I believe the answer is 18 - 3x ≤ 15,
Answer:
- see the attachment for a graph
- yes, you can carry 5 math books in one load (along with 0–2 science books)
Step-by-step explanation:
If x and y represent the number of math and science books you're carrying, respectively, then 3x and 4y represent their weights in pounds.
The total weight of the carry will be 3x+4y, and you want that to be at most 24 pounds. The expression modeling this is ...
... 3x +4y ≤ 24
A graph of this inequality is shown in the attachment. (We have added the constraints that the number of books not be negative.)
___
5 math books will weigh 5·3 = 15 pounds, so will be within the limit you can carry.
Answer:
x ∈ {-4, 2}
Step-by-step explanation:
The x-coefficient (+2) is the sum of the constants in the binomial factors of the equation, and the constant term (-8) is their product.
Since you're familiar with the divisors of 8, you know that the two factors of -8 that total +2 are -2 and +4. These are the constants in the binomial factors:
f(x) = x^2 +2x -8
f(x) = (x -2)(x +4)
The roots of f(x) are the values of x that make these factors be zero. They are x=2 and x=-4.
The roots of f(x) are -4 and 2.
_____
Above is the solution by factoring. We can also "complete the square" to find the roots. Anytime we're looking for roots, we want the values of x that make f(x) = 0.
x^2 +2x -8 = 0
x^2 +2x = 8 . . . . . add the opposite of the constant
x^2 +2x +1 = 8 +1 . . . . . add the square of half the x-coefficient: (2/2)² = 1
(x +1)² = 9 . . . . . . . . . . . write as squares
x +1 = ±√9 = ±3 . . . . . . take the square root
x = -1 ± 3 . . . . . . . . . . . subtract 1
The roots are x=-4, x=2.
The median if golf pro shop is 20 pairs greater than tennis pro shop
The answer is x=2+5i or 2-5i
