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Alecsey [184]
3 years ago
14

A triangle has one side length of 12 inches and another of 8 inches. Describe all possible lengths of the third side. Show and e

xplain your reasoning.
Mathematics
2 answers:
Vinvika [58]3 years ago
6 0

Answer:

The possible lengths are all the real numbers greater than 4 inches and less than 20 inches

Step-by-step explanation:

we know that

<u>The Triangle Inequality Theorem</u> states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Let

c----> the length of the third side of triangle

Applying the triangle inequality theorem

1) 12+8 > c

20 > c

Rewrite

c < 20 in

2) 8+c > 12

c > 12-8

c < 4 in

therefore

4 in < c < 20 in

The possible lengths are all the real numbers greater than 4 inches and less than 20 inches

katrin [286]3 years ago
5 0

Answer:

The third side must be smaller than 20 inches and greater than 4 inches

4

Step-by-step explanation:

Let a, b and c be the lengths of triangle's sides. Then

a+b>c\\ \\a+c>b\\ \\b+c>a

Use this rule in your case. So, if a=12 and b=8, then

12+8>c\\ \\12+c>8\\ \\8+c>12

Hence, you get

c-4\\ \\c>4

From these inequalities, you can state that

4

So, c must be smaller than 20 inches and greater than 4 inches.

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= 9x2 +9x -18,/<br> 3x +6
Ede4ka [16]

Answer:24+3x

Step-by-step explanation:

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3 0
3 years ago
You are dealth one card from a 52-card deck. find the probability that you are dealt a two or a black card
grigory [225]
The probability of getting a 2 or a getting a black card, find individual probabilities; 

A standard deck has 52 cards. 

There are 4 2's in a normal deck; probability of getting it is 4/25 

The probability of getting a black card is; 26/52 since half the deck is red and black. 

Now add up the probabilities since it says "or" 

(4/52)+(26/52)=30/52 probability of the card that you were dealt being a two or a black card. 

Hope I helped :) 
6 0
3 years ago
How do i write a two column proof for this??<br><br>Given: PG ≅ SG and PT ≅ ST . Prove: ∠GPT ≅ ∠GST
Nikolay [14]

Answer:

PG ≅ SG (Given)

PT ≅ ST (Given)

GT = GT (Common)

∴ ∠GPT ≅ ∠GST (SSS Congruency Axiom)

Step-by-step explanation:

<u>Given</u>: PG ≅ SG and PT ≅ ST

<u>To Prove</u>: ∠GPT ≅ ∠GST

<u>Proof</u>:  PG ≅ SG (Given)

PT ≅ ST (Given)

GT = GT (Common)

∴ ∠GPT ≅ ∠GST (SSS Congruency Axiom).

<u>SSS Congruency Axiom</u>:  If three pairs of sides of two triangles are equal in length, then the triangles are congruent.

<u>Congruence</u>: Two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

7 0
4 years ago
How the flibberdoodle do you graph decimals on a coordinate graph?!!
Annette [7]
Plotting coordinates can be a little confusing, but it doesn't have to be as long as you remember a few important details. The first number in the coordinate set tells you how far right (for a positive number) or left (for a negative number) you need to travel on the x-axis. The second number in the coordinate set tells you how far up (for a positive number) or down (for a negative number) you need to travel on the y-axis. Any set of coordinates can be represented by the variables x and y. If you picture (x, y), it will help you remember the x-coordinate comes first, so you will travel either right or left before travelling up or down.

5 0
2 years ago
Read 2 more answers
You and your family are planning a roadtrip. You determine that the distance you need to drive is 660 miles and that you can ave
iris [78.8K]

Answer:

11 hours

Step-by-step explanation:

Find how many hours the trip will take by dividing the number of miles by the rate in miles per hour:

660/60

= 11

So, the trip will take 11 hours

8 0
3 years ago
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