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3 years ago

Solve using the addition or substitution method. 2x + 4y = 8 x = 3 - 2y

Mathematics

1 answer:

polet [3.4K]3 years ago

3 0

2x + 4y = 8
x + 2y = 3
3x + 6y = 11

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Four and sixty eight thousandths in decimal form

kumpel [21]

Answer:4.068

Step-by-step explanation:

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3 years ago

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What is the completely factored form of f(x)=x3+5x2+4x−6?

Gre4nikov [31]

$f(x)=x^3+5x^2+4x-6$
$f(-3)=(-3)^3+5(-3)^2+4(-3)-6=0\implies x+3\text{ is a factor of }f(x)$

Synthetic division yields

-3 | 1   5   4   -6
.    |      -3 -6    6
- - - - - - - - - - - - -
.    | 1   2 -2    0

which translates to

$\dfrac{x^3+5x^2+4x-6}{x+3}=x^2+2x-2$

with remainder 0. Now by the quadratic formula,

$x^2+2x-2=0\implies x=\dfrac{-2\pm\sqrt{2^2-4(1)(-2)}}2=-1\pm\sqrt3$

and so

$f(x)=x^3+5x^2+4x-6=(x+3)(x-(-1+\sqrt3))(x-(-1-\sqrt3))$

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3 years ago

Solve the systems of equations y=2x and y=-x - 6

slava [35]

Answer:

y = -4

x = -2

Step-by-step explanation:

Hi there...

y = 2x

y = -x - 6

Since why is equal to 2x, we can plug it in for y in the second equation. Here's what I mean...

2x = -x - 6

add x on both sides...

3x = -6

divide by 3 on both sides...

x = -2

Now, plug in x for y. Here's what I mean...

y = 2x

y = 2 (-2)

y = -4

Hope this helps :)

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3 years ago

This was given to me during a summative test and the teacher didn't bother giving me the correction. I just cannot figure it out

Dmitry [639]

Base be y

ATQ

$\\ \sf\longmapsto xy=6050\dots 1$

$\\ \sf\longmapsto 2(x+y)=220\implies x+y=110\dots 2$

Now

$\\ \sf\longmapsto (x+y)^2=x^2+y^2+2xy$

$\\ \sf\longmapsto 110^2-2(6050)=x^2+y^2$

$\\ \sf\longmapsto 12100-12100=x^2+y^2$

$\\ \sf\longmapsto x^2+y^2=0\dots(3)$

From all equations

$\\ \sf\longmapsto (x-y)^2=x^2+y^2-2xy$

$\\ \sf\longmapsto (x-y)^2=0-2(6050)$

$\\ \sf\longmapsto (x-y)^2=-12100$

$\\ \sf\longmapsto (x-y)=110\dots(4)$

Now

Adding 3 and 4

$\\ \sf\longmapsto 2x=220$

$\\ \sf\longmapsto x=110m$

One side won't be covered hence

y=2(110)=220m

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3 years ago

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Please help !!! What’s the answer to this??

Aleksandr [31]

Answer:

Average speed is distance/time. You could say, 12/6 = 2 miles per second and say that’s the answer, but we relate to mph so much better. Since there are 60 x 60 = 3600 sec in an hour, that same speed is:

2 x 3600 = 7,200 mph

No “car” can travel this fast. Some rocket cars have gone about 1/10th this speed.

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2 years ago