Answer:
a) The radius of the wheel is 1) more than 25.0 cm.
b) The radius of the wheel is approximately 40.925556... cm
Step-by-step explanation:
S = rθ is the formula to find the radius of the wheel using the arc and the angle discovered, S being the arc and θ the angle. The angle, however, must be in radians. θ = 
is used to convert it. So:
θ =
θ = 
S = rθ
25 = r
900 = 7
r
r = 
r = 40.925556... cm
Answer: Jenny was faster by 116.17
Step-by-step explanation: Jenny: 809.03 meters a minute
Johnny: 692.86 meters a minute
Mary = 3x
Seth = X
If we know that Mary is three times older than Seth, we can set this up into an equation.
3x + x = 76
Now, we can simplify on the left side by adding the Xs together.
4x = 76
X = 19
Therefore, Seth is 19 years old and Mary is 57 years old.
Answer:
(-2, 7); (See attachment)
Step-by-step explanation:
x + 2y = 12
7x + 2y = 0
x + 2y = 12
x = -2y + 12
Solve for y:
7x + 2y = 0
7 (-2y + 12) + 2y = 0
-12y + 84 = 0
-12y = -84
y = 7
Solve for x:
x = -2y + 12
x = -2 (7) + 12
x = -2
x = -2, y = 7
The coefficient of x in the equation of the given line, 3, is its slope. The slope of the perpendicular line is the negatve reciprocal of that, -1/3. You now have the slope and a point on the perpendicular line, so you can write its equation using the point-slope form:
y = m(x -x₁) +y₁
where m is the slope and (x₁, y₁) is the point.
An equation for your perpendicular line is
y = (-1/3)(x -(-1)) -3
y = (-1/3)x -10/3
The slope-intercept form of the equation of the perpendicular line is ...
y = (-1/3)x -10/3
