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2 years ago

-3x + 7x-8 = 34 + 9x - 2

Mathematics

2 answers:

zvonat [6]2 years ago

8 0

Answer:

-8

Step-by-step explanation:

First combine like terms:

4x-8=32+9x

-40=5x

-8=x

padilas [110]2 years ago

7 0

Answer:

X= -8

Step-by-step explanation:

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Show work explain with formulas.

Sedaia [141]

Answer:

$\large\boxed{1.\ a_{44}=481,\ \sum\limits_{n=1}^\infty(11n-3),\ \text{the sum not exist}}$

$\large\boxed{3.\ \sum\limits_{n=1}^{47}(9n+16)=10,904}$

$\large\boxed{4.\ \sum\limits_{n=1}^\infty\bigg(6(2^n)\bigg),\ \text{the sum not exist}}$

Step-by-step explanation:

$1.\\8+19+30+41+...\\\\19-8=11\\30-19=11\\41-30=11\\\\\text{It's an arithmetic series.}\ a_1=8,\ d=11.\\\\\text{The formula for the n-th term of an arithmetic sequence:}\\\\a_n=a_1+(n-1)d\\\\\text{Substitute:}\\\\a_n=8+(n-1)(11)\qquad\text{use the distributive property}\ a(b-c)=ab-ac\\a_n=8+11n-11\\\boxed{a_n=11n-3}\\\\\text{Calculate the 44th term. Put n = 44 to the formula:}\\\\a_{44}=(11)(44)-3=484-3=481$

$\text{The summation notation:}\\\\\sum\limits_{n=1}^\infty(11n-3)\\\\\text{The sum not exist, because}\ d>1,\ \text{therefore}\ 11n-3\rightarrow\infty.$

=======================================================

$3.\\25+34+43+52+...+436\\\\34-25=9\\43-34=9\\52-43=9\\\\\text{It's an arithmetic series.}\ a_1=25,\ d=9.\\\\\text{The formula for the n-th term of an arithmetic sequence:}\\\\a_n=a_1+(n-1)d\\\\\text{Substitute:}\\\\a_n=25+(n-1)(9)\\a_n=25+9n-9\\a_n=9n+16\\\\\text{Calculate which the term of arithmetic series is the number 439.}\\\text{Put}\ a_n=439:\\\\9n+16=439\qquad\text{subtract 16 from both sides}\\9n=423\qquad\text{divide both sides by 9}\\n=47$

$\text{Therefore we have the series in summation notation:}\\\\\sum\limits_{n=1}^{47}(9n+16)\\\\\text{For calculation of the sum we use the formula of a sum of terms}\\\text{of an arithmetic sequence:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\text{Substitute}\ n=47,\ a_1=25,\ a_{47}=439:\\\\S_{47}=\dfrac{25+439}{2}\cdot47=\dfrac{464}{2}\cdot47=232\cdot47=10904\\\\\sum\limits_{n=1}^{47}(9n+16)=10,904$

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$4.\\12+24+48+...\\\\24:12=2\\48:24=2\\\\\text{It's\ a\ geometric series}\ a_1=12,\ r=2.\\\\\text{The formula for the n-th term of a geometic sequence:}\\\\a_n=a_1r^{n-1}\\\\\text{Substitute:}\\\\a_n=(12)(2^{n-1})\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\a_n=(12)\left(\dfrac{2^n}{2^1}\right)\\\\a_n=(6)(2^n)\\\\\text{The summation notation:}\\\\\sum\limits_{n=1}^\infty\bigg(6(2^n)\bigg)\\\\\text{The sum not exist, because}\ r>1,\ \text{therefore}\ 6(2^n)\to\infty$

6 0

3 years ago

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I need help ASAP! Thank you :)

Hitman42 [59]

Answer:

1/3

Step-by-step explanation:

sin=p/h

p/h= 3/9

3/9=1/3

8 0

2 years ago

HELP PLEASE I NEED HELP ON THIS PROBLEM "Three more than 8 times a number is -39.Find the number.

mr_godi [17]

8x + 3 = -39
8x + 3 -3 = -39 - 3
8x = -42
8x/8 = -42/8
x = -5.25

7 0

2 years ago

PLEASE HELP AND HURRY over due and due at 12

forsale [732]

Equations:
Y=-50x+14,040
Y=20x+12,500

Solution X=22, Y=12,950

They will be at the same spot when the graphs intersect and the poi is (22 , 12,940)
So they will meet up at 22, 12,940

7 0

2 years ago

In science class we discovered that 7/8 of an apple is water.What fraction of the apple is not water?

nevsk [136]

Answer:

1/8

Hope this helps

4 0

2 years ago

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