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earnstyle [38]
2 years ago
9

How do you solve 2x-3y=-4 and x=7-3y by substitution?

Mathematics
1 answer:
Evgesh-ka [11]2 years ago
7 0

Answer:

(1, 2)

Step-by-step explanation:

We can solve this system using substitution.

In this case, we can substitute 7-3y for x, as they are of equal value.

Therefore...

2x-3y=-4\\2(7-3y)-3y=-4\\14-6y-3y=-4\\14-9y=-4

Subtract 14 from both sides:

-9y=-18

Divide both sides by -9

y=2

Now, substitute 2 for y to solve for x:

x=7-3y=7-3(2)=7-6=1

Therefore the solution to this system of equations is:

(x, y)=(1, 2)

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This is a 5-digit number.
borishaifa [10]

Answer:

The number is 38,478

Step-by-step explanation:

* Lets explain how to find the number

- The number is 5-digit

* Ones ⇒ the last digit

* Tens

* Hundreds

* Thousands

* Ten thousand

- The ones digit is the same as the last digit of last year's calendar year

∵ The last year is 2018

∴ The last digit is 8

∴ The ones digit is 8

- The ones digit is the same as the thousands digit

∵ The ones digit is 8

∴ The thousands digit is 8

- The ten thousands digit is five less than the thousands digit

∵ The thousands digit is 8

∴ The ten thousands digit is 5 less than 8

∵ 8 - 5 = 3

∴ The ten thousands digit is 3

- The last two digits sum to 15

∵ The last two digits are ones and tens digits

∵ The ones digit is 8

∵ 15 - 8 = 7

∴ The tens digit is 7

- There is one 4 in the number

∵ The hundreds digit is empty

∴ The hundreds digit is 4

* <em>The number is 38,478</em>

8 0
4 years ago
Use stoke's theorem to evaluate∬m(∇×f)⋅ds where m is the hemisphere x^2+y^2+z^2=9, x≥0, with the normal in the direction of the
ludmilkaskok [199]
By Stokes' theorem,

\displaystyle\int_{\partial\mathcal M}\mathbf f\cdot\mathrm d\mathbf r=\iint_{\mathcal M}\nabla\times\mathbf f\cdot\mathrm d\mathbf S

where \mathcal C is the circular boundary of the hemisphere \mathcal M in the y-z plane. We can parameterize the boundary via the "standard" choice of polar coordinates, setting

\mathbf r(t)=\langle 0,3\cos t,3\sin t\rangle

where 0\le t\le2\pi. Then the line integral is

\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=\int_{t=0}^{t=2\pi}\mathbf f(x(t),y(t),z(t))\cdot\dfrac{\mathrm d}{\mathrm dt}\langle x(t),y(t),z(t)\rangle\,\mathrm dt
=\displaystyle\int_0^{2\pi}\langle0,0,3\cos t\rangle\cdot\langle0,-3\sin t,3\cos t\rangle\,\mathrm dt=9\int_0^{2\pi}\cos^2t\,\mathrm dt=9\pi

We can check this result by evaluating the equivalent surface integral. We have

\nabla\times\mathbf f=\langle1,0,0\rangle

and we can parameterize \mathcal M by

\mathbf s(u,v)=\langle3\cos v,3\cos u\sin v,3\sin u\sin v\rangle

so that

\mathrm d\mathbf S=(\mathbf s_v\times\mathbf s_u)\,\mathrm du\,\mathrm dv=\langle9\cos v\sin v,9\cos u\sin^2v,9\sin u\sin^2v\rangle\,\mathrm du\,\mathrm dv

where 0\le v\le\dfrac\pi2 and 0\le u\le2\pi. Then,

\displaystyle\iint_{\mathcal M}\nabla\times\mathbf f\cdot\mathrm d\mathbf S=\int_{v=0}^{v=\pi/2}\int_{u=0}^{u=2\pi}9\cos v\sin v\,\mathrm du\,\mathrm dv=9\pi

as expected.
7 0
3 years ago
Find the circumference of a circle who's diameter is 4
BabaBlast [244]
C=pid
d=diameter
d=4
C=4pi

tada
if you want
aprox pi=3.14
C=12.56 units
4 0
3 years ago
We flip a fair coin 10 times. what is the probability that we get heads in exactly 8 of the 10 flips
Anna35 [415]
1/10 chance that it will be 8
5 0
3 years ago
4. Find the slope of the line that passes through the points:<br> (-6,-1) and (4,1)
finlep [7]

Answer:

Slope: 1/5

Step-by-step explanation:

To find the slope of a line when given two points, you find the change in y over the change in x.

1 - (-1) = 2 (change in y)

4 - (-6) = 10 (change in x)

2/10 simplified is 1/5.

Hope this helps :)

7 0
3 years ago
Read 2 more answers
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