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Inga [223]
2 years ago
12

What are the first five terms of the pattern with formula 3n + 4?

Mathematics
2 answers:
Marina86 [1]2 years ago
6 0
x_{n} =3n + 4 \\  x_{1} =3(1) + 4=7 \\  x_{2} =3(2) + 4=10 \\  x_{3} =3(3) + 4=13 \\  x_{4} =3(4) + 4 =16\\  x_{5} =3(5)+ 4 =19\\
Leviafan [203]2 years ago
4 0
In this equation we start by filling in the N with "1" then"2" then "3" and so on

3n+4=
3(1)+4=7
3(2)+4=10
3(3)+4=13
3(4)+4=16
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anygoal [31]

Option C: x=0 and x=\frac{5}{2} are the solutions.

Explanation:

The equation is \frac{x}{3} =\frac{x^{2} }{x+5}

We shall determine the value of x, by simplifying the equation.

$\begin{aligned} x(x+5) &=3 x^{2} \\ x^{2}+5 x &=3 x^{2} \\ 2 x^{2}-5 x &=0 \\ x(2 x-5) &=0 \end{aligned}$

Thus, x=0 and x=\frac{5}{2} are the solutions.

Now, let us check whether the solutions are extraneous solutions.

Let us substitute x=0 in the original equation to check whether both sides of the equation are equal.

\begin{aligned}&\frac{0}{3}=\frac{0^{2}}{0+5}\\&0=\frac{0}{5}\\&0=0\end{aligned}

Thus, both sides of the equation are equal.

Hence x=0 is a true solution.

Now, Let us substitute x=\frac{5}{2} in the original equation to check whether both sides of the equation are equal.

\begin{aligned}\frac{\left(\frac{5}{2}\right)}{3} &=\frac{\left(\frac{5}{2}\right)^{2}}{\left(\frac{5}{2}\right)+5} \\\frac{5}{6} &=\frac{\left(\frac{25}{4}\right)}{\left(\frac{15}{2}\right)} \\\frac{5}{6} &=\frac{5}{6}\end{aligned}

Thus, both sides of the equation are equal.

Hence, x=\frac{5}{2} is a true solution.

Thus, solutions are not extraneous.

Hence, Option C is the correct answer.

8 0
3 years ago
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