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2 years ago

Can the sides of a triangle have sides of 5, 8, and 16 ???

Mathematics

1 answer:

Nata [24]2 years ago

4 0

Answer:

No.

Step-by-step explanation:

The triangle inequality theorem states that the sum of two sides of a triangle must be greater than the third side.

5 + 8 = 13.

13, which is the sum of two sides, is not larger than 16, the third side.

Therefore, a triangle cannot have these side lengths.

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3 years ago

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The sum of two trinomials is 7x2 - 5x + 4. If one of the trinomials is 3x2 + 2x - 1, then what is the other trinomial?

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2 years ago

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Please help me answer this

KatRina [158]

Answer:

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Step-by-step explanation:

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3 years ago

1. 5 friends share 2 burritos.<br> Each friend gets<br> of the burrito.

DedPeter [7]

Answer:

2/5 each

Step-by-step explanation:

put 2 on top divided (shared) by 5 friends

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2 years ago

Write in logarithmic form: <img src="https://tex.z-dn.net/?f=5%5E%5Cfrac%7B-1%7D%7B2%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B5%7D%20%7D%7

Ket [755]

Answer:

Left-hand side: $\displaystyle -\frac{1}{2}\, \ln(5)$ .

Right-hand side: $\displaystyle \frac{1}{2}\, \ln(5) - \ln(5)$ .

Step-by-step explanation:

Apply the logarithm power rule: $\ln \left(x^{a}\right) = a\, \ln (x)$ for all $x >0$ .

This property is not only true for logarithm to the base $e$ , but for other bases, as well.

Take the logarithm (to the base $e$ ) of the left-hand side of this equation:

$\displaystyle \ln \left(5^{-1/2}\right) = (-1/2)\, \ln(5)$ .

For the right-hand side of this equation, consider the logarithm quotient rule:

$\displaystyle \ln \left(\frac{a}{b}\right) = \ln(a) - \ln (b)$ for all $a> 0$ and $b > 0$ .

Indeed, on the right-hand side of this equation, $\sqrt{5} > 0$ and $5 > 0$ . Therefore:

$\displaystyle \ln\left(\frac{\sqrt{5}}{5}\right) = \ln\left(\sqrt{5}\right) - \ln(5)$ .

This expression could be further simplified. Notice that $\sqrt{x}$ is equivalent to $x^{1/2}$ for all $x \ge 0$ . (Think about how $\sqrt{x} \cdot \sqrt{x} =x$ whereas $x^{1/2} \cdot x^{1/2} = x^{(1/2) + (1/2)} = x$ .)

Therefore, $\ln \left(\sqrt{5}\right)$ would be equivalent to $\ln\left(5^{1/2}\right)$ . Apply the logarithm power rule to show that $\displaystyle \ln\left(5^{1/2}\right) = \frac{1}{2}\, \ln(5)$ .

$\begin{aligned} \text{R.H.S.} &= \ln\left(\frac{\sqrt{5}}{5}\right) \\ &= \ln\left(\sqrt{5}\right) - \ln(5) \\ &= \frac{1}{2}\, \ln(5) - \ln (5) = -\frac{1}{2}\, \ln(5)\end{aligned}$ .

Indeed, the left-hand side of this equation matches the right-hand side.

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2 years ago