The Brown family had cereal for breakfast. *Before breakfast there was 3/4 gallon of milk. *The Brown's drank 1/2 of their milk
1 answer:
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Explanation:
For a quadratic equation in standard form with real coefficients:
The quadratic formula giving its solutions is ...
The quantity under the radical is called the discriminant. If we let d represent it, then ...
d = b²-4ac
and there are three possibilities:
- d < 0. The solutions involve the square root of a negative number, so both are complex. They are conjugates of each other.
- d = 0. There is one real solution. It has multiplicity 2.
- d > 0. There are two distinct real roots.
If the coefficients of the quadratic are rational, the roots will be irrational if and only if d is not a perfect square.
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The above formula still applies when coefficients are complex or irrational (or both). In the case of complex coefficients, the description of the number of roots is accurate, but their description as real or complex may not apply.
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<u>Examples</u>:
(x -1)² +1 = 0 = x² -2x +2 . . . . d = (-2)²-4(1)(2) = -4; roots are x = 1 ± i
(x-2)² = 0 = x² -4x +4 . . . . . . d = (-4)² -4(1)(4) = 0; roots are x = 2 (twice)
(x+3)² -4 = x² +6x +5 . . . . . . d = 6² -4(1)(5) = 16; roots are x = -5 and x = -1
Answer:
Part A)
Part B) The solution in the attached figure
Step-by-step explanation:
<u><em>The complete question is</em></u>
Suppose Rick has 40 ft of fencing with which he can build a rectangular garden. Let X represent the length of the garden and let Y represent the width.
A. Please write an inequality representing the fact that the total perimeter of the garden is at most 40 ft.
B. Please sketch part of the solution set for this inequality that represents all possible values for the length and width of the garden.
Part A)
Let
x ----> the length of the rectangular garden
y ----> the width of the rectangular garden
we know that
The perimeter of the rectangular garden is equal to
In this problem the word "at most" means "less than or equal to"
so
The inequality that represent this situation is
Simplify
Part B) we have
Isolate the variable y
subtract x both sides
The solution of the inequality is the shaded area below the solid line
The slope of the solid line is negative (m=-1)
The y-intercept of the solid line is (0,20)
The x-intercept of the solid line is (20,0)
therefore
The solution is the triangular shaded area
see the attached figure
Remember that
Both the length and the width must be positive
