Question

in the triangle shown, what is the value of tan x°? a) $\frac{1}{26}$ b) $\frac{19}{26}$ c) $\frac{26}{7}$ d) $\frac{33}{7}$ the scatter - plot shows the relationship between x and y. a line of best fit is also shown. which of the following is closest to the slope of the line of best fit shown? a) - 2.27 b) - 0.44 c) 0.44 d) 2.27

Explanation:

Step1: Recall tangent formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For angle $x^{\circ}$, the side opposite to $x^{\circ}$ has length 26 and the side adjacent to $x^{\circ}$ has length 7.

Step2: Calculate $\tan x^{\circ}$

$\tan x^{\circ}=\frac{26}{7}$

Step1: Recall slope formula

The slope $m$ of a line is given by $m = \frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$. We can choose two points on the line of best fit. Let's choose $(1,1)$ and $(5,3)$.

Step2: Calculate the slope

$m=\frac{3 - 1}{5 - 1}=\frac{2}{4}=0.5$. The value closest to 0.5 among the options is 0.44.

Answer:

C. $\frac{26}{7}$