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raketka [301]
3 years ago
10

13. In the triangle below, the sides have length x + 3, 3x - 1. and 4x. Determine the range of possible

Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
7 0

Answer:

Hence as long as x > 2/3, we can form a triangle from the three given sides.

Step-by-step explanation:

Given:

Length of 3 sides of triangle are x+3, 4x,3x-1

Solution:

From the length of the 2nd side 4x, we know that x > 0

Let this be 1 st statement.

Now from the triangle inequality we can say that;

x + 3 + 4x > 3x -1\\5x+3>3x-1\\5x-3x>-1-3\\2x>-2\\x>-1

No new information from this because of the 1st statement above.

Also,  

4x + 3x - 1 > x +3\\7x-1>x+3\\7x-x>3+1\\6x>4\\x>\frac{4}{6}\\\\x>\frac{2}{3}

Lastly,

x+3 +3x - 1 > 4x\\4x-2>4x\\4x-4x>2\\0>2

and again no new information is obtained from this inequality.

Hence as long as x > 2/3, we can form a triangle from the three given sides.

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The sum of three consecutive integers is 312
sdas [7]

Let x be for unknown number. Let x be first number . X+1 To be second number .x+2be third number.  X+(x+1)+(x+2)=312. Simplify to get 3x+3=312 . Subtract 3 from both sides 3x-3=312-3. Once you subtract get 3x=109.then divide 3 both sides . 3x/3=309/3. To get x= 103.   Now once you have that  First number 103. Second number 103+1=104 . And third number 103+2=105.    To check add them 103+104+105=312

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3 years ago
Joe has collections of 35 DVD movies. He received eight of them as gifts. Jobot the rest of his movies over three years. If he b
Yuliya22 [10]
Hello!

Let's subtract the eight DVDs Joe received as gifts, because he didn't buy them on his own.

35 - 8 = 27

Now, divide the remaining CDs by the 3 years he collected his DVDs in.

27 ÷ 3 = 9

A N S W E R:

Joe bought 9 DVDs last year.

Good day!
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3 years ago
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snow_lady [41]

Answer:

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Step-by-step explanation:

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3 years ago
Read 2 more answers
Julia is casting a play with 4 main roles. Six students
aev [14]

Using the combination formula, it is found that Julia can take 15 combinations.

<h3>What is the combination formula?</h3>

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by:

C_{n,x} = \frac{n!}{x!(n-x)!}

For this problem, 4 students are taken from a set of 6, hence the number of combinations is given as follows:

C_{6,4} = \frac{6!}{4!2!} = 15

More can be learned about the combination formula at brainly.com/question/25821700

#SPJ1

7 0
2 years ago
a stage is 10 yards long and 5 yards wide. The orchestra pit in front of the stage is 4 yards long and 2 yards wide. How much fl
Lilit [14]
Well to find this answer, I assume that you want me to help with finding the area. Let's start with the area of the stage. Off of the info you gave me, I assume that the stage and pit are rectangles. So to find the area of the rectangles, we need to use the area formula A=l×w. Plug in the numbers into the formula and we get A=10×5. So the area of the stage is 50 yards. Now do the same thing for the pit, and we get A=4×2. So the pit's area is 8 yards. Add 50 and 8 to get the total area and we get 58. So the stage and the orchestra pit take up 58 yards of floor space. Hope I helped!
7 0
3 years ago
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