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gregori [183]
2 years ago
7

which are the possible sides of a triangle ? a. 15, 9, 3 b. 6, 12, 19 c. 11, 6, 3 d. 4, 8, 10

Mathematics
1 answer:
joja [24]2 years ago
3 0

Answer:

Option d. 4, 8, 10

Step-by-step explanation:

we know that

The<u> Triangle Inequality Theorem</u> states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

<u><em>Verify each case</em></u>

case a) we have

15, 9, 3

Applying the triangle Inequality Theorem

1) 15+9 > 3

24> 3 ------> is true

2) 15+3 > 9

18 > 9 ----> is true

3) 9+3 > 15

12 > 15  ----> is not true

therefore

The set of lengths cannot be used to form the sides of a triangle

case b) we have

6,12,19

Applying the triangle Inequality Theorem

1) 6+12 > 19

18> 19 ------> is not true

therefore

The set of lengths cannot be used to form the sides of a triangle

case c) we have

11,6,3

Applying the triangle Inequality Theorem

1) 11+6 > 3

17> 3 ------> is true

2) 11+3 > 6

14 > 6 ----> is true

3) 6+3 > 11

9 > 11  ----> is not true

therefore

The set of lengths cannot be used to form the sides of a triangle

case d) we have

4,8,10

Applying the triangle Inequality Theorem

1) 4+8 > 10

12> 10 ------> is true

2) 4+10 > 8

14 > 8 ----> is true

3) 8+10 > 4

18 > 4  ----> is true

therefore

The set of lengths can be used to form the sides of a triangle

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solong [7]

Answer:

  1. No
  2. Yes
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Step-by-step explanation:

The first one is incorrect because would be 4,836,000 instead of 4,836,000,000. The correct notion would be 4.836*10^9

6 0
2 years ago
In this diagram which equation could you prove to be true in order to conclude that the lines are parallel
KiRa [710]
I would say that the correct answer is D. because y is always the numerator while x is the denominator for the equation y2 - y1/x2 - x1 which means if there is two y's or two x's on the same line you subtract the second one from the first one. If there is only one y and/or x and the other is 0 on the same line, it stays at y or x without subtracting y2 - y1 or x2 - x1. 

Since b is on the y coordinate and -a is on the x coordinate, you would make it b/a while -a is gonna be a positive since the lines are going up and to the right. Now, since c is the y coordinate and d is the x coordinate, make C the numerator and d the denominator since y is always the numerator and x is the denominator for these parallel line figures on the graph and the equation will be equaled to the fraction to the other fraction for parallel lines. 

So, your answer would be D. b/a = c/d 

Hope this helps, and is correct! 

<em>~ ShadowXReaper069</em>
3 0
3 years ago
Read 2 more answers
Solve the inequality: (x+3)(x−4)&lt;−12
melamori03 [73]

Answer:

0<x<1

Step-by-step explanation:

(x+3)(x−4)<−12

FOIL

x^2 -4x+3x -12 <-12

x^2 -x -12 <-12

Add 12 to each side

x^2 -x -12+12 <-12+12

x^2 -x <0

Factor out an x

x(x-1) <0

Using the zero product property

x(x-1) =0

x=0  x-1=0

x=0  x=1

Check the ranges

x<0

x(x-1) <0        

- * - >0

False

0<x<1

x(x-1) <0        

+ * - <0

True

x>1

x(x-1) <0        

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False

3 0
2 years ago
It takes 8 hours for 4 men to paint a room.
eimsori [14]

Answer:

16 men would be needed to paint the room in 2 hours

Step-by-step explanation:

We can use proportion to solve the problem given, but first we need to determine whether it is a direct or indirect proportion.

If the number of men are increase, the time taken to do the work will decrease, If the number of men are decrease, the time taken to do the work will increase. Therefore, this is an indirect proportion.

We are going to arrange the data inversely.

Let x be the number of men needed to paint the room in two hours

8 hours =  2 hours

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Cross-multiply

2×x = 8×4

2x = 32

Divide both-side of the equation by 2

2x/2 = 32/2

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