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
tigry1 [53]
2 years ago
15

Please solve the question in the picture​

Mathematics
2 answers:
Vanyuwa [196]2 years ago
6 0

Answer:

  • shortest: 11 inches
  • longest: 39 inches

Step-by-step explanation:

Given two side lengths for a triangle, the triangle inequality tells you the third side must have a length between the difference and the sum of the given sides.

__

<h3>A. minimum length</h3>

The difference of the given sides 25 and 15 is ...

  25 -15 = 10

The smallest integer greater than 10 is 11.

The third side must be at least 11 inches long.

__

<h3>B. maximum length</h3>

The sum of the given sides is ...

  25 +15 = 40

The largest integer smaller than 40 is 39.

The third side must be at most 39 inches long.

_____

<em>Additional comment</em>

Formally, the triangle inequality tells you that sides a, b, c must satisfy ...

  a +b > c  and  b +c > a  and  c +a > b

When we're considering the length of third side (c), there are 3 cases to consider. 1) c is shortest; 2) c is between the other lengths; 3) c is longest. Without loss of generality, we can assume a > b.

1) c is shortest:

  • a+b>c is always true.
  • b+c>a ⇒ c>a-b (the positive difference)
  • c+a>b ⇒ c>b-a (the negative difference)

conclusion: c > a-b

2) a > c > b:

  • a+b>c is always true.
  • b+c>a ⇒ c>a-b (the positive difference)
  • c+a>b ⇒ c>b-a (the negative difference)

conclusion: c > a-b

3) c is longest:

  • a+b>c (the sum)
  • b+c>a ⇒ c>a-b (the difference will be less than the sum)
  • c+a>b ⇒ c>b-a (the negative difference will be less than the sum)

conclusion: a -b < c < a+b . . . . . . for a>b

Alexxandr [17]2 years ago
5 0

Answer:

A. 11"

B. 39"

25 - 15 < x < 25 + 15

10 < x < 40

*x = whole number

You might be interested in
Please please help <br><br> Given the function f(x)=1/3x*2-3x+5 determine the inverse relation
yuradex [85]

The inverse relation of the function f(x)=1/3x*2-3x+5 is f-1(x) = 9/2 + √(3x + 21/4)

<h3>How to determine the inverse relation?</h3>

The function is given as

f(x)=1/3x^2-3x+5

Start by rewriting the function in vertex form

f(x) = 1/3(x - 9/2)^2 -7/4

Rewrite the function as

y = 1/3(x - 9/2)^2 -7/4

Swap x and y

x = 1/3(y - 9/2)^2 -7/4

Add 7/4 to both sides

x + 7/4= 1/3(y - 9/2)^2

Multiply by 3

3x + 21/4= (y - 9/2)^2

Take the square roots

y - 9/2 = √(3x + 21/4)

This gives

y = 9/2 + √(3x + 21/4)

Hence, the inverse relation of the function f(x)=1/3x*2-3x+5 is f-1(x) = 9/2 + √(3x + 21/4)

Read more about inverse functions at:

brainly.com/question/14391067

#SPJ1

5 0
1 year ago
What is 1/2 to 1/4 equals
sergey [27]

Do you mean 1/2 of 1/4 if so it’s just timsing the numerator by the numerator and the denominator by the denominator. So, 1 x 1 = 1 and 2 x 4 = 8

Therefore it’s 1/8!

If you didn’t understand I’ll gladly elaborate!

4 0
3 years ago
HELP ME ASAP QUIZ
Gnoma [55]

Answer:

E

Step-by-step explanation:

for b bananas sold 0.40 profit

for a apples

7 0
3 years ago
A flagpole is 12 feet tall. Its shadow is 14 ft long. How far is it from the top of the
Kisachek [45]

Answer:

Step-by-step explanation:

AC = length of flagpole = 12 ft

AB = length of shadow = 14 ft

BC = length from the top of the flagpole to the end of the shadow = x ft

Use Pythagorean theorem to find the length of x,

x² = AC² + BC²

   = 12² + 14²

  = 144 + 196

  = 340

x = √340

x = 18.4 ft

3 0
2 years ago
Which number is the best approximation for π/3 : 1, 1.03, 1.05, or 1.07?​
Evgen [1.6K]

Answer:

1,05

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • What are the intercepts of
    5·2 answers
  • Find the product of (2x + 3) and (x + 5)
    10·1 answer
  • I need help with this math work
    11·1 answer
  • There are 9 players on a baseball team. After the game each player high-fives once with everyone else. How many high-fives were
    15·1 answer
  • For what value of X is line a parallel to line B?<br> (4x+28). 112. 68
    5·2 answers
  • How long does it take a snail to travel 10 inches at a rate of .2 inches per minute.
    10·1 answer
  • PLEASE HELP with math. 15 POINTS!! i need to write a justification for these 4.
    10·1 answer
  • Sub :- Linear Equations
    15·1 answer
  • A farmer has both sheep and chickens on his farm. All the animals have the expected number of parts. When his animals are all
    6·1 answer
  • If brad is x years old and Julie is five years younger than brad how old is Julie
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!