What is the solution to the system of equations?

Mathematics

1 answer:

vesna_86 [32]3 years ago

7 0

The correct answer is (10,-20), because the equation already gives you the correct x value. Then, from there you just plug 10 in for x in the y equation. Giving you a -20, :)

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Answer: 5) r = 5, 8th term = -78,125

6) r = 5, 8th term = -312,500

7) r = 5, {1, 5, 25, 125, 625}

8) r = 5, {-4, -20, -100, -500, -2500}

Step-by-step explanation:

The explicit formula of a geometric sequence is: $a_n=a_1\cdot r^{n-1}$ , where;

n is the number of the term
a₁ is the first term
r is the common ratio

$5)\ a_n=-5^{n-1}\\.\qquad =-1\cdot 5^{n-1}\quad \rightarrow \quad a_1=-1\ and\ r=5\\\\a_8=-5^{8-1}\\.\quad =-5^7\\.\quad =-78,125\\\\\\6)\ a_n=-4\cdot 5^{n-1}\quad \rightarrow \quad a_1=-4\ and\ r=5\\\\a_8=-4\cdot 5^{8-1}\\.\quad =-4\cdot 78,125\\.\quad =-312,500$

$7)\ a_1=1\ and\ r=5\\.\quad a_2=1\cdot 5=\boxed{5}\\.\quad a_3=5\cdot 5=\boxed{25}\\.\quad a_4=25\cdot 5=\boxed{125}\\.\quad a_5=125\cdot 5=\boxed{625}\\\\\\\\8)\ a_1=-4\ and\ r=5\\.\quad a_2=-4\cdot 5=\boxed{-20}\\.\quad a_3=-20\cdot 5=\boxed{-100}\\.\quad a_4=-100\cdot 5=\boxed{-500}\\.\quad a_5=-500\cdot 5=\boxed{-2500}\\\\\\$