Question

question 9 (multiple choice worth 1 points) (08.04 mc) akces wants to hang a mirror in his boat and put a frame around it. the mirror and frame must have an area of 19.25 square feet. the mirror is 3 feet wide and 5 feet long. which quadratic equation can be used to determine the thickness of the frame, ( x )? ( 2x^2 + 8x - 19.25 = 0 ) ( 3x^2 + 5x - 19.25 = 0 ) ( 4x^2 + 16x - 4.25 = 0 ) ( 4x^2 + 16x + 15 = 0 ) question 10 (multiple choice worth 1 points) (08.04 mc) ann pitches a baseball at an initial height of 6 feet with a velocity of 73 feet per second. this can be represented by the function ( h(t) = -16t^2 + 73t + 6 ). if the batter misses, about how long does it take the ball to hit the ground? 4.64 seconds 2.34 seconds 2.28 seconds 0.08 seconds you must check the box below prior to submitting your exam! check this box to indicate you are ready to submit your exam

Explanation:

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Question 9

Step1: Define total width/height

Total width: $3 + 2x$, Total height: $5 + 2x$

Step2: Set area equation

$$(3+2x)(5+2x)=19.25$$

Step3: Expand left side

$$15 + 6x + 10x + 4x^2 = 19.25$$

Step4: Simplify to quadratic

$$4x^2 + 16x - 4.25 = 0$$

Step1: Set $H(t)=0$ (ground height)

$$-16t^2 + 73t + 6 = 0$$

Step2: Use quadratic formula $t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here $a=-16$, $b=73$, $c=6$
$$t=\frac{-73\pm\sqrt{73^2-4(-16)(6)}}{2(-16)}$$

Step3: Calculate discriminant

$$\sqrt{5329 + 384}=\sqrt{5713}\approx75.58$$

Step4: Solve for positive $t$

$$t=\frac{-73 - 75.58}{-32}=\frac{-148.58}{-32}\approx4.64$$

Answer:

$4x^2 + 16x - 4.25 = 0$

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Question 10