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aliina
2 months ago
9

Takuya's parents gave him $100dollar as a birthday gift. Since he loves board games, he spent $20dollar out of his present on bo

ard games at the end of each month until his money ran out. Let f(n) be the amount of money that remained from Takuya's present during month n, where n=1 represents the month he received his present.
f is a sequence. What kind of sequence is it?
p.s" tell me if it is a geometric sequence or arithmetic and find the explicit formula
Mathematics
2 answers:
Inessa [12.5K]2 months ago
8 0
1. Arithmetic 2. f(1)=100 f(n) = f(n−1) + (-20)
Svet_ta [12.7K]2 months ago
3 0
To create a recursive formula, start by identifying if the sequence is geometric (for example, if the same number is being multiplied or divided for one term or more). After that, determine the common ratio (the specific number used for multiplication or division).
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Which are the solutions of x2 = –5x + 8? StartFraction negative 5 minus StartRoot 57 EndRoot Over 2 EndFraction comma StartFract
tester [12383]

Answer:

x=\frac{-5-\sqrt{57} }{2}\ or\ x=\frac{-5+\sqrt{57} }{2}

Detailed solution:

Given:

The problem to solve is:

x^2=-5x+8

Convert the equation into the standard quadratic form ax^2+bx +c =0, where a,\ b,\ and\ c represent constants.

So, by adding 5x-8 to both sides, we get:

x^2+5x-8=0

Note that a=1,b=5,c=-8.

The roots of this quadratic are found by applying the quadratic formula given as:

x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

Substitute a=1,b=5,c=-8 into the formula and calculate for x.

x=\frac{-5\pm \sqrt{5^2-4(1)(-8)}}{2(1)}\\x=\frac{-5\pm \sqrt{25+32}}{2}\\x=\frac{-5\pm \sqrt{57}}{2}\\\\\\\therefore x=\frac{-5-\sqrt{57} }{2}\ or\ x=\frac{-5+\sqrt{57} }{2}

Hence, the roots are:

x=\frac{-5-\sqrt{57} }{2}\ or\ x=\frac{-5+\sqrt{57} }{2}

4 0
3 months ago
Read 2 more answers
Sabra joins a cooking club for $8.50 and pays $6.25 each month. She also joins a movie club for $12 and pays $3.75 each month. W
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The simplified expression is 10m + 20.5, where m stands for the total number of months. Initially, we can express her expenses as follows: 8.5 + 62.5m and 12 + 3.75m. Adding these two expressions together yields a combined equation of: 10m + 20.5.
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Josh Josh estimates the height of his desk what is the reasonable estimate
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The estimated height would be around 3 feet, which would correspond to a level that is approximately at waist height.
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