Find the product 12,-5

which of the three sets could not be the lengths of the sides of a triangle {6,10,12} {5,7,10} {4,4,9} {2,3,3}

Phoenix [80]

So for this, we will be applying the Triangle Inequality Theorem, which states that the sum of 2 sides must be greater than the third side for it to be a triangle. If any inequality turns out to be false, then the set cannot be a triangle.

$A+B>C\\A+C>B\\B+C>A$

<h2>First Option: {6, 10, 12}</h2>

Let A = 6, B = 10, and C = 12:

$6+10>12\\16>12\ \textsf{true}\\\\6+12>10\\18>10\ \textsf{true}\\\\12+10>6\\22>6\ \textsf{true}$

<h2>Second Option: {5, 7, 10}</h2>

Let A = 5, B = 7, and C = 10

$5+7>10\\12>10\ \textsf{true}\\\\5+10>7\\15>7\ \textsf{true}\\\\10+7>5\\17>5\ \textsf{true}$

<h2>Third Option: {4, 4, 9}</h2>

Let A = 4, B = 4, and C = 9

$4+4>9\\8>9\ \textsf{false}\\\\4+9>4\\13>4\ \textsf{true}\\\\4+9>4\\13>4\ \textsf{true}$

<h2>Fourth Option: {2, 3, 3}</h2>

Let A = 2, B = 3, and C = 3

$2+3>3\\5>3\ \textsf{true}\\\\2+3>3\\5>3\ \textsf{true}\\\\3+3>2\\6>2\ \textsf{true}$

<h2>Conclusion:</h2>

Since the third option had an inequality that was false, <u>the third option cannot be a triangle.</u>

5 0

3 years ago

Read 2 more answers

Help me with this math problem i don’t understand it

pav-90 [236]

Answer:

13meters

Step-by-step explanation:

c^2=a^2+b^2

12^2+5^2=169

find squareroot of 169 which is 13meters

4 0

2 years ago

How has the Roaring Twenties been portrayed in modern media?

Alexus [3.1K]

Answer:

The nation's total wealth more than doubled between 1920 and 1929, and this economic growth swept many Americans into an affluent but unfamiliar “consumer society.” People from coast to coast bought the same goods (thanks to nationwide advertising and the spread of chain stores), listened to the same music

6 0

2 years ago

A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win $1.10; if

topjm [15]

Answer:

a) The expected value is $\frac{-1}{15}$

b) The variance is $\frac{49}{45}$

Step-by-step explanation:

We can assume that both marbles are withdrawn at the same time. We will define the probability as follows

#events of interest/total number of events.

We have 10 marbles in total. The number of different ways in which we can withdrawn 2 marbles out of 10 is $\binom{10}{2}$ .

Consider the case in which we choose two of the same color. That is, out of 5, we pick 2. The different ways of choosing 2 out of 5 is $\binom{5}{2}$ . Since we have 2 colors, we can either choose 2 of them blue or 2 of the red, so the total number of ways of choosing is just the double.

Consider the case in which we choose one of each color. Then, out of 5 we pick 1. So, the total number of ways in which we pick 1 of each color is $\binom{5}{1}\cdot \binom{5}{1}$ . So, we define the following probabilities.