Question

Question 1 A)Hassan wants to add a border to a photo he took before he frames it. The final area of the entire framed picture will be 96 square inches. The length of the picture is 10 inches, and the width is 6 inches. Which of the following is the width of the border?(1 point) Responses 1 inch 1 inch 3 inches 3 inches 4 inches 4 inches 9 inches 9 inches Question 2 A)May’s class is testing their egg protection contraptions by dropping them off the roof of their school. Use GeoGebra to graph the situation using the formula y=−16t2+40. Which of the following correctly interprets the height of the school’s roof?(1 point) Responses 40 feet 40 feet 41 feet 41 feet 15 feet 15 feet 20 feet 20 feet Graphing Calculator Question 3 A)Luca is in a culvert below street level. He launches an object at an upward velocity of 40 feet per second. Use GeoGebra to graph the situation using the formula y=−16t2+40t−5. How far above or below street level is Luca’s initial launching point?(1 point) Responses 0 feet above or below 0 feet above or below 2.5 feet below 2.5 feet below 5 feet below 5 feet below 5 feet above 5 feet above Graphing Calculator Question 4 A)Which of the following scenarios would use a quadratic equation to solve?(1 point) Responses The trajectory of a balloon that rises 2 feet per second is modeled to find how high the balloon will be in 5 minutes. The trajectory of a balloon that rises 2 feet per second is modeled to find how high the balloon will be in 5 minutes. An accountant models the growth of a savings account that doubles every month to find how much will be in the account in 10 years. An accountant models the growth of a savings account that doubles every month to find how much will be in the account in 10 years. A child places a quarter into a piggy bank every week. A child places a quarter into a piggy bank every week. A coach models the trajectory of a ball to find out how high the player is kicking the ball. A coach models the trajectory of a ball to find out how high the player is kicking the ball. Graphing Calculator Question 5 A) Use the image to answer the question. A sports analyst graphed the trajectory of a soccer ball that was kicked by a goalkeeper. In the graph, x is the ball’s distance from the goalpost, and y is the height of the ball in meters. What was the goalkeeper’s distance from the goalpost when the ball was kicked? (1 point) Responses 2 meters 2 meters 6 meters 6 meters 0 meters 0 meters 4 meters 4 meters Graphing Calculator

Answer 1

Let's analyze each question one by one.

Question 1:

To find the width of the border, we need to calculate the area of the picture itself and then use the total area of the framed picture to find the dimensions including the border.

1. The area of the picture is \( \text{length} \times \text{width} = 10 \text{ inches} \times 6 \text{ inches} = 60 \text{ square inches} \).
2. The area of the framed picture is given as \( 96 \text{ square inches} \).
3. The area of the border is \( 96 - 60 = 36 \text{ square inches} \).
4. Let \( w \) be the width of the border. The dimensions of the framed picture including the border will be:
   • Length: \( 10 + 2w \)
   • Width: \( 6 + 2w \)

So the area equation becomes: \[ (10 + 2w)(6 + 2w) = 96
\]

Expanding this gives: \[ 60 + 20w + 12w + 4w^2 = 96
\] \[ 4w^2 + 32w - 36 = 0
\]

Dividing everything by 4: \[ w^2 + 8w - 9 = 0
\]

Using the quadratic formula: \[ w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-8 \pm \sqrt{64 + 36}}{2} = \frac{-8 \pm 10}{2} \]

Calculating gives us:

1. \( w = 1 \)
2. \( w = -9 \) (not a valid answer)

Thus, the width of the border is 1 inch.

Question 2:

The formula given is \( y = -16t^2 + 40 \). The maximum height occurs when \( t = 0 \): At \( t = 0 \), \( y = 40 \). So, the height of the school’s roof is 40 feet.

Question 3:

The formula given is \( y = -16t^2 + 40t - 5 \). To find the initial launching point (the value of \( y \) when \( t = 0 \)): \[ y = 40(0) - 5 = -5 \] So, Luca’s initial launching point is 5 feet below street level.

Question 4:

The correct scenario that uses a quadratic equation is: A coach models the trajectory of a ball to find out how high the player is kicking the ball.

Question 5:

Since this question references an image that’s not provided, I’ll assume a standard situation where: If the graph starts at \( (0, h) \), where \( h \) is the initial height, then the goalkeeper’s distance from the goalpost when the ball was kicked would most likely be \( 0 \) meters, as it would represent the starting point of the kick.

Responses Recap:

1. 1 inch
2. 40 feet
3. 5 feet below
4. A coach models the trajectory of a ball to find out how high the player is kicking the ball.
5. 0 meters.

If you have any further questions or need clarifications, feel free to ask!