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2 years ago

Find the distance between to points given?

Mathematics

1 answer:

kondor19780726 [428]2 years ago

5 0

<h3>Answer: 29 goes in the box</h3>

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Explanation:

The two endpoints are (-3,1) and (-1,-4)

Apply the distance formula

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-3-(-1))^2 + (1-(-4))^2}\\\\d = \sqrt{(-3+1)^2 + (1+4)^2}\\\\d = \sqrt{(-2)^2 + (5)^2}\\\\d = \sqrt{4 + 25}\\\\d = \sqrt{29}\\\\d \approx 5.3851648\\\\$

So the approximate distance is roughly 5.38 units and the exact distance is $\sqrt{29}$ units.

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As a slight alternative, you can plot the point (-3,-4) and draw a right triangle. Then apply the pythagorean theorem to find the length of the hypotenuse. The vertical and horizontal legs are 5 and 2 units respectively.

It turns out that the distance formula is essentially a modified form of the pythagorean theorem.

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a square garden has a diagonal of 12 m. What is the perimeter of the garden? Express in simplest radical form

lianna [129]

Answer:

The perimeter of the garden, in meters, is $24\sqrt{2}$

Step-by-step explanation:

Diagonal of a square:

The diagonal of a square is found applying the Pythagorean Theorem.

The diagonal of the square is the hypothenuse, while we have two sides.

Diagonal of 12m:

This means that $d = 12$ , side s. So

$s^2 + s^2 = 12^2$

$2s^2 = 144$

$s^2 = \frac{144}{2}$

$s^2 = 72$

$s = \sqrt{72}$

Factoring 72:

Factoring 72 into prime factors, we have that:

72|2

36|2

18|2

9|3

3|3

$72 = 2^{3}*3^{2}$

So, in simplest radical form:

$s = \sqrt{72} = \sqrt{2^{3}*3^{2}} = \sqrt{2^3}*\sqrt{3^2} = 2\sqrt{2}*3 = 6\sqrt{2}$

Perimeter of the garden:

The perimeter of a square with side of s units is given by:

$P = 4s$

In this question, since $s = 6\sqrt{2}$

$P = 4s = 4*6\sqrt{2} = 24\sqrt{2}$

The perimeter of the garden, in meters, is $24\sqrt{2}$

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2 years ago

What is surface area and what is volume?

natita [175]

Surface area is the areas of all the faces added up. Volume is how much a 3D figure can hold.

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2 years ago

Teresa stated that the heights of the students in her class were not a function of their ages. Which reasoning could justify Ter

jenyasd209 [6]

<h2>Answer:</h2>

Option: A is the correct answer.

A. Two students are the same age but have different heights.

<h2>Step-by-step explanation:</h2>

The height of a student could not be a function of the ages of a student because two or more students with the same age may have the different heights .

This means that a value on a x-axis (i.e. age) is mapped to two or more values i.e. corresponding y-value ( i.e. different heights) which violates the definition of function.

Hence, option: A is the correct answer.

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3 years ago

Read 2 more answers

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