Answer:
1) a = -⅙, b = ⅙, c = 1
2) 6 units
Step-by-step explanation:
1) f(x) = ax² + bx + c
Given the roots, we can write this as:
f(x) = a (x + 2) (x − 3)
We know that f(13) = -25, so we can plug this in to find a:
-25 = a (13 + 2) (13 − 3)
-25 = 150a
a = -⅙
Therefore, the factored form is:
f(x) = -⅙ (x + 2) (x − 3)
Distributing:
f(x) = -⅙ (x² − x − 6)
f(x) = -⅙ x² + ⅙ x + 1
Graph: desmos.com/calculator/6m6tjoodvb
2) Volume of a right prism is area of the base times the height.
V = Ah
The base is an equilateral triangle. Area of a triangle is one half the base times height.
V = ½ ab h
The height of the triangle is the same as the height of the prism.
V = ½ bh²
In an equilateral triangle, the height is equal to half the base times the square root of 3.
V = ½ b (½√3 b)²
V = ⅜ b³
Given that V = 81, solve for b.
81 = ⅜ b³
216 = b³
b = 6
1) 2 with a small 4 at the top like an exponent
Answer:
Option B
Step-by-step explanation:
By applying Pythagoras theorem in the given right triangle,
(Hypotenuse)² = (leg 1)² + (leg 2)²
By substituting the values in the given expression,
7² = x² + 2²
49 = x² + 4
x² = 49 - 4
x² = 45
x = √45
x = 3√5
x = 6.7 ft
Option B will be the correct option.
Answer:
thanks
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let x represent the speed of the slower plane. The faster plane's speed is then x+40. The sum of speeds is ...
x + (x+40) = 1180
2x = 1140 . . . . subtract 40
x = 570 . . . . . .divide by 2
x+40 = 610 . . . . the speed of the faster plane
The two speeds are 570 mph and 610 mph.
