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Svetlanka [38]
2 years ago
12

Which dimensions cannot create a triangle?

Mathematics
2 answers:
zavuch27 [327]2 years ago
7 0
Angles that create a triangle always add up to 180. 

To find sides that create triangles, we have to use the Triangle Inequality Theorem.
It's where side A + B will <em>always</em> be greater than side C
and B + C will always be greater than side A
<em>and</em> A + C will always be greater than side B.

So let's check all of these answers and pick the one that's incorrect.

A.
10 + 25 + 145 = 180?
Correct!

B. 
9 + 15 > 9?
Correct!
15 + 9 > 9?
Correct!
9 + 9 > 15?
Correct!

C. 
40 + 70 + 60 = 180?
Incorrect! 40 + 70 + 60 = 175 which is less than 180.

The answer is three angles measuring 40 m, 70 m, and 60 m.

Hope this helped! If you have anymore questions or don't understand, please comment or DM me. :)
Papessa [141]2 years ago
3 0
For a triangle to be "true", it must either have angle measures that total to 180 degrees or have two sides whose sum is greater than the third side.

For the first one, the angles total to 180 (10+25=35 and 145+35=180). This is a good triangle.

In the second one, the two shorter sides are 9 and 9. Adding these up, we get a sum of 18, and since this is greater than 15 (the third side), this triangle is also good.

The third triangle has angle measures that equal 175. Since it is less than 180 degrees, this is not a good triangle.

Finally for the fourth one, we see that the two shorter sides are 6 and 8. Their sum is 14, and since this is greater than 10, this is a good triangle. 

So our third option is the one that cannot create a triangle.

:)
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Answer:

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Step-by-step explanation:

In order to find these, you need to factor by splitting. For this, we separate out the two halves of the equation and pull out the greatest common factor of each. Let's start with the front end.

r^3 + 4r^2

r^2(r + 4)

Now the second half.

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-25(r + 4)

Since what is left in the parenthesis are exactly the same, we can use that parenthesis next to one with what we pulled out.

(r^2 - 25)(r + 4)

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Now that we are fully factored, set each parenthesis equal to 0 and solve for x.

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Step-by-step explanation:

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Irina18 [472]

Answer:

The equation of the nth term is an = -621 + 42n

Step-by-step explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic sequence:

- U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

- Un = a + (n – 1)d, where a is the first term , d is the difference

  between each two consecutive terms

, n is the position of the term

* Lets solve the problem

∵ an = a + (n - 1)d

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∴ a14 = a + 13d

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∴ a + 13d = -33 ⇒ (1)

- Similar we can find another equation from a15

∵ a15 = a + (15 - 1)d

∴ a15 = a + 14d

∵ a15 = 9

∴ a + 14d = 9 ⇒ (2)

- We will solve equations (1) and (2) to find a and d

* Lets subtract equation (2) from equation (1)

∴ (a - a) + (13 - 14)d = (-33 - 9)

∴ -d = -42 ⇒ × both sides by -1

∴ d = 42

- Substitute this value of d in equation (1) or (2)

∵ a + 13d = -33

∵ d = 42

∴ a + 13(42) = -33

∴ a + 546 = -33 ⇒ subtract 546 from both sides

∴ a = -579

* Now lets write the equation of the nth term

∵ an = a + (n - 1)d

∵ a = -579 and d = 42

∴ an = -579 + (n - 1) 42 ⇒ open the bracket

∴ an = -579 + 42n - 42

∴ an = -621 + 42n

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