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andreyandreev [35.5K]

3 years ago

14

HELPPPPPPP what's the answer and plz explain

1 answer:

Liula [17]3 years ago

4 0

K = 1.2 Short answer.
It's going to seem odd, but one of the ways you could solve this is by multiplying the first equation by 4. I'll tell you why in a moment.

4(0.3x - 0.7y = 1) Now remove the brackets.

1.2x - 2.8y = 4 If you want there to be no solution, the way to do it is the make k = 1.2 The second equation becomes.
1.2x - 2.8y = 3

I'm going to give you the graph of this so you will see why there is no solution. Do you see why?

The lines are parallel!! they never meet.

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The sum of the first n terms of an arithmetic series is n/2(3n-5). If the second and fourth terms of the arithmetic series are t

sergiy2304 [10]

Let <em>a</em> be the first term in the arithmetic sequence. Since it's arithmetic, consecutive terms in the sequence differ by a constant <em>d</em>, so the sequence is

<em>a</em>, <em>a</em> + <em>d</em>, <em>a</em> + 2<em>d</em>, <em>a</em> + 3<em>d</em>, …

with the <em>n</em>-th term, <em>a</em> + (<em>n</em> - 1)<em>d</em>.

The sum of the first <em>n</em> terms of this sequence is given:

$a + (a+d) + (a+2d) + \cdots + (a+(n-1)d) = \dfrac{n(3n-5)}2$

We can simplify the left side as

$\displaystyle \sum_{i=1}^n (a+(i-1)d) = (a-d)\sum_{i=1}^n1 + d\sum_{i=1}^ni = an+\dfrac{dn(n-1)}2$

so that

$an+\dfrac{dn(n-1)}2 = \dfrac{n(3n-5)}2$

or

$a+\dfrac{d(n-1)}2 = \dfrac{3n-5}2$

Let <em>b</em> be the first term in the geometric sequence. Consecutive terms in this sequence are scaled by a fixed factor <em>r</em>, so the sequence is

<em>b</em>, <em>br</em>, <em>br</em> ², <em>br</em> ³, …

with <em>n</em>-th term <em>br</em> ⁿ⁻¹.

The second arithmetic term is equal to the second geometric term, and the fourth arithmetic term is equal to the third geometric term, so

$\begin{cases}a+d = br \\\\ a+3d = br^2\end{cases}$

and it follows that

$\dfrac{br^2}{br} = r = \dfrac{a+3d}{a+d}$

From the earlier result, we then have

$n=7 \implies a+\dfrac{d(7-1)}2 = a+3d = \dfrac{3\cdot7-5}2 = 8$

and

$n=2 \implies a+\dfrac{d(2-1)}2 = a+d = \dfrac{3\cdot2-5}2 = \dfrac12$

so that

$r = \dfrac8{\frac12} = 16$

and since the second arithmetic and geometric terms are both 1/2, this means that

$br=16b=\dfrac12 \implies b = \dfrac1{32}$

The sum of the first 11 terms of the geometric sequence is

<em>S</em> = <em>b</em> + <em>br</em> + <em>br</em> ² + … + <em>br</em> ¹⁰

Multiply both sides by <em>r</em> :

<em>rS</em> = <em>br</em> + <em>br</em> ² + <em>br</em> ³ + … + <em>br</em> ¹¹

Subtract this from <em>S</em>, then solve for <em>S</em> :

<em>S</em> - <em>rS</em> = <em>b</em> - <em>br</em> ¹¹

(1 - <em>r</em> ) <em>S</em> = <em>b</em> (1 - <em>r</em> ¹¹)

<em>S</em> = <em>b</em> (1 - <em>r</em> ¹¹) / (1 - <em>r</em> )

Plug in <em>b</em> = 1/32 and <em>r</em> = 1/2 to get the sum :

$S = \dfrac1{32}\cdot\dfrac{1-\dfrac1{2^{11}}}{1-\dfrac12} = \boxed{\dfrac{2047}{32768}}$

6 0

3 years ago

Find the missing side .Round to the nearest tenth.

amid [387]

Use sine, cosine or tangent of your calculator.
e.g. Q.7
$\tan(16) = \frac{x}{14}$

5 0

3 years ago

Write the decimal -0.43--- as a fraction in simplest form

ohaa [14]

Answer: 43/100

Step-by-step explanation:

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3 years ago

Read 2 more answers

Zielflug [23.3K]

Yes because linear means lines as to lines become a pair which is an angle.

5 0

4 years ago

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Which one doesn't belong? <br><br> A.3:4<br> B.4:3<br> C.chicken nuggets <br> B.dots

maxonik [38]

Answer:

C

Step-by-step explanation:

3:4

4:3

and the dots are 4:3

6 0

3 years ago