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SVETLANKA909090 [29]
3 years ago
14

A red ballon starts at 7 meters off the ground and rises at 3 meters per second. A ballon starts at 12 meters off the ground and

rises at 2 meters per second. Write and solve an equation to determine when the balloons are at the same height
Mathematics
1 answer:
GrogVix [38]3 years ago
4 0
Let x be the no. of seconds it takes for the balloons to be at the same height.
7+3x = 12+2x
Deduct both sides by 2x.
7+x = 12
Deduct both sides by 7.
x = 5
Ans: It will take 5 seconds for the balloons to be at the same height.
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2 years ago
Three functions are given below: f(x), g(x), and h(x). Explain how to find the axis of symmetry for each function, and rank the
LuckyWell [14K]

Answer:

1. x=8 is the line of symmetry for f(x) = -4(x − 8)2 + 3

2. x=-2 is the line of symmetry of g(x) = 3x2 + 12x + 15

3. x=3 is the line of symmetry of h(x), shown in the graph.

Step-by-step explanation:

To find the line of symmetry of a vertical parabola (second degree polynomial), find the value of x that sets the squared term to zero.  This is a vertical line passing through the vertex of the second degree function.

1. f(x) = -4(x − 8)2 + 3

setting x=8 will give f(8) = 3, so x=8 is the line of symmetry

2. g(x) = 3x2 + 12x + 15

here, we need to complete the squares,

g(x) = 3x2 + 12x + 15

g(x) = 3(x^2+4x+5)

g(x) = 3(x^2 + 2(2x) +4 +1)

g(x) = 3((x+2)^2 +1)

So setting x=-2 will anihilate or cancel the squared term, therefore

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b=7

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