The LCM of the denominators is 120. In other words, the denominators can multiply to 120.
3 * 40 = 120
40 * 2 = 80
Tigers: P = 80/120
24 * 5 = 120
24 * 4 = 96
Redbirds: P = 96/120
8 * 15 = 120
3 * 15 = 45
Bulldogs P = 45/120
60 * 2 = 120
60 * 1 = 60
Titans P = 60/120
Answer
Tigers: P = 80/120
Redbirds: P = 96/120
Bulldogs: P = 45/120
Titans: P = 60/120
The vertex form of a quadratic function is:
f(x) = a(x - h)² + k
The coordinate (h, k) represents a parabola's vertex.
In order to convert a quadratic function in standard form to the vertex form, we can complete the square.
y = 2x² - 5x + 13
Move the constant, 13, to the other side of the equation by subtracting it from both sides of the equation.
y - 13 = 2x² - 5x
Factor out 2 on the right side of the equation.
y - 13 = 2(x² - 2.5x)
Add (b/2)² to both sides of the equation, but remember that since we factored 2 out on the right side of the equation we have to multiply (b/2)² by 2 again on the left side.
y - 13 + 2(2.5/2)² = 2(x² - 2.5x + (2.5/2)²)
y - 13 + 3.125 = 2(x² - 2.5x + 1.5625)
Add the constants on the left and factor the expression on the right to a perfect square.
y - 9.875 = 2(x - 1.25)²
Now, we need y to be by itself again so add 9.875 back to both sides of the equation to move it back to the right side.
y = 2(x - 1.25)² + 9.875
Vertex: (1.25, 9.875)
Solution: y = 2(x - 1.25)² + 9.875
Or if you prefer fractions
y = 2(x - 5/4)² + 79/8
Y = x² + 7x - 4
y = -x - 4
x² + 7x - 4 = -x - 4
+ x + x
x² + 8x - 4 = -4
+ 4 + 4
x² + 8x = 0
x(x) + x(8) = 0
x(x + 8) = 0
x = 0 or x + 8 = 0
- 8 - 8
x = -8
y = -x - 4
y = -0 - 4
y = 0 - 4
y = -4
(x, y) = (0, -4)
or
y = -x - 4
y = -(-8) - 4
y = 8 - 4
y = 4
(x, y) = (-8, 4)
The solutions are (0, -4) and (8, -4).
Step-by-step explanation:
Circumference
C = 3.14x3
C = 9.42cm
Area
A = 3.14xr²
A = 3.14x25
A = 78.5ft
Answer:
c = 420t . . . . c is calories burned; t is hours riding at 15 mph
Step-by-step explanation:
There is not enough information given to write a function rule relating all the variables to calories burned. If we assume that calories are burned at the constant rate of 420 calories per hour, then total calories will be that rate multiplied by hours:
c = 420·t
where c is total calories burned by the 154-lb person, and t is hours riding at 15 mph.
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In general, rates are related to quantities by ...
quantity = rate · time . . . . . where the rate is (quantity)/(time period)
