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3 years ago

Given three side lengths, how many triangles can be formed?

Mathematics

2 answers:

alekssr [168]3 years ago

4 0

Given three side lengths, for example, a, b and c, you can form the triangle when

$a+b>c,\\ a+c>b,\\ b+c>a.$

If this property holds, then one triangle you can form. Each next triangle with the same sides lengths will be congruent to the first triangle by SSS postulate.

SSS postulate says: If the three sides of a triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

Answer: 1 triangle, correct option is A.

jeka943 years ago

4 0

We know that

In a triangle, the combined lengths of any two sides must always be greater than the length of the third side. (Triangle Inequality Theorem)

If all three side lengths are given and the combined length of two sides is greater than the length of the third side.

then

one unique triangle can be made

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6+5

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3 years ago

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A rectangular sheet of paper is 25/2cm long and 32/3 cm wide. Find its perimeter. *

Zina [86]

Answer:

46.3cm

Step-by-step explanation:

perimeter is length around shape
25/2 multiply by 2 becoz it's got two equal sides
32/3 multiply by two for the other equal sides
add answers together to give you
46.3cm

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3 years ago

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Expand and simplify (x+5)(x-2)

salantis [7]

Answer:

${x}^{2} - x - 12 = (x + 3)(x - 4)$

${x}^{2} + 3x + 2 = (x + 2)(x + 1)$

${x}^{2} + 3x - 10 = (x + 5)(x - 2)$

Step-by-step explanation:

F [First terms] - Multiply the first terms in each set of parentheses FARTHEST TO THE LEFT

O [Outside terms] - Multiply the first term in the first set of parentheses FARTHEST TO THE LEFT by the last term in the second set of parentheses FARTHEST TO THE RIGHT

I [Inside terms] - Multiply the last term in the first set of parentheses FARTHEST TO THE RIGHT by the first term in the second set of parentheses FARTHEST TO THE LEFT

L [Last terms] - Multiply the last terms in each set of parentheses FARTHEST TO THE RIGHT

${x}^{2} - x - 12 = {x}^{2} - 4x + 3x - 12$

${x}^{2} + 3x + 2 = {x}^{2} + x + 2x + 2$

${x}^{2} + 3x - 10 = {x}^{2} - 2x + 5x - 10$

I am joyous to assist you anytime.

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3 years ago

When expressed as a decimal number which of the following is a repeating decimal

Kamila [148]

Answer:

8/9

Step-by-step explanation:

8/9 has a repeating decimal of 8. No matter how many times you divide it, you will get the answer 0.8888 and to infinty.

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3 years ago

Which system of linear inequalities is represented by the graph? ax – 3y > 6 and y > 2x + 4 bx + 3y > 6 and y > 2x

igor_vitrenko [27]

The correct answer is:

bx + 3y > 6 and y > 2x + 4

Explanation:

Looking at the second inequality, the y-intercept is 4 and the slope is 2. This means the graph of the line crosses the y-axis at (0, 4) and the line goes up 2 and over 1. Since it is greater than, this means the graph is shaded above it. Comparing this to the graph, the line for the blue part crosses the y-axis at (0, 4) and goes up 2 and over 1. The graph is also shaded above the line.

For the first inequality, bx+3y > 6, we want to isolate y. To do this, we subtract bx from each side:

bx+3y-bx > 6-bx

3y > 6-bx

Divide both sides by 3:

3y/3 > 6/3 - bx/3

y > 2 - (b/3)x

This means the line for this will have a y-intercept of 2 and decrease 1 while going over 3. The orange section does this. Additionally, since it is greater than, the graph should be shaded above the line. This one is, so this is the correct answer.

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3 years ago

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