I think it is x= 125
if y=2 and x=50
then y=1 must be x=25
so, y=3 is x=75
y=4 is x=100
and y=5 is x=125
2 (d(h+w) + h w) is the surface area
When we divide the figure in four parts, we obtain four squares with its sides of 5 centimeters of lenght, with quarter circles (two) in each one of them. The limits of the shadded area are arcs of cirncunference
To calculate the area of the shadded part, we must choose one square of 5cmx5cm and divide it in 3 sectors:
a: the area below the shaded area.
b: the area above the shaded area.
c: the shaded area.
The area of the square (As) is:
As=L²
As=(5 cm)²
As=25 cm²
The area of a circunference is: A=πR² (R:radio), but we want the area of the quarter circle, so we must use A=1/4(πR²), to calculate the area of the sectors a+c:
A(a+c)=1/4(π(5)²)
A(a+c)=25π/4
The area of the sector "b" is:
Ab=As-A(a+c)
Ab=25-25π/4
Ab=25(1-π/4)
The area of the sector a+b, is:
A(a+b)=2Ab
A(a+b)=2x25(1-π/4)
A(a+b)=50(1-π/4)
Then, the shadded area (Sector c) is:
Ac=As-A(a+b)
Ac=25-50(1-π/4)
Ac=25-(50-50π/4)
Ac=25-50+50π/4
Ac=(50π/4)-25
Ac=(25π/2)-25
Ac=25(π/2-1)
The area of each shaded part is: 25(π/2-1)
To calculate the perimeter of a shaded part, we must remember that the perimeter of a circunference is: P=2πR. If we want the perimeter of a quarter circle we must use: P= 2πR/4. But there is two quarter circles in the square of 5cmx5cm, so the perimeter of the shaded area is:
P=2(2πR/4)
P=4πR/4
P=πR
P=5π
The perimeter of each shaded part is: 5π
The right answer is Option B: 7p+12t=62
Step-by-step explanation:
Given,
Amount spent by Art and his friends = $62
Cost of one ticket = $12
Cost of t tickets = 12t
Cost of one bucket of popcorn = $7
Cost of p buckets of popcorn =7p
According to given statement;
7p+12t=62
7p+12t=62 represents the number of tickets bought, t, and the number of buckets of popcorn bought, p.
The right answer is Option B: 7p+12t=62
Keywords: addition, linear equation
Learn more about linear equations at:
#LearnwithBrainly
Let x be the number of months.
The first plan is 15 dollars sign up fee and 38 dollars per month. So the equation is 38x + 15.
The second plan is 78 dollars as sign up fee and 31 dollars per month. So the equation is 31x + 78.
We need find when x has the same value in both equations, so we do their equality:
38x + 15 = 31x + 78
Let's subtract 15 from both sides
38x + 15 = 31x + 78
38x + 15 - 15 = 31x + 78 - 15
38x = 31x + 63
Now let's subtract 31x from both sides to have the variables on a side and the numbers on side:
38x = 31x + 63
38x - 31x = 31x - 31x + 63
7x = 63
Divide both sides by 7 to have the variable x on a side and its value on the other:
(7x)/7 = 63/7
x = 9
So at month 9, the 2 plans will cost the same.
Let's check our answers, and let y be the cost:
y = 38x + 15 = 38*9 + 15 = 357
y = 31x + 78 = 31*9 + 78 = 357
Our answer has been approved.
Hope this helps! :D
