72 beacuau it is 90 and 120 72
Answer:
You can't add these because they are different variables
Step-by-step explanation:
Answer:
see explanation
Step-by-step explanation:
Given
y = x² - 2x - 8
To find the x- intercepts let y = 0 , that is
x² - 2x - 8 = 0 ← in standard form
(x - 4)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 2 = 0 ⇒ x = - 2
x- intercepts : x = - 2, x = 4
The x- coordinate of the vertex is mid way between the x- intercepts, that is
= 
= 
= 1
Substitute x = 1 into the equation for corresponding y- coordinate
y = 1² - 2(1) - 8 = 1 - 2 - 8 = - 9
vertex = (1, - 9 )
9514 1404 393
Answer:
split the number into equal pieces
Step-by-step explanation:
Assuming "splitting any number" means identifying parts that have the number as their sum, the maximum product of the parts will be found where the parts all have equal values.
We have to assume that the number being split is positive and all of the parts are positive.
<h3>2 parts</h3>
If we divide number n into parts x and (n -x), their product is the quadratic function x(n -x). The graph of this function opens downward and has zeros at x=0 and x=n. The vertex (maximum product) is halfway between the zeros, at x = (0 + n)/2 = n/2.
<h3>3 parts</h3>
Similarly, we can look at how to divide a (positive) number into 3 parts that have the largest product. Let's assume that one part is x. Then the other two parts will have a maximum product when they are equal. Their values will be (n-x)/2, and their product will be ((n -x)/2)^2. Then the product of the three numbers is ...
p = x(x^2 -2nx +n^2)/4 = (x^3 -2nx^2 +xn^2)/4
This will be maximized where its derivative is zero:
p' = (1/4)(3x^2 -4nx +n^2) = 0
(3x -n)(x -n) = 0 . . . . . . . . . . . . . factor
x = n/3 or n
We know that x=n will give a minimum product (0), so the maximum product is obtained when x = n/3.
<h3>more parts</h3>
A similar development can prove by induction that the parts must all be equal.
Answer:
B'(- 2, 2 )
Step-by-step explanation:
Given the translation rule (x, y ) → (x + 3, y - 2 )
This means add 3 to the original x- coordinate and subtract 2 from the original y- coordinate, that is
B(- 5, 4 ) → B'(- 5 + 3, 4 - 2 ) → B'(- 2, 2 )
