Genevieve buys 4 dance tickets for $15 bill buys 16 dance tickets for $75 did they pay at the same rate?
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:
No , any two quadrilaterals may not be similar if their corresponding angles are congruent.
Step-by-step explanation:
We need to check that whether two quadrilaterals are similar if
their corresponding angles are congruent.
A quadrilateral is a polygon having two sides .
Two figures are said to be similar if they have same shape .
Two angles are said to be congruent if they have same measure .
Consider two quadrilaterals : rectangle and square
Each angle of square and rectangle is equal to . So, their corresponding angles are congruent .
But square and rectangle are not similar as they have different shape .