We want to solve 9a² = 16a for a.
Because the a is on both sides, a good strategy is to get all the a terms on one side and set it equal to zero. Then we apply the Zero Product Property (if the product is zero then so are its pieces and Factoring.
9a² = 16a
9a² - 16a = 0 <-----subtract 16a from both sides
a (9a - 16) = 0 <-----factor the common a on the left side
a = 0 OR 9a - 16 =0 <----apply Zero Product Property
Since a = 0 is already solved we work on the other equation.
9a - 16 = 0
9a = 16 <----------- add 16 to both sides
a = 16/9 <----------- divide both sides by 9
Thus a = 0 or a = 16/9
Answer:
Step-by-step explanation:
Length of the garden = 4 - 21*x - 28*y
Width of the garden = -6*x*y
Perimeter of the garden = 2*(Length + Width)
P = 8 - 42*x - 56*y - 12*x*y
Answer:
The graph in the attached figure
Step-by-step explanation:
we have

This is a vertical parabola open upward (because the leading coefficient is positive)
The vertex is a minimum
step 1
Find the vertex of the quadratic equation
Convert the equation in vertex form
Complete the squares



Rewrite as perfect squares

The vertex is the point (3.5,0.25)
step 2
Find the x-intercepts
The x-intercepts are the values of x when the value of the function is equal to zero
we have

solve for x

square root both sides




therefore
The x-intercepts are the points (3,0) and (4,0)
step 3
Find the y-intercept
The y-intercept is the value of y when the value of x is equal to zero
we have

For x=0


The y-intercept is the point (0,12)
step 4
Graph the quadratic equation
we have
The vertex (3.5,0.25)
The x-intercepts (3,0) and (4,0)
The y-intercept (0,12)
using a graphing tool
Plot the points and draw the figure
The graph in the attached figure