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Mathematics

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Parametric equations and and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction of motion.x = 5t + 2, y = 15t + 2, -? ? t ? ?

A. y = 3x + 4; Entire line, from left to right

B. y = 3x - 4; Entire line, from right to left

C. y = 3x - 4; Entire line, from left to right

D. y = 3x + 4; Entire line, from right to left

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Mathematics

Solve the problem.The table shows the number of new cases (in thousands) of a certain disease diagnosed in a country in various years. Let n = f(t) be the number of new cases (in thousands) of the disease diagnosed at t years since 2010. Suppose that you wish to model f using a quadratic equation. What is the vertex of the model? What does it mean in this situation?

A. (7, 45.7); the largest number of new cases diagnosed was 45,700 in the year 2017 B. (0, 49.4); the largest number of new cases diagnosed was 49,400 in the year 2010 C. (3, 39.3); the smallest number of new cases diagnosed was 39,300 in the year 2013 D. (0, 39.3); the smallest number of new cases diagnosed was 39,300 in the year 2013

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Mathematics

Find the center, transverse axis, vertices, and foci of the hyperbola.25y2 - 36x2 = 900

A. center at (0, 0)
transverse axis is x-axis
vertices: (-5, 0), (5, 0)
foci: (- , 0) , (, 0)
B. center at (0, 0)
transverse axis is y-axis
vertices at (0, -6) and (0, 6)
foci at (0, - ) and (0, )
C. center at (0, 0)
transverse axis is x-axis
vertices: (-6, 0), (6, 0)
foci: (-5, 0), (5, 0)

D. center at (0, 0)
transverse axis is y-axis
vertices: (0, -6), (0, 6)
foci: (- , 0) , (, 0)