Given that there are <span>6 boys and 6 girls in a birthday party, the number of different arrangements of</span><span> first, second, and third is given by:
</span>
Answer:
- b. y = 2/3x +5
- c. y = -3 or -1/2
Step-by-step explanation:
b. The particualar steps for solving a linear equation such as this may vary from one equation to another. In general, you want to put all the y-terms on one side of the equal sign and everything else on the other side. Here's how we'll do that in this case.
Use the distributive property to eliminate parentheses.
... 6x -3y +12 = 4x -3
Find the unwanted terms on the side of the equation where y is, then add their opposite. In this case, we're adding -(6x+12)
... -3y = (4x -3) -(6x +12) = -2x -15
Divide by the coefficient of y.
... y = -2x/(-3) -15/(-3)
... y = 2/3x +5
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c. This is a 2nd-degree (quadratic) equation with y as its only variable. The factor (2y+1) appears in both terms so we can use the distributive property to factor it out. Then the equation becomes ...
... (y +3)(2y +1) = 0
The zero product rule tells us this product will be zero only when one or the other of the factors is zero. This fact helps us find the values of y that are the solution to the equation.
For y+3 = 0:
... y + 3 = 0
... y = -3 . . . . . . add -3 to both sides of the equation
For 2y +1 = 0:
... 2y +1 = 0
... y +1/2 = 0 . . . . divide by 2
... y = -1/2 . . . . . . add -1/2
The solutions are y = -3 or y = -1/2.
Answer:
a) 6, 7, 8, 9, ... , 15
b) 1, 3, 5, 7, ... , 19
Step-by-step explanation:
plug in the position as n
