A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC onto ∆A′B′C′ is a followed by

Answer: B: n^2+6n+1

Step-by-step explanation:

A=n

B=2n+6

C=n^2-1

AB-C

n(2n+6)-n^2-1

2n^2+6n-n^2+1

n^2+6n+1

Answer:

The regression line is not an appropriate model due to the existence of a pattern in the residual plot.

Step-by-step explanation:

A residual plot has been provided for a certain data set.

The residual plot indicates a scatter relationship between x and y.

The plotted points demonstrate that a linear relation is unlikely; it appears to be more parabolic or exponential in nature.

This suggests the regression line is not a suitable model as the residuals do not converge towards 0.

Additionally, a linear trend pattern is absent.

D) The regression line is not a suitable model as it exhibits a pattern in the residual plot.

The maximum area that can be enclosed is 64 ft². To achieve the largest area while minimizing the perimeter, the dimensions should be as equal as possible. Allocating 32 feet of fencing for four sides gives us 8 feet per side, resulting in a square with a side length of 8; thus, the area equals 8*8 = 64.

To formulate a system of equations for Naomi and Hudson, who work at a dry cleaners where Naomi can iron 35 shirts per hour and Hudson can manage 20 shirts per hour, we know that together they worked 13 hours and completed a total of 395 shirts. Naomi, during her 13 hours, could potentially iron 455 shirts (13 x 35), meaning each hour Hudson worked lessens that number by 15 shirts. The difference of 60 shirts (455 - 395) indicates that Hudson worked for 3 hours and Naomi, therefore, for 10 hours. The resulting equation reflects this relationship: 35Y + 20X = 395.

The bus's speed is calculated as: velocity (bus) = 36 miles / 40 min, which simplifies to velocity (bus) = 0.9 miles / min. Given that the car's speed is 1.5 times that of the bus, we find: velocity (car) = 1.5 * 0.9 miles / min, leading to velocity (car) = 1.35 miles / min. At the point where they meet, the total distance covered equals 36 miles. Hence: 1.35 t + 0.9 t = 36, and thus 2.25 t = 36 resulting in t = 16 min. They will converge after 16 minutes.