The accurate selections are: 1. For both families, the graph representing the connection between the number of pizzas (x) and the amount of slices (y) intersects at the origin (0, 0) and forms a straight line. 2. If the Wilson family orders 3 large pizzas from the same pizza shop as the Hernandez family, they will have a greater number of slices than the Hernandez family once the pizzas are sliced. The equations for the relationships between total slices (y) and pizzas ordered (x) are as follows: y = a × x, where 'a' indicates slices per pizza. For the Hernandez family, we have y = 24 when x = 3, resulting in a = 24/3 = 8 slices per pizza, producing the equation y = 8 × x. For the Wilson family, the relationship is represented by y = 10 × x. When both families’ equations are plotted, the result is straight-line graphs with a y-intercept of 0, meaning they pass through (0, 0). Thus, if the Wilsons order 3 large pizzas, they will have y = 10 × 3 = 30 slices, exceeding the Hernandez family's 24 slices.
From a distance of 300 feet, a car approaches you at a speed of 48 feet per second. The distance d (in feet) of the car from you after t seconds can be described by the equation d=|300−48t|. At what moments does the car find itself 60 feet away from you?
Answer:
Detailed steps:
y – 4 = –1 (x – 2)
y – 7 = –1 (x + 1)
y = –x + 6
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Answer: To eliminate the y terms and solve for x with minimum steps, we should multiply the first equation by 9 and the second equation by -4.
Step-by-step explanation:
Given: Equation (1) 5x − 4y = 28
Equation (2) 3x - 9y = 30
To eliminate the y-terms and determine x in the fewest operations, it requires us to multiply equation (1) by 9 and equation (2) by -4 to have
9(5x − 4y) =9 (28) ⇒ 45x - 36y = 252
-4(3x - 9y) = -4(30) ⇒ -12x + 36y = -120
By adding both equations together, the y-term is eliminated, leading to 45x - 12x = 132
⇒ 33x = 132 ⇒ x = 4.
