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astraxan [27]
3 years ago
10

4x+5=45 (Show work to get brainliest) A) 5 B) 10 C) 15 D) 20

Mathematics
2 answers:
solmaris [256]3 years ago
6 0

Answer: x = 10

Step-by-step explanation: To solve for <em>x</em> in the equation you see here, our goal is to get <em>x</em> by itself on one side of the equation.

Our first step will be to isolate the term containing <em>x</em> which in this case is 4x. To isolate 4x, we have to get rid of the +5 by subtracting 5 from both sides of the equation.

On the left, +5 -5 cancels and we're left with 4x. On the right, 45 - 5 simplifies to 5.

So our equation now reads 4x = 40.

To get <em>x</em> by itself since it's being multiplied by 4, we just divide both sides of the equation by 4. On the left, the 4's cancel and we're left with <em>x</em>. On the right, 40/4 simplifies to 10 so our answer is <em>x = 10</em>.

jasenka [17]3 years ago
3 0

Answer:

B) 10

Step-by-step explanation:

4x+5=45

     -5   -5

4x=40

/4    /4

x=10

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x^2+\dfrac1{x^2}=3\implies x^4+1=3x^2\implies x^4-3x^2+1=0

By the quadratic formula,

x^2=\dfrac{3\pm\sqrt5}2\implies x^2+1=\dfrac{5\pm\sqrt5}2

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(x^2+1)^2=\dfrac{25\pm10\sqrt5+5}4=\dfrac{15\pm5\sqrt5}2

\implies\dfrac{x^2}{(x^2+1)^2}=\dfrac{\frac{3\pm\sqrt5}2}{\frac{15\pm5\sqrt5}2}=\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}

Multiply numerator and denominator by the denominator's conjugate:

\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}\cdot\dfrac{15\mp5\sqrt5}{15\mp5\sqrt5}=\dfrac{45\pm15\sqrt5\mp15\sqrt5-25}{15^2-(5\sqrt5)^2}=\dfrac{20}{100}=\dfrac15

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3 years ago
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