32% = 0.32
we know that 0.32 × a number = 8
we can set this number as the variable x
0.32 x = 8
÷0.32 ÷0.32
x = 8
therefore the number is 8
Multiplication because you undo it
Let x = Wally's age now
Then, 3x = Jose's age now
Wally's age 5 years from now = x+5
Jose's age 5 years from now = 3x+5
(x+5) + (3x+5) = 42
4x + 10 = 42
4x = 32 x = 8
Wally is 8 years old and Jose is 24.
Answer:
(- 2, - 9 )
Step-by-step explanation:
The axis of symmetry passes through the vertex of the parabola.
Thus the x- coordinate of the vertex is x = - 2
To find y substitute x = - 2 into f(x)
f(- 2) = (- 2)² + 4(- 2) - 5 = 4 - 8 - 5 = - 9
Vertex = (- 2, - 9 )
First, let's use the given information to determine the function's amplitude, midline, and period.
Then, we should determine whether to use a sine or a cosine function, based on the point where x=0.
Finally, we should determine the parameters of the function's formula by considering all the above.
Determining the amplitude, midline, and period
The midline intersection is at y=5 so this is the midline.
The maximum point is 1 unit above the midline, so the amplitude is 1.
The maximum point is π units to the right of the midline intersection, so the period is 4 * π.
Determining the type of function to use
Since the graph intersects its midline at x=0, we should use thesine function and not the cosine function.
This means there's no horizontal shift, so the function is of the form -
a sin(bx)+d
Since the midline intersection at x=0 is followed by a maximumpoint, we know that a > 0.
The amplitude is 1, so |a| = 1. Since a >0 we can conclude that a=1.
The midline is y=5, so d=5.
The period is 4π so b = 2π / 4π = 1/2 simplified.
f(x)1 sin 1/3x+5 = Solution
