You are playing a card game with a standard deck of cards. How many way

The hypotenuse of a right triangle is √18 units. what are the lengths of the legs of the triangle? How many different answers ca

storchak [24]

Since a right triangle has special rules to it such that the hypotenuse squared equals the sum of the squares of the other 2 sides. In other words, if the hypotenuse = c, and the 2 smaller sides are a and b, then:
${c}^{2} = {a}^{2} + {b}^{2}$
Solving for c (hypotenuse), we get:
$\sqrt{({c}^{2})} = \sqrt{({a}^{2}+{b}^{2} )} \\ c = \sqrt{({a}^{2}+{b}^{2} )}$
Therefore c is the root of the square of the other sides. So by having root18, it's like saying:
$\sqrt{18} = \sqrt{({a}^{2} + {b}^{2} )} \\ 18 = {a}^{2} + {b}^{2}$
Getting rid of the square root, so sides a and b must have their squares total 18:
the only squares < 18 are: 16 (4×4), 9 (3×3), 4 (2×2), and 1 (1×1)
of those above added in any order of two of them, only 16+4
$18 = 17 + 1 - - > \sqrt{17} \: and \: 1 \\ 18 = 16 + 2 - - > \sqrt{16} \: and \: \sqrt{2} \\ ... \: 4 \: and \: \sqrt{2} \\ 18 = 15 + 3 - - > \sqrt{15} \: and \: \sqrt{3}$
$18 = 14 + 4 - - > \sqrt{14} \: and \: \sqrt{4} \\ ... \sqrt{14} \: and \: 2 \\ 18 = 13 + 5 - - > \sqrt{13} \: and \: \sqrt{5} \\ 18 = 12+ 6 - - > \sqrt{12} \: and \: \sqrt{6}$
$18 = 11 + 7 - - > \sqrt{11} \: and \: \sqrt{7} \\ 18 = 10 + 8 - - > \sqrt{10} \: and \: \sqrt{8} \\ ... \sqrt{10} \: and \: 2 \sqrt{2} \\ 18 = 9 + 9 - - > \sqrt{9} = 3 \: and \: 3$
I HOPE THAT IS ALONG THE LINE THAT WAS ASKED FOR!!! :-D

7 0

3 years ago

The expression 1000(1.1)t represents the value of a $1000 investment that earns 10% interest per year, compounded annually for t

melamori03 [73]

1000(1.1)4
multiply the numbers
$4400

3 0

3 years ago

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what is the volume of this cone use Pi 3.14 and round your answer to the nearest hundredth radius 14 height 14

Anton [14]

The volume of the cone is 3.14 x 14 x 14

3 0

3 years ago

Triangular numbers can be represented with equilateral triangles formed by dots the first fire triangle numbers are 1 3 6 10 and

zhannawk [14.2K]

Answer:

There's no direct variation

Step-by-step explanation:

Required

Determine if there's a direct variation between the number and its position

I'll start by giving an illustration of how the triangle is represented using stars (*)

*

**

***

****

*****

Represent the line number with y and it's position with x

On line 1:

y = 1, x = 1

On line 2:

y = 2, x = 3

On line 3:

y = 3, x = 6

On line 4:

y = 4, x = 10

On line 5:

y = 5, x = 15

Note that, x is gotten by calculating the accumulated number of stars while y is the line number.

Direct variation is represented by

y = kx

Or

kx = y

Where k is the constant of variation

For line 1:

Substitute 1 for y and 1 for x

k * 1 = 1

k = 1

For line 2:

Substitute 2 for y and 3 for x

k * 3 = 2

Divide through by 3

k = ⅔

Note that the values of k in both computations differ.

This implies that there's no direct variation and there's no need to check further.

3 0

2 years ago

A. Equilateral B. Right C. Obtuse D. Acute E. Scalene

faltersainse [42]

Answer:

A) Scalene E) Obtuse

Detailed Explanation:

A) Scalene

This triangle would be classified as scalene because none of the angles are equal.

____________________________________________________________

E) Obtuse

This triangle would be classified as an scalene triangle because one of the angles is larger than 90 degrees.

8 0

3 years ago

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