Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
To calculate m use the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (2,2) and (x₂, y₂ ) = (8, 5) ← 2 points on the line
m = 
= 
= 
the line crosses the y-axis at (0, 1) ⇒ c = 1
y = x + 1 ← equation in slope- intercept form
Desmond's times are proportional. for every 2 laps he takes 146
146 / 2 = 73
292 / 4 = 73
584 / 8 = 73
Maria's time are not proportional
150 / 2 = 75
320 / 4 = 80
580 / 6 = 96.67
Answer:
-1.
Step-by-step explanation:
First find the derivative of f(x):
f'(x) = -3x^2 + 12x - 9 = 0 for a maximum or minimum.
-3(x^2 - 4x + 3) = 0
(x - 1)(x - 3) = 0
x = 1, 3.
To find which gives a relative maximum we find the second derivative:
f"(x) = -6x + 12
When x = 1 f"(x) = 6, positive.
when x = 3, f"(x) = -6, negative.
So x = 3 gives a maximum value of f(x).
f(3) = -(3)^3 + 6*(3)^2 - 9(3) - 1 = -1 (answer).
Answer:
460 m
Step-by-step explanation:
Use right triangle PSR with right angle S to find the length of PS.
The Pythagorean theorem can be used for this.
a^2 + b^2 = c^2
(PS)^2 + (SR)^2 = (PR)^2
(PS)^2 + (150 m)^2 = (170 m)^2
(PS)^2 = 22500 m^2 = 28900 m^2
(PS)^2 = 6400 m^2
PS = 80 m
PS = 80 m; SR = 150 m
perimeter = 2(length + width)
perimeter = 2(150 m + 80 m)
perimeter = 2(230 m)
perimeter = 460 m
He would need 24 more sales. 24 sales at $14.25 each = $342.
$342
+$375
-----------
$717
