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:
y = 3
Step-by-step explanation:
Calculate the slope between the 2 points using the slope formula, then equate to - 3
m =
with (x₁, y₁ ) = (12, - 12 ) and (x₂, y₂ ) = (7, y )
m = =
= - 3 ( multiply both sides by - 5 )
y + 12 = 15 ( subtract 12 from both sides )
y = 3
Answer:
<em>The gaph is shown in the image below</em>
Step-by-step explanation:
<u>Graph of Inequalities</u>
Let's graph the region of the inequality
Since there is no indication, we'll assume the variable p to be in the horizontal axis and m in the vertical axis. Let's solve for m
Since both m and p are positive, we can assume
Or, equivalently
Thus, we can give p any value between 0 and 5,000 to get the corresponding values for m. Let's select the values p=0, p=1,000, p=5,000 to get the points
( 0 ; 2,500 ) ( 1,000 ; 2,000 ) ( 5,000 ; 0 )
With these points we can plot the line representing the function. To know which area must be shaded, we only need to test one point below or above the line. If it fulfills the inequality, then the whole area is shaded.
Let's test the point ( 1,000 ; 1,000 )
Since the condition is met, the area below the line must be shaded as the solution of the inequality
The gaph is shown in the image below
