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Vikentia [17]
3 years ago
12

A triangle has two sides of lengths 4 and 5. What value could the length of the third side be?

Mathematics
2 answers:
Olin [163]3 years ago
6 0

Answer:

2, 3, 4, 5, 6, 7 or 8.

Step-by-step explanation:

We know that the sum of two sides on a triangle should ALWAYS be greater than the third side. Then we have:

5-4 < x < 5 + 4

1 < x < 9

Therefore, the lenght of the third side could be any number between 1 and 9. If the lenght of the third side is an integrer, then the lenght could be:

2, 3, 4, 5, 6, 7 or 8.

ANTONII [103]3 years ago
4 0

Answer:

The length of the third side could be all real numbers greater than 1 unit and less than 9 units

Step-by-step explanation:

we know that

The <u>Triangle Inequality Theorem,</u>   states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

so

Applying the triangle inequality theorem

Let

x ----> the length of the third side

1) 4+5 > x

9 > x

Rewrite

x < 9 units

2) 4+x > 5

x > 5-4

x > 1 units

therefore

The solution for the third side is the interval -----> (1,9)

All real numbers greater than 1 unit and less than 9 units

therefore

The length of the third side could be all real numbers greater than 1 unit and less than 9 units

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(4/3a - 3c - 5b) + (-a-2b+4c)
Darina [25.2K]

━━━━━━━☆☆━━━━━━━

▹ Answer

<em>1/3a + c - 7b</em>

▹ Step-by-Step Explanation

(4/3a - 3c - 5b) + (-a - 2b + 4c)

<u>Remove the parentheses</u>

(4/3a - 3c - 5b) + (-a - 2b + 4c)

<u>Rewrite</u>

4/3a - 3c - 5b - a - 2b + 4c

<u>Calculate</u>

1/3a - 3c - 5b - 2b + 4c

<u>Final Answer</u>

1/3a + c - 7b

Hope this helps!

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5 0
4 years ago
Judy bought a coat at a 20% discount sale for $72. what was thw original price of the coat
Rama09 [41]
The original price of the coat is $90
6 0
4 years ago
What is (10y+6) (8y-6) ?
ANEK [815]

Answer:

y = 3/4 or y = -3/5

Step-by-step explanation:

Solve for y:

(8 y - 6) (10 y + 6) = 0

Hint: | Find the roots of each term in the product separately.

Split into two equations:

8 y - 6 = 0 or 10 y + 6 = 0

Hint: | Look at the first equation: Factor the left hand side.

Factor constant terms from the left hand side:

2 (4 y - 3) = 0 or 10 y + 6 = 0

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides by 2:

4 y - 3 = 0 or 10 y + 6 = 0

Hint: | Isolate terms with y to the left hand side.

Add 3 to both sides:

4 y = 3 or 10 y + 6 = 0

Hint: | Solve for y.

Divide both sides by 4:

y = 3/4 or 10 y + 6 = 0

Hint: | Look at the second equation: Factor the left hand side.

Factor constant terms from the left hand side:

y = 3/4 or 2 (5 y + 3) = 0

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides by 2:

y = 3/4 or 5 y + 3 = 0

Hint: | Isolate terms with y to the left hand side.

Subtract 3 from both sides:

y = 3/4 or 5 y = -3

Hint: | Solve for y.

Divide both sides by 5:

Answer: y = 3/4 or y = -3/5

4 0
4 years ago
Carla and Benicio work in a men's clothing store. They earn commission from each suit and each pair of shows they sell. For sell
qwelly [4]

Answer:

The salespeople earn for the sale of a suit = $13.

The salespeople earn for the sale of a pair of shoes = $8.

Step-by-step explanation:

Let x be the commission for each suit and y be commission for each pair of shoes.

We have been given that for selling 3 suits and one pair of shoes, Carla has earned $47 in commission. We can represent this information as:

3x+y=47...(1)

We are also told that for selling 7 suits and 2 pairs of shoes, Benicio has earned $107 in commission. We can represent this information as:

7x+2y=107...(2)

We will use substitution method to solve our system of linear equations. From equation (1) we will get,

y=47-3x

Substituting this value in equation (2) we will get,

7x+2(47-3x)=107

7x+94-6x=107

Upon combining like terms we will get,

7x-6x=107-94

x=13

Therefore, the salespeople earn $13 for the sale of a suit.

Let us substitute x=13 in equation (1).

3*13+y=47

39+y=47

y=47-39

y=8

Therefore, the salespeople earn $8 for the sale of a pair of shoes.

8 0
4 years ago
How does lack of sleep affect risk of injury?
prohojiy [21]

Answer:

D. It interferes with motor responses

Step-by-step explanation:

Don't ask why I know this

8 0
3 years ago
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