@bot make this shorter
There are two conditions that must be met in order for three side lengths, a, b, and c, to create a triangle:
1. The sum of any two sides of the triangle must be greater than the third side.
Mathematically:
a + b > c
a + c > b
b + c > a
2. The difference between any two sides of the triangle must be less than the third side.
Mathematically:
|a - b| < c
|a - c| < b
|b - c| < a
Both of these conditions must be met in order for three side lengths to form a triangle.
Use the drop-down menu to complete the sentence.
One negative aspect of Brazil’s government in the second half of the 1900s was that
Brazil's economy made little progress.
10 answers
Conditions for triangle formation:
1. Sum of any two sides > third side
2. Difference between any two sides < third side
1. Sum of any two sides > third side
2. Difference between any two sides < third side
a little more formal
In order for three side lengths, a, b, and c, to create a triangle, it is necessary for two conditions to be met:
1. The sum of any two sides of the triangle must be greater than the third side. This can be expressed mathematically as:
a + b > c
a + c > b
b + c > a
2. The difference between any two sides of the triangle must be less than the third side. Mathematically, this can be represented as:
|a - b| < c
|a - c| < b
|b - c| < a
If both of these conditions are satisfied, the three side lengths can form a valid triangle.
1. The sum of any two sides of the triangle must be greater than the third side. This can be expressed mathematically as:
a + b > c
a + c > b
b + c > a
2. The difference between any two sides of the triangle must be less than the third side. Mathematically, this can be represented as:
|a - b| < c
|a - c| < b
|b - c| < a
If both of these conditions are satisfied, the three side lengths can form a valid triangle.
@bot
Complete the inequality so that it represents the whole-number values that side a
could be to create a triangle.
An illustration of a triangle shows an equation along the base as b equals 6 and the hypotenuse as c equals 7. The third side on the triangle is labeled as a.
1$$<a<
2$$
Correct answers:
11
213
Complete the inequality so that it represents the whole-number values that side a
could be to create a triangle.
An illustration of a triangle shows an equation along the base as b equals 6 and the hypotenuse as c equals 7. The third side on the triangle is labeled as a.
1$$<a<
2$$
Correct answers:
11
213
Using the triangle inequality theorem, we know that for a triangle with sides a, b, and c, the sum of any two sides must be greater than the third side. Therefore, for this problem:
a + b > c
a + 6 > 7
a > 1
a + c > b
a + 7 > 6
a > -1 (this doesn't help us since we want whole-number values)
b + c > a
6 + 7 > a
13 > a
So, the correct inequality would be:
1 < a < 13
Therefore, the only correct answer is 11.
a + b > c
a + 6 > 7
a > 1
a + c > b
a + 7 > 6
a > -1 (this doesn't help us since we want whole-number values)
b + c > a
6 + 7 > a
13 > a
So, the correct inequality would be:
1 < a < 13
Therefore, the only correct answer is 11.
make it shorter
The correct inequality for finding whole-number values for side a in a triangle with sides of 6, a, and 7 is:
1 < a < 13
The only correct answer from the list given is 11.
1 < a < 13
The only correct answer from the list given is 11.
explain it
This question is asking us to find the possible whole-number values for the length of the third side, a, of a triangle with sides of 6 and 7. To do this, we need to use the triangle inequality theorem which states that the sum of any two sides of a triangle must be greater than the third side. By applying this theorem, we can write two inequalities as follows:
a + 6 > 7
This inequality tells us that the sum of sides a and 6 must be greater than 7.
a + 7 > 6
This inequality tells us that the sum of sides a and 7 must be greater than 6.
Simplifying each inequality, we get:
a > 1
This means that a must be greater than 1.
a > -1
This inequality does not help us.
6 + 7 > a
This inequality tells us that the sum of sides 6 and 7 must be greater than a.
Combining the above inequalities, we get:
1 < a < 13
This means that a can take on any value between 1 and 13. However, we are only given the options of 11 or 213, so the correct answer is 11 as it falls within the range of the inequality.
a + 6 > 7
This inequality tells us that the sum of sides a and 6 must be greater than 7.
a + 7 > 6
This inequality tells us that the sum of sides a and 7 must be greater than 6.
Simplifying each inequality, we get:
a > 1
This means that a must be greater than 1.
a > -1
This inequality does not help us.
6 + 7 > a
This inequality tells us that the sum of sides 6 and 7 must be greater than a.
Combining the above inequalities, we get:
1 < a < 13
This means that a can take on any value between 1 and 13. However, we are only given the options of 11 or 213, so the correct answer is 11 as it falls within the range of the inequality.
28 answers