First, we are going to find the vertex of our quadratic. Remember that to find the vertex

of a quadratic equation of the form

, we use the vertex formula

, and then, we evaluate our equation at

to find

.
We now from our quadratic that

and

, so lets use our formula:




Now we can evaluate our quadratic at 8 to find

:




So the vertex of our function is (8,-72)
Next, we are going to use the vertex to rewrite our quadratic equation:



The x-coordinate of the minimum will be the x-coordinate of the vertex; in other words: 8.
We can conclude that:
The rewritten equation is

The x-coordinate of the minimum is 8
42/12 = 3.5, 63/18 = 3.5, therefore we will be multiplying the last time by 3.5. 40x3.5= 140, and therefore, the number of pencils produced in 40 seconds is 140
9514 1404 393
Answer:
(b) 23
Step-by-step explanation:
The diagonals of a rectangle are the same length, so ...
AC = BD
2x +10 = 56
x +5 = 28 . . . . . divide by 2
x = 23 . . . . . . . . subtract 5
Answer:
(a) √25 rational
(b) √30 irrational
Step-by-step explanation:
Note : only perfect squares have rational roots
25 = 5² then 25 is a perfect square
therefore √25 = 5 is a rational number
30 cannot be written in the form a² where ‘a’ I start a natural number then 30 is not a perfect square
Therefore √30 is irrational.