Answer:
32
Step-by-step explanation:
Step 1: Define
f(x) = 3x² - 5x - 4
g(x) = -4x - 12
Step 2: Find f(g(x))
f(g(x)) = 3(-4x - 12)² - 5(-4x - 12) - 4
f(g(x)) = 3(16x² + 96x + 144) + 20x + 60 + 4
f(g(x)) = 48x² + 288x + 432 + 20x + 64
f(g(x)) = 48x² + 308x + 496
Step 3: Find f(g(-4))
f(g(-4)) = 48(-4)² + 308(-4) + 496
f(g(-4)) = 48(16) - 1232 + 496
f(g(-4)) = 768 - 736
f(g(-4)) = 32
Answer: Aproximately 2,525 balloons
Step-by-step explanation:
1. Find the volume of a balloon with the formula given in the problem, where 
is the radius (
), then:
2. Convert the volume from m³ to lliters by multiplying it by 1,000:
3. You know that that 1 liter of helium can lift 1 gram and that Ryan weighs 5 stone and 5 pounds. So you must make the following conversions:
1 g=0.0022 lb
From 5 stones to pounds
4. Then Ryan's weigh is:
5lb+70lb=75lb
5. Then, if 1 liter of helium can lift 0.0022 lb, to lift 75 lb (which is the weight of Ryan) they need:
6. Then, to calculate the aproximated number of balloons they need to make him float (which can call 
), you must divide the liters of helium needed to lift the weight of Ryan by the volume of a balloon, then the result is:
≈2,525 balloons.
Answer:
The question is incorrect. please provide a diagram.
The x coordinate of the vertex will be the average of the two zeros, here -3 and 5, so x=(-3+5)/2 = 1, f(1)=(1+3)(1-5) = -16.
Answer: (1, -16)
Let's do it some other ways. How about completing the square to turn f in to vertex form?
f(x) = (x+3)(x-5) = x² - 2x - 15 = (x² - 2x + 1) - 1 - 15 = (x-1)² - 16
and now we can read off (1, -16) as the vertex.
The other method is the vertex is x= - b/2a = - (-2)/2(1) = 1.
Three methods, same answer. Good.
Greatest to least: 4/9, 44/100, 0.4.
