⁵ (3 A Number pattern has 75 as the first
The rule of the number pattern
Subtract 6 to get the next number
What will be the fifth number in the
sequence

9514 1404 393

  51

Step-by-step explanation:

The rule gives the sequence ...

  75, 69, 63, 57, 51, 45, ...

The 5th number in the sequence is 51.

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Alternate solution

The equation for the general term of an arithmetic sequence is ...

  an = a1 +d(n -1) . . . . . for first term a1 and common difference d

Your sequence has first term 75 and common difference -6, so the equation is ...

  an = 75 -6(n -1)

Then for n=5, the term is ...

  a5 = 75 -6(5 -4) = 75 -24 = 51

The 5th term is 51.

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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