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2 years ago

How many solutions are there to the equation below 9x + 27 = 9( x + 2 ) + 9

Mathematics

2 answers:

Nataly [62]2 years ago

7 0

Let's solve the equation:

9x+27 = 9(x+2)+9 ← Distribute 9 to the x and 2

9x+27 = 9x+18+9 ← Combine like terms

9x+27 = 9x + 27 ← Subtract 27 from both sides

9x = 9x

Infinitely many solutions would be correct because no matter what x is, it will always equal each other the both sides of the equation because it is 9 times x on both sides.

Mama L [17]2 years ago

6 0

9x + 27 = 9(x + 2) + 9

Simplify both sides of equation:

9x + 27 = 9(x + 2) + 9

9x + 27 = (9)(x) + (9)(2) + 9 (Distribute)

9x + 27 = 9x + 18 + 9

9x + 27 = (9x) + ( 18 + 9)

(Combine Like Terms:)

9x + 27 = 9x + 27

Subtract 9x from both sides:

9x + 27 - 9x = 9x + 27 - 9x

27 = 27

Subtract 27 from both sides:

27 - 27 = 27 - 27

0 = 0

Equations is always true

Answer: All real numbers are solutions: (Infinitely many solutions:)

Hope that helps!!! ( Answer: Letter Choice (B), Infinitely many solutions.).

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astra-53 [7]

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2 years ago

Read 2 more answers

Can I get help with finding the Fourier cosine series of F(x) = x - x^2

trapecia [35]

Assuming you want the cosine series expansion over an arbitrary symmetric interval $[-L,L]$ , $L\neq0$ , the cosine series is given by

$f_C(x)=\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos nx$

You have

$a_0=\displaystyle\frac1L\int_{-L}^Lf(x)\,\mathrm dx$
$a_0=\dfrac1L\left(\dfrac{x^2}2-\dfrac{x^3}3\right)\bigg|_{x=-L}^{x=L}$
$a_0=\dfrac1L\left(\left(\dfrac{L^2}2-\dfrac{L^3}3\right)-\left(\dfrac{(-L)^2}2-\dfrac{(-L)^3}3\right)\right)$
$a_0=-\dfrac{2L^2}3$

$a_n=\displaystyle\frac1L\int_{-L}^Lf(x)\cos nx\,\mathrm dx$

Two successive rounds of integration by parts (I leave the details to you) gives an antiderivative of

$\displaystyle\int(x-x^2)\cos nx\,\mathrm dx=\frac{(1-2x)\cos nx}{n^2}-\dfrac{(2+n^2x-n^2x^2)\sin nx}{n^3}$

and so

$a_n=-\dfrac{4L\cos nL}{n^2}+\dfrac{(4-2n^2L^2)\sin nL}{n^3}$

So the cosine series for $f(x)$ periodic over an interval $[-L,L]$ is

$f_C(x)=-\dfrac{L^2}3+\displaystyle\sum_{n\ge1}\left(-\dfrac{4L\cos nL}{n^2L}+\dfrac{(4-2n^2L^2)\sin nL}{n^3L}\right)\cos nx$

4 0

3 years ago

Backpack is normally $64.99, put on sale it is marked down to $45.49 what percent off is the sale price

pogonyaev

Answer:

The percent off on the sale price is 30%.

Step-by-step explanation:

Marked up price = $64.99

marked down Price = $45.49

Let us assume the off percentage = k%

Now, the Amount off on the sale = Marked up price - Marked down price

= $64.99 - $45.49 = $19.5

⇒ k% off on Marked up Price $64.99 = $19.5

or, $\frac{k}{100} \times 64.99 = 19.5\\\implies k = \frac{19.5 \times 100}{64.99} = 30$

or, k = 30%

Hence, the percent off on the sale price is 30%

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2 years ago

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quester [9]

That would depend on what x is equal to. So, there's not enough information to fully determine an answer.

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