Question

(02.06) which of the following is a solution of 4x² = - 9x - 4? a. $\frac{9pmsqrt{17}}{8}$ b. $\frac{-9pmsqrt{145}}{8}$ c. $\frac{9pmsqrt{145}}{8}$ d. $\frac{-9pmsqrt{17}}{8}$ pregunta 5 (2 puntos) (02.06) if a football player passes a football from 4 feet off the ground with an initial velocity of 6 feet per second, how long will it take the football to hit the ground? use the equation h = -16t² + 6t + 4. round your answer to the nearest hundredth. a. 0.72 b. 0.65 c. 0.35 d. 0.27

Explanation:

Step1: Rewrite first equation in standard form

$4x^{2}+9x + 4=0$. For a quadratic equation $ax^{2}+bx + c = 0$ ($a = 4$, $b=9$, $c = 4$), the quadratic - formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.

Step2: Calculate the discriminant $\Delta=b^{2}-4ac$

$\Delta=(9)^{2}-4\times4\times4=81 - 64=17$.

Step3: Find the solutions using the quadratic formula

$x=\frac{-9\pm\sqrt{17}}{8}$.

Step4: Solve the second problem. Set $h = 0$ in $h=-16t^{2}+6t + 4$

We get $-16t^{2}+6t + 4 = 0$. Divide through by - 2 to simplify: $8t^{2}-3t - 2=0$. Here $a = 8$, $b=-3$, $c=-2$.

Step5: Calculate the discriminant for the second - equation

$\Delta=(-3)^{2}-4\times8\times(-2)=9 + 64 = 73$.

Step6: Find the solutions using the quadratic formula

$t=\frac{3\pm\sqrt{73}}{16}$. We take the positive root since time cannot be negative. $t=\frac{3+\sqrt{73}}{16}\approx\frac{3 + 8.544}{16}=\frac{11.544}{16}\approx0.72$.

Answer:

1. d. $\frac{-9\pm\sqrt{17}}{8}$
2. a. $0.72$