To find the distance between the two points [tex]\((-9, 0)\)[/tex] and [tex]\((2, 5)\)[/tex], we use the distance formula. The distance [tex]\(d\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Let's identify the coordinates for our points:
- [tex]\( (x_1, y_1) = (-9, 0) \)[/tex]
- [tex]\( (x_2, y_2) = (2, 5) \)[/tex]
First, calculate the differences in the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] coordinates:
[tex]\[
x_2 - x_1 = 2 - (-9) = 2 + 9 = 11
\][/tex]
[tex]\[
y_2 - y_1 = 5 - 0 = 5
\][/tex]
Now, substitute these values into the distance formula:
[tex]\[
d = \sqrt{(11)^2 + (5)^2}
\][/tex]
[tex]\[
d = \sqrt{121 + 25}
\][/tex]
[tex]\[
d = \sqrt{146}
\][/tex]
Finally, evaluate the square root:
[tex]\[
d \approx 12.08
\][/tex]
Therefore, the distance between the points [tex]\((-9, 0)\)[/tex] and [tex]\((2, 5)\)[/tex] is approximately [tex]\(12.08\)[/tex]. The correct answer is:
[tex]\[
\boxed{12.08}
\][/tex]
