Diameter = 2*(radius)
The radius is half of the diameter, so if you were given the radius and need to find the diameter, multiply the radius by two. If you were given the diameter and need to find the radius, divide the dimaeter by two
We have to present the number 41 as the sum of two squares of consecutive positive integers.
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
16 + 25 = 41
<h3>Answer: 4 and 5</h3>
Other method:
n, n + 1 - two consecutive positive integers
The equation:
n² + (n + 1)² = 41 <em>use (a + b)² = a² + 2ab + b²</em>
n² + n² + 2(n)(1) + 1² = 41
2n² + 2n + 1 = 41 <em>subtract 41 from both sides</em>
2n² + 2n - 40 = 0 <em>divide both sides by 2</em>
n² + n - 20 = 0
n² + 5n - 4n - 20= 0
n(n + 5) - 4(n + 5) = 0
(n + 5)(n - 4) = 0 ↔ n + 5 = 0 ∨ n - 4 =0
n = -5 < 0 ∨ n = 4 >0
n = 4
n + 1 = 4 + 1 = 5
<h3>Answer: 4 and 5.</h3>
Solve your system of equations step by step.
x−2y=14;x+3y=9
Solve x−2y=14 for x:
x−2y+2y=14+2y (Add 2y to both sides)
x=2y+14
Substitute (2y+14) for x in x+3y=9:
x+3y=9
2y+14+3y=9
5y+14=9(Simplify both sides of the equation)
5y+14+−14=9+−14 (Add -14 to both sides)
5y=−5
5y5=−55 (Divide both sides by 5)
y=−1
Substitute (−1) for y in x=2y+14:
x=2y+14
x=(2)(−1)+14
x=12(Simplify both sides of the equation)
So,
y=-1
x=12
Answer is C)
Part A:
Circumference = πd
Circle A: d = 7
7π = 21.98
π = 21.98/7 = 3.14
Circle B: d = 6
6π = 18.84
π = 3.14
Part B:
Area = πr^2
Circle A: r = 3.5
π3.5^2 = 38.465
12.25π = 38.465
π = 3.14
Circle B: r = 3
π3^2 = 28.26
9π = 28.26
π = 3.14
Part C: The value of π is the same in circles A and B
