1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ASHA 777 [7]
2 years ago
9

1

Mathematics
1 answer:
Marianna [84]2 years ago
4 0

Answer:

  B. {16, 19, 20}

Step-by-step explanation:

The <em>triangle inequality</em> requires for any sides a, b, c you must have ...

  a + b > c

  b + c > a

  c + a > b

The net result of those requirements are ...

  • the sum of the two shortest sides must be greater than the longest side
  • the length of the third side lies between the difference and sum of the other two sides

__

If we look at the offered side length choices, we see ...

  A: 8+11 = 19 . . . not > 19; not a triangle

  B: 16+19 = 35 > 20; could be a triangle

  C: 3+4 = 7 . . . not > 8; not a triangle

  D: 5+5 = 10 . . . not > 11; not a triangle

The side lengths {16, 19, 20} could represent the sides of a triangle.

_____

<em>Additional comment</em>

The version of triangle inequality shown above ensures that a triangle will have non-zero area.

The alternative version of the triangle inequality uses ≥ instead of >. Triangles where a+b=c will look like a line segment--they will have zero area. Many authors disallow this case. (If it were allowed, then {8, 11, 19} would also be a "triangle.")

You might be interested in
Pls dont guess on it
yuradex [85]

Answer:

2(8a + 8)

Step-by-step explanation:

The easiest way to do this is to substitute <em>a</em> for a number. For example, let's just make things easy and make <em>a </em> = 1.

So, if a = 1, the expression 16a + 8 would be 16(1) + 8 = 24.

Let's find all the expressions that would also equal 24 if <em>a = </em>24.

Plug in 1 for <em>a</em> in each of the equations. You will find that 2(8a + 8) will not equal 24 if <em>a </em>equals 1.

2(8a + 8)

2(8(1) + 8

2(8 + 8)

2(16)

32

4 0
2 years ago
David wants to my have a board for $398.50. He has saved $350 so far. Stores offering a discount for 15% for the month of Januar
bija089 [108]

Answer:

Yes, he will

Step-by-step explanation:

398.50 x .15 = 59.775

398.50-59.775=338.725

350>338.725

5 0
3 years ago
Jamaal bounces on a trampoline. His height, as a function of time, is modeled by y = -6x2 + 20x +4
kykrilka [37]

Answer: The function is no linear

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Amya spends 2 hours doing her homework. She daydreams about a robot that could do her homework in 10 minutes. If Amya did have t
ryzh [129]

Answer:

t=34.64 mins

Step-by-step explanation:

let Arya be A, Robot be B and Combined time be t

A+B=\frac{1}{t}\\A=\frac{1}{t+120}\\B=\frac{1}{t+10}\\\frac{1}{t+10}+\frac{1}{t+120}=t\\\frac{1}{t+10}=\frac{t+120-t}{t+120}\\t^2+120t=120t+1200\\t^2=1200\\t=34.6410

4 0
3 years ago
Can somebody prove this mathmatical induction?
Flauer [41]

Answer:

See explanation

Step-by-step explanation:

1 step:

n=1, then

\sum \limits_{j=1}^1 2^j=2^1=2\\ \\2(2^1-1)=2(2-1)=2\cdot 1=2

So, for j=1 this statement is true

2 step:

Assume that for n=k the following statement is true

\sum \limits_{j=1}^k2^j=2(2^k-1)

3 step:

Check for n=k+1 whether the statement

\sum \limits_{j=1}^{k+1}2^j=2(2^{k+1}-1)

is true.

Start with the left side:

\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}\ \ (\ast)

According to the 2nd step,

\sum \limits_{j=1}^k2^j=2(2^k-1)

Substitute it into the \ast

\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}=2(2^k-1)+2^{k+1}=2^{k+1}-2+2^{k+1}=2\cdot 2^{k+1}-2=2^{k+2}-2=2(2^{k+1}-1)

So, you have proved the initial statement

4 0
3 years ago
Other questions:
  • Hank the hiker would like to go on a hike. He only has four hours available today for the hike. The expression 1/2d + 1/2e is us
    11·1 answer
  • Factorize (4y-5)²+80y ​
    9·2 answers
  • Charlie is the quarterback for the cougars football team. His team had three penalties in a row for -5 yards each. How many yard
    6·1 answer
  • ILL MARK U BRAINLIEST!!
    15·2 answers
  • Help! Geometry! 5(x-2) = -2(x+6)
    15·1 answer
  • Which mathematical inequality represents the following statement?
    15·1 answer
  • Multiple answers please help!!
    9·1 answer
  • Can someone answer this please quick
    11·1 answer
  • The scatter plot shows the association between the population of various states in the United States and the number of cellular
    14·1 answer
  • I'm struggling in this subject so if you'd give a step-by-step explanation that'd be great thx​
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!