Provide an appropriate response.Explain why the discriminant can indicate the number of x-intercepts of the graph of a quadratic equation 
What will be an ideal response?
If b2 - 4ac > 0, then 
has two real-number solutions and, hence, two x-intercepts. If 
then 
has exactly one real-number solution and, hence, one x-intercept. If 
, then 
has no real-number solutions and, hence, no x-intercepts.
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Find the unit tangent vector of the given curve.r(t) = (8t cos t - 8 sin t)j + (8t sin t + 8 cos t)k
A. T(t) = - 
(sin t)j + 
(cos t)k
B. T(t) = (-sin t)j + (cos t)k
C. T(t) = (8 cos t)j - (8 sin t)k
D. T(t) = (-8 sin t)j + (8 cos t)k
Divide. Express your answer in simplest form.-1
÷ -1
A. 1
B. -1
C. 2
D. 1
Find anand a6 for the following arithmetic sequence.a12 = 73x + 1, a14 = 75x + 11
A. an = (61 + n)x - 59 + 5n, a6 = 67x - 29 B. an = (62 - n)x - 54 - 5n, a6 = 56x - 84 C. an = (62 + n)x - 54 + 5n, a6 = 68x - 24 D. an = (62 + n)x - 49 + 5n, a6 = 68x - 79
Solve the problem.A piece of farm machinery costs 
and depreciates at the rate of 
per year.a) If y represents the the value of the machinery after x years, write an equation for the value of the machinery.b) Graph the equation.c) What is the relationship between the slope of the line and the per-year depreciation?
A. a) y = 510x - 6000
b) 
c) The magnitude of the slope of the line is
the same as the per-year depreciation.
B. a) y = 510x + 6000
b) 
c) The magnitude of the slope of the line is
the same as the per-year depreciation.
C. a) 6000 = y - 510x
b) 
c) The magnitude of the slope of the line is
the same as the per-year depreciation.
D. a) y = 6000 - 510x
b) 
c) The magnitude of the slope of the line is
the same as the per-year depreciation.