Factor Completely: 10x + 15

Mathematics

2 answers:

Volgvan1 year ago

5 0

Answer:

5(2x + 3)

Step-by-step explanation:

\begin{gathered}10x + 15 \\ \\ = 2 \times 5 \times x + 3 \times 5 \\ ( take \: common \: factors \: out )\\ = 5(2 \times x + 3) \\ \\ = 5(2x + 3)\end{gathered}

10x+15

=2×5×x+3×5

(takecommonfactorsout)

=5(2×x+3)

=5(2x+3)

tankabanditka [31]1 year ago

3 0

Answer:

5(2x + 3)

Step-by-step explanation:

$10x + 15 \\ \\ = 2 \times 5 \times x + 3 \times 5 \\ ( take \: common \: factors \: out )\\ = 5(2 \times x + 3) \\ \\ = 5(2x + 3)$

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Which equation represents the equation of the parabola with focus (-3 3) and directrix y=7?

Artemon [7]

Answer:

The equation $y=\frac{-x^2-6x+31}{8}$ represents the equation of the parabola with focus (-3, 3) and directrix y = 7.

Step-by-step explanation:

To find the equation of the parabola with focus (-3, 3) and directrix y = 7. We start by assuming a general point on the parabola (x, y).

Using the distance formula $d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }$ , we find that the distance between (x, y) is

$\sqrt{(x+3)^2+(y-3)^2}$

and the distance between (x, y) and the directrix y = 7 is

$\sqrt{(y-7)^2}$ .

On the parabola, these distances are equal so, we solve for y:

$\sqrt{(x+3)^2+(y-3)^2}=\sqrt{(y-7)^2}\\\\\left(\sqrt{\left(x+3\right)^2+\left(y-3\right)^2}\right)^2=\left(\sqrt{\left(y-7\right)^2}\right)^2\\\\x^2+6x+y^2+18-6y=\left(y-7\right)^2\\\\x^2+6x+y^2+18-6y=y^2-14y+49\\\\y=\frac{-x^2-6x+31}{8}$