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aleksklad [387]
3 years ago
15

Rearrange the equation so n is the independent variable. 3m-2n=12 m=

Mathematics
1 answer:
Rina8888 [55]3 years ago
3 0
Downloaded Photomath it’s going to help you a lot, and show you step by step, also it’s free.
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What is the sum of the infinite geometric series 9−6+4−83+...9-6+4-83+...??
vivado [14]
Successive terms have a common factor of -\dfrac23, which means the nth partial sum of the series can be written as

S_n=9-6+4-\dfrac83+\cdots+9\left(-\dfrac23\right)^{n-1}
S_n=9\left(1+\left(-\dfrac23\right)^1+\left(-\dfrac23\right)^2+\left(-\dfrac23\right)^3+\cdots+\left(-\dfrac23\right)^{n-1}

\implies-\dfrac23S_n=9\left(\left(-\dfrac23\right)^1+\left(-\dfrac23\right)^2+\left(-\dfrac23\right)^3+\left(-\dfrac23\right)^4+\cdots+\left(-\dfrac23\right)^n\right)

\implies S_n-\left(-\dfrac23\right)S_n=9\left(1-\left(-\dfrac23\right)^n\right)
\dfrac53S_n=9\left(1-\left(-\dfrac23\right)^n\right)
S_n=\dfrac{27}5\left(1-\left(-\dfrac23\right)^n\right)

As n\to\infty, the geometric term vanishes, leaving you with

S=\displaystyle\lim_{n\to\infty}S_n=\dfrac{27}5
7 0
3 years ago
Solve for x.<br> 6(x - 1) = 9(x + 2)<br> x = -8<br> X = -3<br> X = 3<br> x = 8
Wewaii [24]

Answer:

x=-8

Step-by-step explanation:

6\left(x-1\right)=9\left(x+2\right)\\\mathrm{Expand\:}6\left(x-1\right):\quad 6x-6\\6\left(x-1\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=6,\:b=x,\:c=1\\=6x-6\cdot \:1\\\mathrm{Expand\:}9\left(x+2\right):\quad 9x+18\\9\left(x+2\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=9,\:b=x,\:c=2\\=9x+9\cdot \:2\\\mathrm{Multiply\:the\:numbers:}\:9\cdot \:2=18\\=9x+18\\6x-6=9x+18\\\mathrm{Add\:}6\mathrm{\:to\:both\:sides}

6x-6+6=9x+18+6\\Simplify\\6x=9x+24\\\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}\\6x-9x=9x+24-9x\\Simplify\\-3x=24\\\mathrm{Divide\:both\:sides\:by\:}-3\\\frac{-3x}{-3}=\frac{24}{-3}\\Simplify\\\frac{-3x}{-3}=\frac{24}{-3}\\\mathrm{Simplify\:}\frac{-3x}{-3}:\quad x\\\frac{-3x}{-3}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{3x}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{3}{3}=1\\=x\\\mathrm{Simplify\:}\frac{24}{-3}:\quad -8\\\frac{24}{-3}

\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}\\=-\frac{24}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{24}{3}=8\\=-8\\

4 0
3 years ago
Read 2 more answers
Here are two expressions whose product is a new expression, :
Vera_Pavlovna [14]

Answer:

1. Fill in the box with 1

2. Fill in the box with -2

Step-by-step explanation:

Expression:

(-2x^3 + [\ ]x)(x^{[\ ]}+1.5) = A

Solving (1): Fill in the box to make it a polynomial.

To make it a polynomial, we simply fill in the box with a positive integer (say 1)

Fill in the box with 1

(-2x^3 + [1]x)(x^{[1]}+1.5) = A

Remove the square brackets

(-2x^3 + x)(x^1+1.5) = A

(-2x^3 + x)(x+1.5) = A

Open bracket

-2x^4 - 3x^3 + x^2 + 1.5x = A

Reorder

A = -2x^4 - 3x^3 + x^2 + 1.5x

The above expression is a polynomial.

This will work for any positive integer filled in the box

Solving (2): Fill in the box to make it not a polynomial.

The powers of a polynomial are greater than or equal to 0.

So, when the boxes are filled with a negative integer (say -2), the expression will cease to be a polynomial

Fill in the box with -2

(-2x^3 + [-2]x)(x^{[-2]}+1.5) = A

Remove the square brackets

(-2x^3 - 2x)(x^{-2}+1.5) = A

Reorder

A = (-2x^3 - 2x)(x^{-2}+1.5)

Open brackets

A = -2x-3x^3-2x^{-1}-3x

Collect Like Terms

A = -3x^3-2x-3x-2x^{-1}

A = -3x^3-5x-2x^{-1}

Notice that the least power of x is -1.

Hence, this is not a polynomial.

3 0
3 years ago
Given that x = 7.4 m and θ = 31°, work out BC rounded to 3 SF<br>I NEED THIS ANSWER NOW​
Len [333]

Answer:

59.0

Step-by-step explanation:

c=31

b=90

90+31=121

180-121=59

56 rounded to the nearest 3 sf=59.0

please mark as brainliest if correct

thank you

5 0
3 years ago
Read 2 more answers
PLEASE I NEED HELP. I Don't get this at all:(
klemol [59]

Answer: :,)

Step-by-step explanation:

so u see were the b is in the triangle it want u to find how much b is worth

8 0
3 years ago
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