Use the following isosceles triangle to find valur of x and the length of ac.

1 answer:

3 0

Given that the triangle is isosceles, we can say that AB = AC. Using the given expressions we can form the following equation.

$\begin{gathered} AB=AC \\ 5x+8=7x-6 \end{gathered}$

Let's solve for x.

$\begin{gathered} 8+6=7x-5x \\ 14=2x \\ x=\frac{14}{2} \\ x=7 \end{gathered}$

Once we have the value of the variable, we can find the length of AC.

$\begin{gathered} AC=7x-6 \\ AC=7(7)-6 \\ AC=49-6 \\ AC=43 \end{gathered}$ <h2>Therefore, the length of AC is 43.</h2>

You might be interested in

How do you find the normal approximation without using the continuity correction?

Dennis_Churaev [7]

Let's say you want to compute the probability $\mathbb P(a\le X\le b)$ where $X$ converges in distribution to $Y$ , and $Y$ follows a normal distribution. The normal approximation (without the continuity correction) basically involves choosing $Y$ such that its mean and variance are the same as those for $X$ .

Example: If $X$ is binomially distributed with $n=100$ and $p=0.1$ , then $X$ has mean $np=10$ and variance $np(1-p)=9$ . So you can approximate a probability in terms of $X$ with a probability in terms of $Y$ :

$\mathbb P(a\le X\le b)\approx\mathbb P(a\le Y\le b)=\mathbb P\left(\dfrac{a-10}3\le\dfrac{Y-10}3\le\dfrac{b-10}3\right)=\mathbb P(a^*\le Z\le b^*)$

where $Z$ follows the standard normal distribution.