Explanation:
All of the points must be contained within a circle that will circumscribe an equilateral triangle of area 1. (We refer to this as the inscribed triangle.) Any points on the circle that do not form an equilateral triangle will form a triangle with an area less than 1. Likewise for any points within the circle.
The circle can be circumscribed by an equilateral triangle whose side length is double that of the inscribed triangle. Since the side length is double, the circumscribing triangle will have an area 2² = 4 times that of the inscribed triangle.
The inscribed triangle has an area of 1, so the circumscribing triangle must have an area of 4.
Answer:
x
2
+6xy+9y
2
+4x+12y−5=0
Step-by-step explanation:
x
2
+6xy+9y
2
+4x+12y−5=0
Comparing the equation with the general equation of second degree gives
a=1,b=9,h=3,g=2,f=6,c=−5
Angle between a pair of straight lines that is tanθ=
∣
∣
∣
∣
∣
∣
a+b
2
h
2
−ab
∣
∣
∣
∣
∣
∣
tanθ=
∣
∣
∣
∣
∣
1+9
2
9−1×9
∣
∣
∣
∣
∣
=
9
0
tanθ=0
⇒θ=tan
−
(0)=0
∘
Angle between the pair of straight lines is zero therefore the lines are parallel.
Hence proved
Answer:
Cameron and Rebecca are organizing a lunch for their friends. Within the dishes to be served, they will prepare a tomato, carrot and broccoli salad. The number of tomatoes and carrots are 10-partners and the total amount of vegetables is 12. If we increase the number of broccoli by three and decrease the number of tomatoes by two, the amount of tomatoes and broccoli will also be 10-partners. What is the number of tomatoes, carrots and broccoli bought by Cameron and Rebecca?
<u>Cameron and Rebecca purchased 7 tomatoes, 3 carrots and 2 broccoli.</u>
Step-by-step explanation:
Number of tomatoes = x
Number of carrots = 10 - x
Number of broccoli = y
System of Equations:
x + 10 - x + y = 12
y = 12 - 10
y = 2
x - 2 + y + 3 = 10 (If we increase the number of broccoli by three and decrease the number of tomatoes by two, the amount of tomatoes and broccoli will also be 10-partners)
x + 1 + y = 10
x + y = 9
y = 9 - x
Substitution of y:
x + 10 - x + y = 12
x + 10 - x + 9 - x = 12
-x + 19 = 12
-x = 12 - 19
x = 7 ⇒ 10 - x = 3
<u>Cameron and Rebecca purchased 7 tomatoes, 3 carrots and 2 broccoli.</u>
Answer:
-f(3x - 1) + 2 = -18x² + 12x + 1
Step-by-step explanation:
Step 1: Find f(3x - 1)
f(3x - 1) = 2(3x - 1)² - 1
f(3x - 1) = 2(9x² - 6x + 1) - 1
f(3x - 1) = 18x² - 12x + 2 - 1
f(3x - 1) = 18x² - 12x + 1
Step 2: Plug in f(3x - 1)
-(18x² - 12x + 1) + 2
Step 3: Evaluate
-18x² + 12x - 1 + 2
-f(3x - 1) + 2 = -18x² + 12x + 1
