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3 years ago

What's the inequality describes all possible length of AB?

Mathematics

1 answer:

romanna [79]3 years ago

5 0

Answer:

We conclude that inequality describes all possible lengths of AB

13 < x < 35

Option C is true.

Step-by-step explanation:

We know that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Now, checking the interval of the length of the side 'x', such as:

24 + 11 = 35

24 - 11 = 13

so the possible lengths of the side 'x' will be:

13 < x < 35

Therefore, we conclude that inequality describes all possible lengths of AB

13 < x < 35

Hence, option C is true.

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What’s the right answer

ruslelena [56]

Answer:

false

Step-by-step explanation:

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3 years ago

Find x?<br> In 3x - In(x - 4) = ln(2x - 1) +ln3

earnstyle [38]

Answer:

$x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

Step-by-step explanation:

Because $3\, x$ is found in the input to a logarithm function in the original equation, it must be true that $3\, x > 0$ . Therefore, $x > 0$ .

Similarly, because $(x - 4)$ and $(2\, x - 1)$ are two other inputs to the logarithm function in the original equation, they should also be positive. Therefore, $x > 4$ .

Let $a$ and $b$ represent two positive numbers (that is: $a > 0$ and $b > 0$ .) The following are two properties of logarithm:

$\displaystyle \ln (a) + \ln(b) = \ln\left(a \cdot b\right)$ .

$\displaystyle \ln (a) - \ln(b) = \ln\left(\frac{a}{b}\right)$ .

Apply these two properties to rewrite the original equation.

Left-hand side of this equation:

$\begin{aligned}&\ln(3\, x) - \ln(x - 4)= \ln\left(\frac{3\, x}{x -4}\right)\end{aligned}$

Right-hand side of this equation:

$\ln(2\, x- 1) + \ln(3) = \ln\left(3 \left(2\, x - 1\right)\right)$ .

Equate these two expressions:

$\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ .

The natural logarithm function $\ln$ is one-to-one for all positive inputs. Therefore, for the equality $\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ to hold, the two inputs to the logarithm function have to be equal and positive. That is:

$\displaystyle \frac{3\ x}{x - 4} = 3\, (2\, x - 1)$ .

Simplify and solve this equation for $x$ :

$x^2 - 5\, x + 2 = 0$ .

There are two real (but not rational) solutions to this quadratic equation: $\displaystyle \frac{5 + \sqrt{17}}{2}$ and $\displaystyle \frac{5 - \sqrt{17}}{2}$ .

However, the second solution, $\displaystyle \frac{5 - \sqrt{17}}{2}$ , is not suitable. The reason is that if $x = \displaystyle \frac{5 - \sqrt{17}}{2}$ , then $(x - 4)$ , one of the inputs to the logarithm function in the original equation, would be smaller than zero. That is not acceptable because the inputs to logarithm functions should be greater than zero.

The only solution that satisfies the requirements would be $\displaystyle \frac{5 + \sqrt{17}}{2}$ .

Therefore, $x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

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3 years ago

LeBron goes to the store with six dollars and buys four packs of gum. James goes to the store with five dollars and buys two pac

lilavasa [31]

G = the cost of one pack of gum
LeBron : 6 - 4g
James : 5 - 2g

what they both have after buying gum..
6 - 4g + 5 - 2g = 11 - 6g

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3 years ago

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Find the average rate of change of f(x)= x^3 over the interval -2 to 3

Travka [436]

48.012001 is the answer to this problem

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3 years ago

Mark values his drum set at $800 and ella values her guitar at $1,000. suppose that mark trades his drum set for ella's guitar.

Novosadov [1.4K]

If they made this trade, it would make sense that Mark would also have to give Ella $200. This is because the difference in value is that amount in the favor of Ella. You can see that by subtracting the two values from each other.

$1000 - $800 = $200

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4 years ago