:
18
Step-by-step explanation:
To find the second term of the coefficient, multiply out the left hand side of the equation.
The value of b is 18.
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1 answer:
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Answer:
$4
Step-by-step explanation:
The two purchases can be written in terms of the cost of an adult ticket (a) and the cost of a student ticket (s):
7a +16s = 120 . . . . . . . . price for the first purchase
13a +9s = 140 . . . . . . . . price for the second purchase
Using Cramer's rule, the value of s can be found as ...
s = (120·13 -140·7)/(16·13 -9·7) = 580/145 = 4
The cost of a student ticket is $4.
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<em>Comment on Cramer's Rule</em>
Cramer's rule is particularly useful for systems that don't have "nice" numbers that would make substitution or elimination easy methods to use. If you locate the numbers in the equation, you can see the X-patterns that are used to compute the numerator and denominator differences.
The value of a is (16·140 -9·120)/(same denominator) = 1160/145 = 8. I wanted to show you these numbers so you could see the numerator X-pattern for the first variable.
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Of course, graphical methods can be quick and easy, too.
Answer:
The length of the shorter part of the wire is 24 centimeters.
Step-by-step explanation:
Let the total length of the piece of wire, where
and
are the perimeters of the greater and lesser squares. All lengths are measured in centimeters. Since squares have four sides of equal length, the side lengths for the greater and lesser squares are
and
. From statement we find that the sum of the areas of the two squares (
), measured in square centimeters, is represented by the following expression:
(1)
And we expand this polynomial below:
(2)
If we know that and
, then the length of the shorter part of the wire is:
By the Quadratic Formula, we determine the roots associated with the polynomial:
,
The length of the shorter part of the wire corresponds to the second root. Hence, the length of the shorter part of the wire is 24 centimeters.