The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The correct option is C.
<h3>What is the
triangle inequality theorem?</h3>
The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
Given the length of the two sides of the triangle, therefore, we can write the inequalities,
8 + 5 > x ⇒ 13 > x
8 + x > 5 ⇒ x > - 3
5 + x > 8 ⇒ x > 3
Now, as per the inequality the value of x can lie between 3 to 13, but as the side needs to be greatest, therefore, the value of x will be 12.
Hence, the correct option is C.
Learn more about the Triangle Inequality Theorem:
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Answer:
∠A=65º
Step-by-step explanation:
- A angle of a line is 180º, so we can say that angle ABC=(180-6x)º
- The interior angkes of a triangle is 180º, so (x+40)º+(3x+10)º+(180-6x)º=180º
- Remove parenthesis, x+40+3x+10+180-6x=180
- Combine like terms, -2x+230=180
- Subtract 180, -2x=-50
- Divide by -2, so x=25
Now:
- ∠CAB=(25+40)º=65º
- ∠ABC=[180-6(25)]º=30º
- ∠BCA=[3(25)+10]=85º
B. the line is going up so it’s going to be positive not negative. the b value is gonna be negative 1 instead of positive because it crosses the y axis closer to -1 than it does 1
Answer:
D
Step-by-step explanation:
The expression ![\sqrt[5]{x} *\sqrt[5]{x}* \sqrt[5]{x} *\sqrt[5]{x}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7Bx%7D%20%2A%5Csqrt%5B5%5D%7Bx%7D%2A%20%5Csqrt%5B5%5D%7Bx%7D%20%2A%5Csqrt%5B5%5D%7Bx%7D)
simplifies to ![\sqrt[5]{x*x*x*x} = \sqrt[5]{x^4}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7Bx%2Ax%2Ax%2Ax%7D%20%3D%20%5Csqrt%5B5%5D%7Bx%5E4%7D)
A radical can be written as a fractional exponent. The index of a radical is the denominator of its fractional exponent.
Answer:
x=4 and the solution is not extraneous
Step-by-step explanation:
This solution is not extraneous, because plugging it back in you get:
Hope this helps!
