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3 years ago

Y = - 2x + 1 2x - 2y = 4 Solve systems of equations by substitutions

Mathematics

1 answer:

astraxan [27]3 years ago

6 0

Answer:

x= 1

y= -1

Step-by-step explanation:

y=-2x+1

2x-2y=4

substitute for y

2x-2(-2x+1)=4

reduce

2x+4x-2=4

6x=6

x=1

y= -2(1)+1

y= -1

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Solve Sine inverse x +sine inverse 2x = π/3

sergeinik [125]

$\arcsin x+\arcsin2x=\dfrac\pi3$
$\sin\left(\arcsin x+\arcsin2x\right)=\sin\dfrac\pi3$
$\sin(\arcsin x)\cos(\arcsin2x)+\sin(\arcsin2x)\cos(\arcsin x)=\dfrac{\sqrt3}2$

Note that $\arcsin x$ is defined for $|x|\le1$ , and $\arcsin2x$ is defined for $|x|\le\dfrac12$ , where the latter will be the "total" domain. Under this condition, you have $\sin(\arcsin x)=x$ and $\sin(\arcsin2x)=2x$ . The cosine terms can be found with Pythagoras' theorem.

So provided that $|x|\le\dfrac12$ , it follows that the above reduces to

$x\sqrt{1-4x^2}+2x\sqrt{1-x^2}=\dfrac{\sqrt3}2$

Squaring both sides gives

$x^2(1-4x^2)+4x^2\sqrt{(1-4x^2)(1-x^2)}+4x^2(1-x^2)=\dfrac34$
$5x^2-8x^4+4x^2\sqrt{(1-4x^2)(1-x^2)}=\dfrac34$
$8x^4-5x^2+\dfrac34=4x^2\sqrt{(1-4x^2)(1-x^2)}$

Squaring both sides again gives

$\left(8x^4-5x^2+\dfrac34\right)^2=16x^4(1-4x^2)(1-x^2)$
$64x^8-80x^6+37x^4-\dfrac{15}2x^2+\dfrac9{16}=64x^8-80x^6+16x^4$
$21x^4-\dfrac{15}2x^2+\dfrac9{16}=0$
$112x^4-40x^2+3=0$
$(4x^2-1)(28x^2-3)=0$
$(2x-1)(2x+1)(\sqrt{28}x-\sqrt3)(\sqrt{28}x+\sqrt3)=0$

$\implies x=\pm\dfrac12,\pm\sqrt{\dfrac3{28}}$

Three of these solutions are extraneous, however.

When $x=-\dfrac12$ , we have $\arcsin x+\arcsin2x=-\dfrac{2\pi}3$ .

When $x=\dfrac12$ , we have $\arcsin x+\arcsin2x=\dfrac{2\pi}3$ .

When $x=-\sqrt{\dfrac3{28}}$ , we have $\arcsin x+\arcsin2x=-\dfrac\pi3$ .

Finally, when $x=\sqrt{\dfrac3{28}}$ , we have $\arcsin x+\arcsin2x=\dfrac\pi3$ , so this is our only solution.

7 0

3 years ago

Ill give brainliest please help with this algebra!!

enot [183]

Answer:

You didnt post a picture of the 3 expressions so therefor I cant help but if you post them then I can try to help. :)

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

What does this say? Please Help me!

kvasek [131]

Answer:

That is a child mom with triplets.

Step-by-step explanation:

7 0

3 years ago

12. Which of the following pairs of numbers contains like fractions?

stepladder [879]

So will be choice D.

bc. 5/6 = 10/12 = 2*5/2*6 = 5/6

4 0

3 years ago

Need help use screenshot(SAT Prep) In △ABC, AB = BC = 20 and DE ≈ 9.28. Approximate BD. bd equals?

Lilit [14]

Answer:

5.36

Step-by-step explanation:

Given that:

<BAD = <CAE, therefore, BD = EC

Let's take x to be the length of BD = EC

BD + DE + EC = BC

BC = 20,

BD = EC = x

DE ≈ 9.28

Thus,

x + 9.28 + x = 20

x + x + 9.28 = 20

2x + 9.28 = 20

Subtract 9.28 from both sides

2x + 9.28 - 9.28 = 20 - 9.28

2x = 10.72

Divided both sides by 2 to solve for x

$\frac{2x}{2} = \frac{10.72}{2}$

$x = \frac{10.72}{2}$

$x = 5.36$

BD ≈ 5.36

4 0

4 years ago