maggie123433

maggie123433

21.08.2019 •

Mathematics

Afootball team scored 529 points one season and then 376 points the next. about how many points less did the team score in the second season? round to the nearest ten.

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Ответ:

lordcaos066

10.11.2021

Option A -37.2°

Step-by-step explanation:

Given : Δ XYZ has vertices X(x_1,y_1)=(-1,-1) , Y(x_2,y_2)=(-2,1) and Z(x_3,y_3)=(1,2)

To find: Measure of angle Z (let $\theta$ )

Solution :

Since we know the vertices we find the slope of line by

Slope formula : $m=\frac{y_2-y_1}{x_2-x_1}$

Let m_1 be the slope between X and Z

$m_1=\frac{y_3-y_1}{x_3-x_1}$

$m_1=\frac{2-(-1)}{1-(-1)}$

$m_1=\frac{3}{2}$

Now, let m_2 be the slope between Y and Z

$m_2=\frac{y_3-y_2}{x_3-x_2}$

$m_2=\frac{2-1}{1-(-2)}$

$m_2=\frac{1}{3}$

Now, to find angle we apply angle-slope formula

Angle-slope formula → $tan\theta=\begin{vmatrix} \frac{m_1-m_2}{1+m_1m_2} \end{vmatrix}$

Putting values of slopes in the formula,

$tan\theta=\begin{vmatrix} \frac{\frac{3}{2}-\frac{1}{3}}{1+\frac{3}{2}\times\frac{1}{3}} \end{vmatrix}$

$tan\theta=\begin{vmatrix} \frac{\frac{7}{6}}{1+\frac{1}{2}} \end{vmatrix}$

$tan\theta=\begin{vmatrix} \frac{\frac{7}{6}}{\frac{3}{2}} \end{vmatrix}$

$tan\theta=\begin{vmatrix} \frac{7\times 2}{6\times 3} \end{vmatrix}$

$tan\theta=\begin{vmatrix} \frac{7}{9} \end{vmatrix}$

$tan\theta=\frac{7}{9}$

$\theta=tan^{-1}\frac{7}{9}$

$\theta=37.2^{\circ}$

Refer the attached graph

Therefore, ∠Z= 37.2° option A

Triangle xyz has vertices x(–1, –1), y(–2, 1), and z(1, 2). what is the approximate measure of angle

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