The inequality is
13x-8≤-32
The solution
13x-8≤-32
13x-8+8≤-32+8
13x≤-24
13x/13≤24/13
x≤24/13
Answer:
x = -3
x = 7
Step-by-step explanation:
If either term is zero the product is zero
(2x + 6)(x - 7) = 0
2x + 6 = 0
2x = -6
x = -3
x - 7 = 0
x = 7
Answer: the function that has the smaller minimum is g(x), and the cordinates are (0,3)
Step-by-step explanation:
We have a function for f(x) and a table for g(x)
first, quadratic functions are symmetrical.
This means that if the minimum/maximum is located at x = x0, we will have that:
f(x0 + A) = f(x0 - A)
For any real value of A.
Then when we look at the table, we can see that:
g(-1) = 7
g(0) = 3
g(1) = 7
then the minimum of g(x) must be at x = 0, and we can see that the minimum value of g(x) is 3.
Now let's analyze f(x).
When we have a quadratic equation of the shape.
y = a*x^2 + b*x + c
the minimum/maximum will be located at:
x = -b/2a
In our function we have:
a = 3
b = 6
then the minimum is at:
X = -6/2*3 = -1
f(-1) = 3*(-1)^2 + 6*-1 + 7 = 3 - 6 + 7 = 3 + 1 = 4
Then the function that has the smaller minimum is g(x), and the cordinates are (0,3)
Answer:
96
Step-by-step explanation:
If the hourly production rate is p parts, then the daily production quantity for an 8-hour day is 8p. If changing the rate to p+4 per hour means the same quantity can be produced in 6 hours, then we can write the equation ...
6(p+4) = 8p
6p + 24 = 8p . . . eliminate parentheses
24 = 2p . . . . . . . subtract 6p
12 = p . . . . . . . . . normal hourly production rate
8p = 8·12 = 96 . . . . scheduled daily production quantity
The worker has to finish 96 parts during the day according to the schedule.
So if the store bought the cereal at $2.50 and sold it for $3.50 there is a $1 markup. This in terms of percentages is 1/2.50 = 0.4, which is a 40% markup.