Hi there,
$167.67 - base fee
$167.67 - $17.95
= $149.72
Divide the remaining amount by the
cost per mile.
$149.72 / $0.76
= 197
Boris drove 197 miles.
Hope this helps :-)
a. The general equation for a circle centered at with radius is
The described circle has equation
We know the circle passes through the origin. This means that the equation above holds for and . The distance between any point on the circle and its center is the radius, so we can use this fact to determine :
So the circle's equation is
b. If the distance between point B and the center is less than , then B lies inside the circle. If the distance is greater than , it falls outside the circle. Otherwise, if the distance is exactly , then B lies on the circle.
The distance from B to the center is
, so , which means B falls outside the circle.
We let x and y be the measures of the sides of the rectangular garden. The perimeter subtracted with the other side should be equal to
2x + y = 92
The value of y in terms of x is equal to,
y = 92 – 2x
The area is the product of the two sides,
A = xy
Substituting,
A = x (92 – 2x) = 92x – 2x2
Solving for the derivative and equating to zero,
0 = 92 – 4x ; x = 23
Therefore, the area of the garden is,
<span> A = 23(92 – 2(23)) = 1058 yard<span>2</span></span>
Z^2−6z−27=0
Factor left side of equation.
(z+3)(z−9)=0
Set factors equal to 0.
z+3=0 or z−9=0
z=−3 or z=9
<h3>
The constant of proportionality is k = 5</h3>
For direct proportion equations, you divide the y value over its corresponding x value to get the value of k.
For example, the point (x,y) = (2,10) is on the diagonal line. So k = y/x = 10/2 = 5.
Another example: the point (x,y) = (6, 30) is also on the same diagonal line, so k = y/x = 30/6 = 5 is the same result as before.
You can use any point on the diagonal line as long as it is not (0,0). This is because division by zero is not allowed.
side note: the direct proportion equation y = k*x becomes y = 5*x which is the graph of that diagonal line. The slope is m = 5, the y intercept is b = 0. All direct proportion graphs go through the origin as shown in the diagram.