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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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Bad White [126]
Hey, Imherkk!
You can check by using a calculator.
Another way is doing 17*6.
If you get 102(you do) then you're answer is right.
I hope this helps;)
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3 years ago
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A fisherman can row upstream at 4 mph and downstream at 6 mph. He started rowing upstream until he got tired and then rowed down
shepuryov [24]

A fisherman can row upstream at 4 mph and downstream at 6 mph. He started rowing upstream until he got tired and then rowed downstream to his starting point. The distance of how far the fisherman row if the entire trip took 2 hours is  9.6 miles

<u />

The speed of an object refers to the change of the object's distance within a specified time.

Mathematically, we can have;

\mathbf{Speed =\dfrac{distance}{time}}

Distance = speed × time

From the information given;

  • The fisherman row upstream for 4 miles/ hour.
  • The distance covered by the fisherman = 4 × t₁  ----- (1)

  • The fisherman row downstream at 6 miles/ hour
  • The distance covered by the fisherman = 6 × t₂  ------ (2)

  • SInce it took the entire trip 2 hours, we can infer that:

  • t₁ + t₂ = 2
  • t₂ = 2 - t₁

From equation (2), replace the above value of t₂ into equation (2)

  • d = 6 t₂
  • d = 6(2 - t₁)
  • d = 12 - 6t₁

From equation (1)

  • d = 4 t₁  

Equation both distance together, we have:

  • 12 - 6t₁ = 4t₁
  • 12 = 4t₁ + 6t₁
  • 12 = 10t₁
  • t₁ = 12/10
  • t₁ = 1.2  hours

From t₂ = 2 - t₁

  • t₂ = 2 - 1.2
  • t₂ = 0.8 hours

From d = 4t₁

Replace t₁ with 1.2 hours

  • d = 4(1.2 hours)
  • d = 4.8 miles

Also, from d = 6t₂

  • d = 6(0.8)
  • d = 4.8 miles

Therefore, we can conclude that the distance of how far the fisherman row if the entire trip took 2 hours is (4.8+4.8) miles = 9.6 miles

Learn more about distance here:

brainly.com/question/12319416?referrer=searchResults

3 0
2 years ago
Suppose an amount increases by 100% percent, then decreases by 100% percent. Find the final amount. Would the situation change i
Oksi-84 [34.3K]
No it will not change it will be 250% then it will decrease 100% down again back to 150%
6 0
3 years ago
HELP! i’ll mark you as brainliest
Nadya [2.5K]

Answer:

m<F = 79 degrees

Step-by-step explanation:

As per the given information;

m<E = 22, the triangle EDF (the one that is given in the picture) is isosceles (meaning that the sides are congruent).

In an isosceles triangle, (a triangle where the sides are congruent) the base angles (the angles opposite to the two congruent sides) are also congruent. One should also know, that in an isosceles triangle, like in any triangle, the sum of the measures of the angles equals 180 degrees.

Using this we can say that

m<D = m<F

To keep it simple while solving the problem, let's say that they have a value of x degrees.

So,

m<E + m<D + m<F =180

Subsitute

22 + x + x = 180

Simplify and inverse operations

22 + x + x = 180

-22              -22

2x = 158

/2     /2

x = 79

So the measure of <D and <F is 79 degrees.

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Divide 43.54 by 3.5
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