Question

1) Dados os pontos A (1/4, 1/2) e B (2/3, 3/4). Calcule:

A- a equação da reta que passa pelos pontos A e B.
B- f( 1 ).
C- X para que f(x)= 2

Answer 1

Resposta:

$\left[\begin{array}{ccccc}x&y&1&x&y&\frac{1}{4}&\frac{1}{2}&1&\frac{1}{4}&\frac{1}{2}&\frac{2}{3}&\frac{3}{4}&1&\frac{2}{3}&\frac{3}{4}\end{array}\right]=0\\\\a)(&\frac{x}{2}+&\frac{2y}{3}+&\frac{3}{16})-&\frac{y}{4}-&\frac{3x}{4}-&\frac{1}{3}=0\\\\&\frac{24x+32y+9-12y-36x-16}{48}=0\\24x-36x+32y-12y+9-16=0\\-12x+20y-7=0\\E.reduzida;\\20y=12x+7\\y=\frac{12x}{20}+\frac{7}{20}\\A)\boxed{y=\frac{3}{5}x+\frac{7}{20}}$

$B)f(1)=y=\frac{3}{5}x+\frac{7}{20}\\y=(\frac{3}{5}*1)+\frac{7}{20}\\y=\frac{3}{5}+\frac{7}{20}\\y=\boxed{\frac{19}{20}}\\\\\\C)f(x)=2\\2=\frac{3}{5}x+\frac{7}{20}\\40=12x+7\\40-7=12x\\33=12x\\x=\frac{33}{12}\\C)\boxed{x=\frac{11}{4}}$

Explicação passo-a-passo: