solve each proportion. 3) -7/4=-8/b a) 8 b) 4.57 c) 7 d) 9 find the missing side lengths. leave your answers…

solve each proportion. 3) -7/4=-8/b a) 8 b) 4.57 c) 7 d) 9 find the missing side lengths. leave your answers 4) a) x = 14√3, y = 7√3 b) x = 14, y = 7√3 c) x = 7√3, y = 14√3 d) x = 7√3, y = 14

solve each proportion. 3) -7/4=-8/b a) 8 b) 4.57 c) 7 d) 9 find the missing side lengths. leave your answers 4) a) x = 14√3, y = 7√3 b) x = 14, y = 7√3 c) x = 7√3, y = 14√3 d) x = 7√3, y = 14

Answer

Explanation:

Step1: Solve the proportion

Cross - multiply the proportion $-\frac{7}{4}=-\frac{8}{b}$. We get $-7b=-32$.

Step2: Isolate the variable

Divide both sides of the equation $-7b = - 32$ by $-7$. So $b=\frac{32}{7}\approx4.57$.

Step3: Analyze the right - triangle

In a right - triangle with an angle of $30^{\circ}$, if the side opposite the $30^{\circ}$ angle is $7$ (assume this is the given side). The hypotenuse $y$ is related to the side opposite the $30^{\circ}$ angle by the rule $y = 2\times$ (side opposite $30^{\circ}$ angle), so $y = 14$. The side adjacent to the $30^{\circ}$ angle $x$ can be found using the Pythagorean theorem or the relationship $x=\sqrt{y^{2}-7^{2}}=\sqrt{14^{2}-7^{2}}=\sqrt{(14 + 7)(14 - 7)}=\sqrt{21\times7}=7\sqrt{3}$.

Answer:

  1. B. $4.57$
  2. D. $x = 7\sqrt{3},y = 14$