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
Answer:
6(8w + 7x)
Step-by-step explanation:
Hello!
The greatest common factor between 48 and 42 is 6. We can factor out 6 from each term.
<h3>Factor</h3>
- 48w + 42x
- 6(8w) + 6(7x)
- 6(8w + 7x)
The expression is 6(8w + 7x).
Answer:
Step-by-step explanation:
Slope-intercept form of an equation is written as 
, where 
is the slope and 
is the y-intercept.
The slope of a line that passes through the points 
and 
is 
. Using the coordinates 
and 
as given in the problem, we have slope of this line to be:
.
Now using this slope we've found and any point the line passes through, we can find the y-intercept of this equation:
Therefore, the equation of this line in slope-intercept form is 
.
