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wariber [46]
3 years ago
15

Solve the equation for x by graphing -2x + 3 = -3(-x) - 2

Mathematics
1 answer:
adoni [48]3 years ago
6 0

Answer:

  x = 1

Step-by-step explanation:

There are a couple of ways to solve this. One is to graph the left side of the equation, graph the right side of the equation, and look for the point where those graphs intersect. It is at x = 1. The first attached graph shows this solution.

__

Another method for solving such an equation is to subtract one side from the other and look for the value of x that makes the resulting expression zero.

  (-2x +3) -(-3(-x) -2) = 0

A graphing calculator doesn't need to have this simplified. If it is simplified, it becomes ...

  -5x +5 = 0

So, the graphed line is y = -5x+5. Its x-intercept is x=1, the solution of the original equation. The graph of this is shown in the second attachment.

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Find the value of tan(sin^-1(1/2))
suter [353]

If you know that \sin\dfrac\pi3=\dfrac12, then you know right away

\tan\left(\sin^{-1}\dfrac12\right)=\tan\dfrac\pi3=\dfrac1{\sqrt}3=\dfrac{\sqrt3}3

###

Otherwise, you can derive the same result. Let \theta=\sin^{-1}\dfrac12, so that \sin\theta=\dfrac12. \sin^{-1} is bounded, so we know -\dfrac\pi2\le\theta\le\dfrac\pi2. For these values of \theta, we always have \cos\theta\ge0.

So, recalling the Pythagorean theorem, we find

\cos^2\theta+\sin^2\theta=1\implies\cos\theta=\sqrt{1-\sin^2\theta}=\sqrt{1-\left(\dfrac12\right)^2}=\dfrac{\sqrt3}2

Then

\tan\theta=\tan\left(\sin^{-1}\dfrac12\right)=\dfrac{\sin\theta}{\cos\theta}=\dfrac{\frac12}{\frac{\sqrt3}2}=\dfrac1{\sqrt3}=\dfrac{\sqrt3}3

as expected.

5 0
3 years ago
Read 2 more answers
Write the numbers three hundred and fifty-four thousand, two hundred and ten in figures (354,210).
GalinKa [24]

Answer:

Three hundred and fifty-four thousand, two hundred and ten =354210

Hundred thousand║Ten thousand║Thousand║Hundred║Tens║Ones

           3                             5                     4                   2           1          0

Step-by-step explanation:

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Kenji is traveling in Europe and renting a car. He is used to thinking of gasoline amounts in gallons, but in Europe it is sold
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10.3 gallons

Good luck!!!!!
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18. Let z = a + bi represent a general complex number. As noted in the lesson, the conjugate of z, abbreviated conj(z) or conj(a
AnnyKZ [126]

Question (18):

Answer: (A) All of the following

(I am using z^* in place of conj(z)

z*z^*=(a+ib)(a-ib)=a^2-(ib)^2= a^2+b^2=\mbox{modulus(z)}^2

z+z^*=a+ib+a-ib=2a\\z-z^*=a+ib-a+ib=2bi


Question (19):

Answer: (B) -7

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the other choices are all < 7


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3 years ago
If the sin 30 = 1/2, then which statement is true?
egoroff_w [7]

Answer:

cos 60° = 1/2 because the angles are complements.

Step-by-step explanation:

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