Choose a quadratic inequality that satisfies the following conditions.
All the values of a, b, and c of the quadratic expression are negative, and the value of its quadratic expression is at most 20.
One possible quadratic inequality that satisfies the given conditions is:
-9x^2 - 5x - 6 ≤ 20
1. Choose a quadratic inequality that satisfies the following conditions.
All the values of a, b, and c of the quadratic expression are negative, and the value of its quadratic expression is at most 20.
A. −2x^2−x−5<20
B. 2x^2−x−5≤20
C. 2x^2−x−5<20
D. −2x2−x−5≤20
The correct answer is C. 2x^2−x−5<20.
1.
creator: John Wronn
A small rectangular city park has a width of 110 feet and a length of 270 feet. The city wants to make the park larger by adding x feet to its width and 2x feet to its length. The total area needs to be no more than 30,000 square feet. Which inequality should be used to find all values of x? Remember that the area, A, of a rectangle is given by the formula
ℎA=bh where b is the base and h is the height.
A. (110+x)(270+2x)≤30,000
B. (110+x)(270+2x)≥30,000
C. (110+2x)(270+x)≥30,000
D. (110+2x)(270+x)≤30,000
The correct inequality to find all values of x in this scenario would be D. (110+2x)(270+x)≤30,000.
To find a quadratic inequality that satisfies these conditions, we can start by considering a general form of a quadratic expression:
f(x) = ax^2 + bx + c,
Given that all values of a, b, and c are negative, we can write:
f(x) = -ax^2 - bx - c.
To ensure that the value of the quadratic expression is at most 20, we can add the constraint:
-ax^2 - bx - c ≤ 20.
Since all the coefficients are negative, we can multiply both sides by -1 to flip the inequality:
ax^2 + bx + c ≥ -20.
Therefore, a quadratic inequality that satisfies the given conditions is:
ax^2 + bx + c ≥ -20,
where a, b, and c are all negative values.
To find a quadratic inequality that satisfies the given conditions, we need to consider three factors: the negativity of the coefficients (a, b, c), the quadratic expression, and the constraint on the expression being less than or equal to 20.
Let's start by assuming the quadratic expression is of the form:
f(x) = ax^2 + bx + c
Since we want all the coefficients (a, b, and c) to be negative, let's choose:
a = -1, b = -1, c = -1
Substituting these values into the quadratic expression, we get:
f(x) = -x^2 - x - 1
Now, let's consider the constraint that the value of f(x) should be at most 20. We can represent this as:
f(x) ≤ 20
Substituting the expression for f(x), we have:
- x^2 - x - 1 ≤ 20
Rearranging this inequality, we get:
x^2 + x + 21 ≥ 0
Therefore, the quadratic inequality that satisfies all the given conditions is:
x^2 + x + 21 ≥ 0