All categories

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)

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

then

one unique triangle can be made

You might be interested in

The first number in a pattern is 246, and the rule is subtract 10. What is the next number in the pattern?

kumpel [21]

Answer : 236
246 - 10 = 236

3 0

2 years ago

Read 2 more answers

How many yards are in 1 mile 60 feet

AfilCa [17]

1760 yards in 1 mile

4 0

3 years ago

Read 2 more answers

Tickets to a sporting event cost $125 each. What's a reasonable domain and range.

djverab [1.8K]

The domain and the range of a function is the set of input and output values of the function.

The domain is the set of all whole numbers.

The range is the set of all whole numbers.

Let the number of tickets be x, and the revenue be y.

So, the revenue function will be:

y = 125

The number of tickets cannot be less than 0.

So, the domain of the revenue function is

domain=0,∞

The above means that, the domain is the set of all whole numbers

Similarly, the revenue cannot be less than 0.

So, the range of the revenue function is

range = 0,∞

The above means that, the range is also the set of all whole numbers (in multiples of 125).

to know more about range and domain;

visit;brainly.com/question/28135761

#SPJ9

3 0

1 year ago

Let f(x)=x+a/x+b such that f(f(1)=0 & f(2)=-3 then a&b resctivily are.

Yuliya22 [10]

Answer:

The value of a = - 1 , And b = $\frac{ - 7 }{3}$

Step-by-step explanation:

Given as :

Function f(x) = $\frac{(x + a)}{(x + b)}$

And f(f(1)) = 0 And f(2) = - 3

Now For , x = 2 , y = - 3

I.e f(2) = $\frac{(2 + a)}{(2 + b)}$

or, - 3 = $\frac{(2 + a)}{(2 + b)}$

I.e 2 + a = - 6 - 3b

Or, a + 3b = - 8 ....... 1

Again f(f(1)) = 0

So, $\frac{(1 + a)}{(1 + b)}$ = 0

Or, 1 + a = 0

∴ a = - 1

So , put htis value of a i n eq 1 , we get value of b

So , - 1 + 3b = - 8

Or, 3b = - 7

∴ b = $\frac{ - 7 }{3}$

Hence The value of a = - 1 , And b = $\frac{ - 7 }{3}$ Answer

3 0

3 years ago

ALGEBRA 2!!!!!!!!! SHOW YOUR WORK!!!!!!!!!!!!!<br> Do f(g(x)) and g(f(x))

bezimeni [28]

$\bf f(x)=\cfrac{2x-3}{x+1}~\hspace{10em}g(x)=\cfrac{x+3}{2-x}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
f(~~g(x)~~)\implies \cfrac{2[g(x)]-3}{[g(x)]+1}\implies \cfrac{2\left( \frac{x+3}{2-x} \right)-3}{\left( \frac{x+3}{2-x} \right)+1}\implies
\cfrac{\frac{2x+6}{2-x}-3}{\frac{x+3}{2-x}+1}
\\\\\\
\cfrac{\frac{2x+6-6+3x}{2-x}}{\frac{x+3+2-x}{2-x}}\implies \cfrac{2x+6-6+3x}{2-x}\cdot \cfrac{2-x}{x+3+2-x}\implies \cfrac{5x}{5}\implies x$

$\bf \rule{34em}{0.25pt}\\\\
g(~~f(x)~~)\implies \cfrac{[f(x)]+3}{2-[f(x)]}\implies \cfrac{\frac{2x-3}{x+1}+3}{2-\frac{2x-3}{x+1}}\implies \cfrac{\frac{2x-3+3x+3}{x+1}}{\frac{2x+2-(2x-3)}{x+1}}
\\\\\\
\cfrac{2x-3+3x+3}{x+1}\cdot \cfrac{x+1}{2x+2-(2x-3)}\implies \cfrac{2x-3+3x+3}{x+1}\cdot \cfrac{x+1}{2x+2-2x+3}
\\\\\\
\cfrac{5x}{5}\implies x$

and in case you recall your inverses, when f( g(x) ) = x, or g( f(x) ) = x, simply means, they're inverse of each other.

4 0

3 years ago