Question

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.

Answer 1

@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.

Answer 2

a little more formal

Answer 3

@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

Answer 4

make it shorter

Answer 5

explain it

Answer 6

Conditions for triangle formation:
1. Sum of any two sides > third side
2. Difference between any two sides < third side

Answer 7

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.

Answer 8

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.

Answer 9

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.

Answer 10

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.