Answer:
{1, 2, 3}, {3, 4, 5}
Step-by-step explanation:
Write expressions for three consecutive integers: n, n + 1, n + 2.
Set up an equation for the verbal description: the product (mulitplication) of the two larger integers (the last two) is one less than 7 times the smallest (the first one).
(n + 1)(n + 2) = 7n - 1
Multiply (FOIL) the left side.
n^2 + 3n + 2 = 7n - 1
Subtract 7n and subtract 1 to make the right side 0.
n^2 - 4n + 3 = 0
Factor.
(n - 1)(n - 3) = 0
Set the two factors equal to 0
n - 1 = 0, n - 3 = 0
Solve for n.
n = 1, n = 3
One set of integers begins with 1, so it's {1, 2, 3}.
The other set begins with 3, so it's {3, 4, 5}
Answer:
Winchester Heights Middle School plan to have 385 students in the upcoming school year.
Step-by-step explanation:
Total number of students in the seventh grade at Winchester Heights Middle School = 350
For the upcoming school year, they are planning to increase the number of seventh graders by 10%.
Rate of increase = r = 10% = 0.1
Formula :
Where 
= initial population = 350
r = rate of increase =0.1
N(t)=Population after t years
t = time in years
So, Population after 1 year = 
Hence Winchester Heights Middle School plan to have 385 students in the upcoming school year.
Answer:
x= 50
Step-by-step explanation:
7/x = 14/100
14x = 700
x = 50
the reason behind my calculations were to get the same ratios and because they gave us percentage and the actual number, we can set them; 14 percent 14/100, however, the 7/x is because we don't know the 100 percent of the coins which is what we look for. Therefore, you cross multiply and get x.
I hope this helped
Answer:
756
Step-by-step explanation:
The ratio of areas is the square of the scale factor.
First, we find the scale factor from the blue solid to the red solid.
scale factor = 6/4 = 3/2
The ratio of areas is the square of the scale factor:
ratio of areas = (3/2)^2 = 9/4
volume of red solid = volume of blue solid * ratio of areas
volume of red solid = 336 m^2 * 9/4 = 756 m^2
Answer: S = 756 m^2
