Find the distance between point a (-5, five) and B (five, 12). Round your answer to the nearest 10th even an answer like 15 should be written as 15.0.

Answer 1

To find the distance between points A (-5, 5) and B (5, 12), we use the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Here, \( (x_1, y_1) = (-5, 5) \) and \( (x_2, y_2) = (5, 12) \).

Substituting the coordinates into the formula:

\[ d = \sqrt{(5 - (-5))^2 + (12 - 5)^2} \]

This simplifies to:

\[ d = \sqrt{(5 + 5)^2 + (12 - 5)^2} \] \[ d = \sqrt{(10)^2 + (7)^2} \] \[ d = \sqrt{100 + 49} \] \[ d = \sqrt{149} \]

Now calculating \( \sqrt{149} \):

\[ \sqrt{149} \approx 12.206 \]

Rounding this to the nearest tenth gives:

\[ \approx 12.2 \]

Thus, the distance between points A and B is approximately 12.2.

Answer 2

Distance between point A (four, two) and B (14, 14). Round your answer to the nearest 10th.

Answer 3

To find the distance between points A (4, 2) and B (14, 14), we will use the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Here, \( (x_1, y_1) = (4, 2) \) and \( (x_2, y_2) = (14, 14) \).

Now substituting the coordinates into the formula:

\[ d = \sqrt{(14 - 4)^2 + (14 - 2)^2} \]

This simplifies to:

\[ d = \sqrt{(10)^2 + (12)^2} \] \[ d = \sqrt{100 + 144} \] \[ d = \sqrt{244} \]

Calculating \( \sqrt{244} \):

\[ \sqrt{244} \approx 15.620 \]

Rounding this to the nearest tenth gives:

\[ \approx 15.6 \]

Thus, the distance between points A and B is approximately 15.6.

Answer 4

Find the distance for line a (-9, 10)(-5, nine) round to the nearest 10th

Answer 5

To find the distance between the points A (-9, 10) and B (-5, 9), we will use the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Here, \( (x_1, y_1) = (-9, 10) \) and \( (x_2, y_2) = (-5, 9) \).

Substituting these coordinates into the formula:

\[ d = \sqrt{(-5 - (-9))^2 + (9 - 10)^2} \]

This simplifies to:

\[ d = \sqrt{(-5 + 9)^2 + (-1)^2} \] \[ d = \sqrt{(4)^2 + (-1)^2} \] \[ d = \sqrt{16 + 1} \] \[ d = \sqrt{17} \]

Now calculating \( \sqrt{17} \):

\[ \sqrt{17} \approx 4.123 \]

Rounding this to the nearest tenth gives:

\[ \approx 4.1 \]

Thus, the distance between points A and B is approximately 4.1.

Answer 6

Find the distance between point A (-5, nine) and B (three, 17) round your answer to the nearest 10th

Answer 7

To find the distance between points A (-5, 9) and B (3, 17), we will use the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Where:

• \( (x_1, y_1) = (-5, 9) \)
• \( (x_2, y_2) = (3, 17) \)

Plugging in the coordinates:

\[ d = \sqrt{(3 - (-5))^2 + (17 - 9)^2} \]

This simplifies to:

\[ d = \sqrt{(3 + 5)^2 + (17 - 9)^2} \] \[ d = \sqrt{(8)^2 + (8)^2} \] \[ d = \sqrt{64 + 64} \] \[ d = \sqrt{128} \]

Calculating \( \sqrt{128} \):

\[ \sqrt{128} = \sqrt{64 \times 2} = 8\sqrt{2} \approx 8 \times 1.414 \approx 11.312 \]

Rounding this to the nearest tenth gives:

\[ \approx 11.3 \]

Thus, the distance between points A and B is approximately 11.3.

Answer 8

Look at the square pyramid below one line is 35MI and another one is 12 MI
How many miles is the slant height of the square pyramid?

Answer 9

To find the slant height of a square pyramid, we need to use the Pythagorean theorem, as the slant height forms a right triangle with half of the base of the pyramid and the vertical height of the pyramid.

1. Identify the dimensions:

   • Base side length of the square pyramid: \( s = 35 , \text{mi} \) (assuming this is the side length of the base).
   • Vertical height of the pyramid: \( h = 12 , \text{mi} \).

2. Calculate half the base length:

   • Half of the base length, denoted as \( a \), is: \[ a = \frac{s}{2} = \frac{35}{2} = 17.5 , \text{mi} \]

3. Apply the Pythagorean theorem:

   • Let \( l \) be the slant height. According to the Pythagorean theorem: \[ l^2 = a^2 + h^2 \] Plugging in the values: \[ l^2 = (17.5)^2 + (12)^2 \] \[ l^2 = 306.25 + 144 \] \[ l^2 = 450.25 \] \[ l = \sqrt{450.25} \approx 21.2 , \text{mi} \]

Thus, the slant height of the square pyramid is approximately 21.2 miles.

Answer 10

Look at the square pyramid one is 12 MI and another line is 13 MI and you’re wanting to know the bottom line how many miles long is the base of the square pyramid

Answer 11

To determine the length of the base of the square pyramid, we need to clarify the relationship between the given measurements. Assuming that "one is 12 MI" refers to the vertical height \( h \) of the pyramid, and "another line is 13 MI" refers to the slant height \( l \), we can use the Pythagorean theorem.

Given:

• Slant height \( l = 13 , \text{mi} \)
• Vertical height \( h = 12 , \text{mi} \)

We need to find the half-length of the base, denoted as \( a \), and then determine the full length of the base \( s \).

The relationship is given by the Pythagorean theorem in the right triangle formed by half the base, the height, and the slant height:

\[ l^2 = a^2 + h^2 \]

Step 1: Substitute the known values:

\[ 13^2 = a^2 + 12^2 \]

\[ 169 = a^2 + 144 \]

Step 2: Solve for \( a^2 \):

\[ a^2 = 169 - 144 \]

\[ a^2 = 25 \]

\[ a = \sqrt{25} = 5 , \text{mi} \]

Step 3: Find the full base length \( s \):

Since \( a \) is half of the base, the full base length \( s \) is:

\[ s = 2a = 2 \times 5 = 10 , \text{mi} \]

Thus, the length of the base of the square pyramid is 10 miles.