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monitta
3 years ago
15

Solve the equation without the use of a calculator. please Help!!! Thank you!!! 12x^3-30x=5-2x^2

Mathematics
1 answer:
nata0808 [166]3 years ago
4 0

So, since we have a cubic equation with 4 terms, the first thing we should try is factoring by grouping, so:

12x^3+2x^2-30x+5 =0 \implies \\ 2x^2(6x+1)-5(6x+1)=0 \implies \\ (2x^2-5)(6x+1) = 0

Now that we've factored our equation, we can use ZPP and break it up:

2x^2-5 = 0 \implies \\ 2x^2=5 \implies\\ x^2=\frac{5}{2} \implies\\ x=\pm\frac{\sqrt{5}}{\sqrt{2}}=\pm\frac{\sqrt{10}}{2} \\ \\ 6x+1 =0 \implies \\ 6x=-1 \implies\\ x=\frac{-1}{6}

So, our solutions are:

x\in \{\frac{\sqrt{10}}{2},-\frac{\sqrt{10}}{2},-\frac{1}{6}\}

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90-55=35 degrees ;)

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Step-by-step explanation:

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What is the smallest positive integer for x so that f(x)=200(2)* is greater than the value of g(x)=500x+400?
Goshia [24]
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f(x)\ \textgreater \ g(x) \\ \therefore 200(2)^{x}\ \textgreater \ 500x+400

Let's solve this problem by using the trial and error method:

for \ x=1 \\f(1)=400 \\ g(1)=900 \\ Then \ f(1) \ \textless \ g(1) \\ \\ \\ for \ x=2 \\f(2)=800 \\ g(2)=1400\\ Then \ f(2)\ \textless \ g(2) \\ \\ \\ for \ x=3 \\f(3)=1600 \\ g(3)=1900 \\ Then \ f(3)\ \textless \ g(3) \\ \\ \\ for \ x=4 \\f(4)=3200 \\ g(4)=2400 \\ \boxed{Then \ f(4)\ \textgreater \ g(4)}

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8 0
3 years ago
The expression 62.4d - 210 gives the number of Indian rupees you receive when you exchange $d at the local
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Answer:

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Step-by-step explanation:

Because 62.4d-210 is the expression per dollar, and you are exchanging 13 dollars, you need to plug in 13 for d, because 13 is the number of dollars, and d represents the number of dollars.

62.4(13)-210     solve.

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601.2 The answer is then 601.2

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3 years ago
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Answer:

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