Answer:
- 18x + 15y ≤ 300
- x ≥ 0; y ≥ 6
Step-by-step explanation:
Variables are defined in the problem statement.
18x +15y ≤ 300 . . . . total budget
y ≥ 6 . . . . . . . . . . . . minimum number of annuals
x ≥ 0 . . . . . number of perennials cannot be negative
This system of inequalities describes the situation.
Answer:
-12 ≤ p ≤ 12
Step-by-step explanation:
If the absolute value inequality is
|p| ≤ 12,
then the answer is
-12 ≤ p ≤ 12
Answer:
x<5
Step-by-step explanation:
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Answer:
P and Q are two points on the line x-y+1=0 and are at a distant of 5 units from the origin. Find the area of triangle POQ.
Step-by-step explanation:
P and Q are the intersection points of
x-y+1 = 0 and the circle x^2 + y^2 = 25
sub y = x+1 into the circle
x^2 + (x+1)^2 = 25
x^2 + x^2 + 2x + 1 - 25 = 0
x^2 + x - 12 = 0
(x+4)(x-3) = 0
x = 3 or x = -4
y = 4 or y = -3
so P(3,4) and Q(-4,3) are our two points
Height of triangle.
h = |0 - 0 + 1|/√2 = 1/√2
PQ = √( (-7)^2 + 1^2) = √50 = 5√2
area POQ = (1/2)(1/√2)(5√2) = 5/2 square units
hope this helped
Answer:
6
Step-by-step explanation:
Since the degree of the angle is 45, we know that the triangle is isosceles. That means that the sides of the triangle, not including the hypotenuse, has a length of 3√2.
Using the Pythagorean theorem, which is a^2 + b^2 = c^2, we have (3√2)^2 + (3√2)^2 = c^2.
Note: c is the hypotenuse of the triangle.
18 + 18 = c^2
= 36 = c^2
Therefore, c = 6.
