A balloon is leaking air, and the rate of change in volume is proportional to the volume. Let V denote the volume, in liters, of air in the balloon after t seconds, and take -0.03 to be the constant of proportionality.
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A: Write an equation of change satisfied by 
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B: If there are initially 8 liters of air in the balloon, find a formula that gives V as a function of t. Write your answer using the alternative form for an exponential function.
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C: How long will it take for 10% of the initial volume of air to leak from the balloon? Round your answer to two decimal places.
What will be an ideal response?
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B: 
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C: 3.51 seconds
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Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. f(x) = (x - 4)2(x2 - 25)
A. 4, touches the x-axis and turns around; -5, crosses the x-axis; 5, crosses the x-axis B. 4, touches the x-axis and turns around; 25, touches the x-axis and turns around C. -4, touches the x-axis and turns around; 25, crosses the x-axis D. 4, touches the x-axis and turns around; -5, touches the x-axis and turns around; 5, touches the x-axis and turns around
Provide an appropriate response.Which of the following statements are true?I: 2v1 + 2v2 - 3v3 is an affine combination of the 3 vectors.II: The affine hull of two distinct points is a plane.III: If S = {x}, then aff S = {x}. IV: If a set of vectors in ?n is linearly independent, then every vector in ?n can be written as an affine combination of these vectors.
A. I and III B. I , III, and IV C. I and II D. II and IV
Determine if each statement is true if
(i) ABCD is a parallelogram
(ii) ABCD is a rhombus
In each case, if true, explain why.
(a) AE = DE
(b) AE = CE
(c) AC = AB
(d) AB = CD
Match the polynomial with its binomial factors.5x2 + 22x + 21
A. (x - 3)(5x - 7) B. (x + 3)(4x + 7) C. (x + 7)(5x + 3) D. (x + 3)(5x + 7)