Answer:
(1) 2π - x² = 0 (2) x = 2.5 cm (3) perimeter = 10 cm
Step-by-step explanation:
(1)The area of the circular coin without the inner square removed is πr² where r = 3 cm is the radius of the coin. So, the area of the coin without the inner square removed is πr² = π(3 cm)² = 9π cm²
The area of the square of x sides removed from its center is x².
The area A of the each face of the coin is thus A = 9π - x²
Since the area of each face of the coin A = 7π cm²,
then
7π = 9π - x²
9π - 7π - x² = 0
2π - x² = 0
(2) Solve the equation 2π - x² = 0
2π - x² = 0
x² = 2π
x = ±√(2π)
x = ± 2.51 cm
Since x cannot be negative, we take the positive answer.
So, x = 2.51 cm
≅ 2.5 cm
(3) Find the perimeter of the square
The perimeter of the square, p is given by p = 4x
p = 4 × 2.51 cm
= 10.04 cm
≅ 10 cm
Answers are in bold:
-1=3x-2
add 2 to both sides
-1+2=3x-2+2
1=3x
divide both sides by 3
1÷3=3x÷3
1/3=x
-3x=9
divide both sides by -3
-3x÷-3=9÷-3
x=-3
-10=-5x
divide both sides by -5
-10÷-5=-5x÷-5
2=x
I hope this is good enough:
57 - 4t > = 13.....subtract 57 from both sides
-4t > = 13 - 57
-4t > = - 44 ...divide both sides by -4, and change the inequality sign
t < = -44 / -4
t < = 11
u solve inequalities much like u do equations except for one very important rule. In an inequality, if u divide/multiply by a negative number, u have to change the inequality sign.
Answer:
Step-by-step explanation:
Use the point-slope formula.
y - y_1 = m(x - x_1) .... x_1 = 3 and y_1 = - 1
m is the slope to x - 3y = 9 because (lines are parallel )
calculate : m by equation x - 3y = 9 :
x = 3y +9
divid by : 3 1/3 x = y + 3
y = (1/3) x - 3 so : m = 1/3
an equation parallel to x - 3y = 9 that passes through the point ( 3, -1 ) is :
y +1 = (1/3)(x - 3)
Answer:
32 orders
Step-by-step explanation:
# of orders = 2^5=32 different orders
