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Nuetrik [128]
3 years ago
5

Given triangle ABC with sides AB = 3x + 4 , BC = 2x + 5 , and AC = 4x , determine the values of x such that triangle ABC exists

Mathematics
1 answer:
Jlenok [28]3 years ago
8 0

Answer:

  x > 1/5

Step-by-step explanation:

All of these three triangle inequalities must be satisfied:

  AB +BC > AC

  BC +CA > BA

  CA +AB > CB

___

Taking these one at a time, we have ...

  AB +BC > AC

  3x +4 + 2x +5 > 4x

  x +9 > 0 . . . . . subtract 4x

  x > -9

__

  BC +CA > BA

  2x +5 + 4x > 3x +4

  3x > -1 . . . . . . subtract 3x+5

  x > -1/3 . . . . . divide by 3

__

  CA + AB > CB

  4x + 3x +4 > 2x +5

  5x > 1 . . . . . . subtract 2x+4

  x > 1/5

___

The only values of x that satisfy all of these inequalities are those such that ...

  x > 1/5

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Complete the equation so that it has infinitely many solutions.<br> 8x - 14 = 8x -
kati45 [8]

Answer:

8x-14=8x-14

Step-by-step explanation:

So if both the equations are the same, that means that any value of x put in the equation will equal itself, so that means that there are infinite solutions to the equation

If you try to solve this equation, this happens

8x-14=8x-14

add 14 to both sides

8x=8x

divide by 8 both sides

x=x

This means that there are infinite solutions because any number could be x and it would still work

6 0
3 years ago
Read 2 more answers
F(x) = 2x^2 − 3x − 5 Part
riadik2000 [5.3K]

Answer:  Answer  is in the steps..

Step-by-step explanation:

f(x)= 2x^{2} - 3x -5        

A) To find the x intercepts of a parabola we have to set the whole equation equal zero because the x intercept is when y equal zero in other words where f(x) equal zero.

 2x^{2}  - 3x - 5 = 0     Now solve using quadratic formula.

  x = -b±\frac{\sqrt{b^2 -4ac } }{2a}    

  x = 3 ± \sqrt{9+40} /2a  

   x = 3 ± \sqrt{49}  / 2a

   x= 3 ± 7 /4

   x= -1   or x = 5/2  

The x intercepts are  (5/2,0)  and (-1,0)

   

B)  The graph vertex of the graph of f(x)  is going to be at a minimum because the leading coefficient of the function has a positive integer which means the parabola will open up and its vertex will be at the minimum point.

 Using the  x coordinates  we could find their average and find the x coordinate of the   vertex.

\frac{5}{2} + -\frac{1}{1}  =  \frac{3}{2} / \frac{2}{1} = 3/4  

The x coordinate of the vertex  is 3/4 so we will input that into the equation and solve for the y coordinate  

2(\frac{3}{4})^2 - 3 (\frac{3}{4}) - 5   = 18/16 - 9/4 -5  =  -49/8

The y coordinate of the vertex  is  -49/8

So the vertex is (3/4, -49/8)  

C)   First  I will graph the vertex and then graph he two x intercepts and connect then like a U shape.

5 0
3 years ago
X + 2 = 1 what is it
Alexus [3.1K]
-1 as a negative would = X
8 0
3 years ago
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The square shown has a perimeter of 32 units. The square is rotated about line k. what is the circumfrence of the base
boyakko [2]

The circumference equal to 25 units

<h3>What is perimeter of square?</h3>

The perimeter of square is 4 times the side.

P= 4* side

The perimeter of the square,

4x = P

Now P is =  32 units then,

32 units = 4(x)

x = 8 inches

So,  the diameter of the cylinder formed by the rotation of 8 inches  

Now, the circumference of the base is

C = 2πr = πD

If r =8  inches

                           

C = π(8 units) = 8π units

C = 8(3.14) = 25.12 units

Hence, the circumference equal to 25 units

Learn more about perimeter of square here:

brainly.com/question/11495285

#SPJ1

6 0
2 years ago
The cook at the diner has 72 eggs.her recipe says each omelet needs 3 eggs .Does the cook have enough eggs to make 24 order
Anna007 [38]

Answer:

Yes she has just enough

Step-by-step explanation:

3 eggs per each order of omelet

24 orders so 3x24=72

5 0
3 years ago
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