All categories

2 years ago

Which system of equations is equivalent to the system of equations shown? 2x + 5y = -2 4x + 7y = 8

Mathematics

1 answer:

Elis [28]2 years ago

3 0

Answer:

x=9, y=-4. (9, -4).

Step-by-step explanation:

2x+5y=-2

4x+7y=8

--------------

-2(2x+5y)=-2(-2)

4x+7y=8

---------------------

-4x-10y=4

4x+7y=8

--------------

-3y=12

y=12/-3

y=-4

2x+5(-4)=-2

2x-20=-2

2x=-2+20

2x=18

x=18/2

x=9

You might be interested in

Round 17,519 to the underlined place value. 17,500 20,000 18,000 17,000

Ira Lisetskai [31]

17500 i think but u didn’t give enough info so it could be any without the extra info

5 0

2 years ago

If you have three cups of pineapple Juice How many total cups of Punch Can you make

Mama L [17]

Answer: 2 cups

Step-by-step explanation:

5 0

2 years ago

Find the Fourier series of f on the given interval. f(x) = 1, ?7 < x < 0 1 + x, 0 ? x < 7

Zolol [24]

$f(x)=\begin{cases}1&\text{for }-7$

The Fourier series expansion of $f(x)$ is given by

$\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos\frac{n\pi x}7+\sum_{n\ge1}b_n\sin\frac{n\pi x}7$

where we have

$a_0=\displaystyle\frac17\int_{-7}^7f(x)\,\mathrm dx$
$a_0=\displaystyle\frac17\left(\int_{-7}^0\mathrm dx+\int_0^7(1+x)\,\mathrm dx\right)$
$a_0=\dfrac{7+\frac{63}2}7=\dfrac{11}2$

The coefficients of the cosine series are

$a_n=\displaystyle\frac17\int_{-7}^7f(x)\cos\dfrac{n\pi x}7\,\mathrm dx$
$a_n=\displaystyle\frac17\left(\int_{-7}^0\cos\frac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\cos\frac{n\pi x}7\,\mathrm dx\right)$
$a_n=\dfrac{9\sin n\pi}{n\pi}+\dfrac{7\cos n\pi-7}{n^2\pi^2}$
$a_n=\dfrac{7(-1)^n-7}{n^2\pi^2}$

When $n$ is even, the numerator vanishes, so we consider odd $n$ , i.e. $n=2k-1$ for $k\in\mathbb N$ , leaving us with

$a_n=a_{2k-1}=\dfrac{7(-1)-7}{(2k-1)^2\pi^2}=-\dfrac{14}{(2k-1)^2\pi^2}$

Meanwhile, the coefficients of the sine series are given by

$b_n=\displaystyle\frac17\int_{-7}^7f(x)\sin\dfrac{n\pi x}7\,\mathrm dx$
$b_n=\displaystyle\frac17\left(\int_{-7}^0\sin\dfrac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\sin\dfrac{n\pi x}7\,\mathrm dx\right)$
$b_n=-\dfrac{7\cos n\pi}{n\pi}+\dfrac{7\sin n\pi}{n^2\pi^2}$
$b_n=\dfrac{7(-1)^{n+1}}{n\pi}$

So the Fourier series expansion for $f(x)$ is

$f(x)\sim\dfrac{11}4-\dfrac{14}{\pi^2}\displaystyle\sum_{n\ge1}\frac1{(2n-1)^2}\cos\frac{(2n-1)\pi x}7+\frac7\pi\sum_{n\ge1}\frac{(-1)^{n+1}}n\sin\frac{n\pi x}7$

3 0

2 years ago

What is the solution to this equation 1/2n^2+18=0

ololo11 [35]

Answer:

n = ±6 .

Step-by-step explanation:

A quadratic equation is given to us and we need to find out the solution of the given equation . The given equation is ,

$\rm\implies -\dfrac{1}{2}n^2+18=0$

Subtracting 18 both sides ,

$\rm\implies -\dfrac{1}{2}n^2 = -18$

Multiplying both sides by -2 ,

$\rm\implies -2\times\dfrac{1}{2}n^2 = -2\times -18$

On simplyfing , we get ,

$\rm\implies n^2= 36$

Putting squareroot both sides ,

$\rm\implies n= \sqrt{36}$

This equals to ,

$\rm\implies \boxed{\quad\blue{\rm n =\pm 6 }}$

Hence the value of n is ±6 .

6 0

3 years ago

What is the value of the underlined digit in 16,403

Ilia_Sergeevich [38]

If the 1 were underlined it would be 10,000
If the 6 were underlined it would be 6,000
If the 4 were underlined it would be 400
If the 0 were underlined it would be 0
If the 3 were underlined it would be 3

8 0

3 years ago