Question
Consider this system of equations. Which shows the second equation written in slope-intercept form?
A. 
B. 
C. 
D. 
Response:
B.
Detailed explanation:
Given
Equation 1:
Equation 2:
Required:
Equivalent of equation 2
To achieve an equivalence of equation 2 (in slope-intercept form), we must first simplify it
Open the brackets
Simplify the fractions
Divide by 2
Re-arrange
Next, we compare options A through D with
A. is not equal to
Next, we check the second option
B.
matches
This option represents the second equation in slope-intercept format.
We check for further options
C.
Convert the fraction into a decimal
This does not equal
D.
Convert the fraction to decimal
This also does not equal to
Therefore, the only option equivalent to the second equation in slope-intercept form is Option B
<span>Determine the configuration of columns and rows for the rectangular arrangement of 120 cupcakes.
=> There must be an even number of rows and an odd number of columns.
=> 120 = 2 x 2 x 2 x 15
=> 120 = 8 x 15
=> 120 = 120
Consequently, the glee club should organize the cupcakes in 8 rows and 15 columns.
This totals up to 120 cupcakes altogether.
</span>
Answer:
Each of the 4 arrangements will produce a rectangle.
Explanation:
Transforming a rectangle through rotation or translation will not alter its rectangular shape. This principle also applies when reflecting it across any axis. Thus, every sequence among the four provided will result in a rectangle.
<span>15000 feet
The height of Mt. Whitney is listed as 14,505 feet. To round this figure to the closest thousand, we examine the hundreds digit, which is 5. According to the rounding rule, "5 or above, round up, 4 or below, round down". Given that the digit is 5, we round up to yield 15000 feet</span>
The average speed for his entire journey from York to Blackpool is about 61.41 km/h.
Here’s a breakdown of how we arrive at this:
The distance he travelled from York to Leeds is 45 km,
and the speed during that section was 54 km/h.
Therefore, the time taken to travel from York to Leeds is 45/54 hours (since Time = Distance/Speed).
Next, the distance from Leeds to Blackpool is 42 km,
and the time for that leg of the journey is 35 minutes, which is 35/60 hours.
This leads to the total duration for his trip as
hours.
The cumulative distance covered equals 45 + 42 = 87 km.
Thus, his average speed is calculated as:
