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3 years ago

Is this solution, infinitely many solutions, one solution, or no solution?

Mathematics

1 answer:

oksano4ka [1.4K]3 years ago

6 0

Simplifying

7(42x + -8) = 17(49 + x)

Reorder the terms:

7(-8 + 42x) = 17(49 + x)

(-8 * 7 + 42x * 7) = 17(49 + x)

(-56 + 294x) = 17(49 + x)

-56 + 294x = (49 * 17 + x * 17)

-56 + 294x = (833 + 17x)

Solving

-56 + 294x = 833 + 17x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-17x' to each side of the equation.

-56 + 294x + -17x = 833 + 17x + -17x

Combine like terms: 294x + -17x = 277x

-56 + 277x = 833 + 17x + -17x

Combine like terms: 17x + -17x = 0

-56 + 277x = 833 + 0

-56 + 277x = 833

Add '56' to each side of the equation.

-56 + 56 + 277x = 833 + 56

Combine like terms: -56 + 56 = 0

0 + 277x = 833 + 56

277x = 833 + 56

Combine like terms: 833 + 56 = 889

277x = 889

Divide each side by '277'.

x = 3.209386282

Simplifying

x = 3.209386282

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PLEASE ANSWER ASAP!!! SHOW ALL THE STEPS.

fenix001 [56]

Answer:

For the first question $x = 4\\ y = -1$ and

For the second question $x = 0.5\\ y = -1$

Step-by-step explanation:

Given:

x - 3y = 7

3x + 3y = 9

8x+ 3y = 1

4x + 2y = 0

Elimination method :

In the elimination method we need to make the coefficient of x or the coefficient of y same in both the equation so by adding or subtracting we can eliminate the x term or the y term.

Then substitute that values which you will get on eliminating in any equation you will get the corresponding value.

For the first question, the y coefficient is same hence by adding both the equation we can eliminate 3y term. so on solving we get

$(x - 3y) + (3x + 3y) = 7 + 9\\4x = 16\\x = \frac{16}{4}\\x = 4$

Now substitute X equal to 4 in equation x -3y = 7 we get

$4 - 3y = 7\\-3y = 7 - 4\\-3y = 3\\y = \frac{3}{-3}\\ y = -1\\$

This way we have x is equal to 4 and y is equal to -1 for question number 1.

For the second question, we will make X coefficient same in the second equation that is multiplying by 2 to the equation 4x + 2y = 0 then we get

$8x + 4y = 0\\$

Now the coefficient of x term become same now we will subtract the two equations that is 8x + 3y = 1 and 8x + 4y =0 we get

$(8x + 3y) - (8x + 4y) = 1 - 0\\3y - 4y = 1\\ -y = 1\\y = -1$

Now substitute y equal to -1 in equation 8x +3y = 1 we get

$8x + 3\times -1 = 1\\8x - 3 = 1\\8x = 1 + 3\\8x = 4\\x = \frac{4}{8}\\ x = 0.5\\$

This way we have x is equal to 0.5 and y is equal to -1 for question number 2.

3 0

3 years ago

Find e^cos(2+3i) as a complex number expressed in Cartesian form.

ozzi

Answer:

The complex number $e^{\cos(2+31)} = \exp(\cos(2+3i))$ has Cartesian form

$\exp\left(\cosh 3\cos 2\right)\cos(\sinh 3\sin 2)-i\exp\left(\cosh 3\cos 2\right)\sin(\sinh 3\sin 2)$ .

Step-by-step explanation:

First, we need to recall the definition of $\cos z$ when $z$ is a complex number:

$\cos z = \cos(x+iy) = \frac{e^{iz}+e^{-iz}}{2}$ .

Then,

$\cos(2+3i) = \frac{e^{i(2+31)} + e^{-i(2+31)}}{2} = \frac{e^{2i-3}+e^{-2i+3}}{2}$ . (I)

Now, recall the definition of the complex exponential:

$e^{z}=e^{x+iy} = e^x(\cos y +i\sin y)$ .

So,

$e^{2i-3} = e^{-3}(\cos 2+i\sin 2)$

$e^{-2i+3} = e^{3}(\cos 2-i\sin 2)$ (we use that $\sin(-y)=-\sin y)$ .

Thus,

$e^{2i-3}+e^{-2i+3} = e^{-3}\cos 2+ie^{-3}\sin 2 + e^{3}\cos 2-ie^{3}\sin 2)$

Now we group conveniently in the above expression:

$e^{2i-3}+e^{-2i+3} = (e^{-3}+e^{3})\cos 2 + i(e^{-3}-e^{3})\sin 2$ .

Now, substituting this equality in (I) we get

$\cos(2+3i) = \frac{e^{-3}+e^{3}}{2}\cos 2 -i\frac{e^{3}-e^{-3}}{2}\sin 2 = \cosh 3\cos 2-i\sinh 3\sin 2$ .

Thus,

$\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2-i\sinh 3\sin 2\right)$

$\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2\right)\left[ \cos(\sinh 3\sin 2)-i\sin(\sinh 3\sin 2)\right]$ .

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3 years ago

How do you solve this linear equation 3x+2=x+2x+4 ?

Svetach [21]

3x+2=x+2x+4
-2 -2
3x=x+2x+4-2
3x=3x+4-2
-3x -3x
x= 4-2
x=2

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3 years ago

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What is the solutionfor this equation? 5x +9=2.5 I really need to make sure I did this right

solmaris [256]

Answer:

x = -1.3

Step-by-step explanation:

5x +9=2.5

subtract 9 from both sides

5x = -6.6

divide both sides by 5

x=-1.3

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3 years ago

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2(1/2q+1)=-3(2q-1)+4(29+1)

mel-nik [20]

In not sure about the
+4 (29+1)
part
and if there was supposed to be a "q" in there but this is the answer

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4 years ago