Answer:
Inverse functions Inverse Functions If f is a one-to-one function with domain A and range B, we can de ne an inverse function f 1 (with domain B ) by the rule f 1(y) = x if and only if f(x) = y: This is a sound de nition of a function, precisely because each value of y in the domain of f 1 has exactly one x in A associated to it by the rule y = f(x).
Step-by-step explanation:
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Answer:
Rhombus
Step-by-step explanation:
The given points are A(−5, 6), B(−1, 8), C(3, 6), D(−1, 4).
We use the distance formula to find the length of AB.
The length of AD is
The length of BC is:
The length of CD is
Since all sides are congruent the quadrilateral could be a rhombus or a square.
Slope of AB
Slope of BC
Since the slopes of the adjacent sides are not negative reciprocals of each other, the quadrilateral cannot be a square. It is a rhombus
Answer:
Step-by-step explanation:
step 1
Find the slope of the line
The formula to calculate the slope between two points is equal to
we have the points
(2,24) and (6,16)
substitute in the formula
step 2
Find the equation of the line in slope intercept form
we have
----> the k-intercept is the point (0,28) see the graph
substitute
Answer:
The coach can choose a lineup of 11 players in 6,047,981,701,347 different ways.
Step-by-step explanation:
Since the varsity soccer team has 20 players, and three of the players are trained to be goalies while the remaining 17 can play any position, and only 11 players can be on the field at once, and the coach wants to make sure there is exactly one goalie on the field, to determine how many ways can the coach choose a lineup of 11 players if exactly 1 player must be a goalie the following calculation has to be made:
3 x 17 ^ 10 = X
3 x 2,015,993,900,449 = X
6,047,981,701,347 = X
Therefore, the coach can choose a lineup of 11 players in 6,047,981,701,347 different ways.