Algebra II Semester 2 Practice Final _18 Pages

ID: A
52. Write an equation of an ellipse in standard form
with the center at the origin and with the given
characteristics.
vertices at (–5, 0) and co-vertices (0, 4)
x
a.
2
25 + y 2
16 = 1
b.
c.
d.
x 2
16 + y 2
25 = 1
x 2
5 + y 2
4 = 1
x 2
4 + y 2
5 = 1
53. Find the inverse of y = 7x 2 + 7.
a. y =±
b. x =
x − 7
7
y − 7
7
x + 7
c. y =±
7
d. y 2 = x + 7
7
54. Rationalize the denominator of the expression.
Assume that all variables are positive.
7x 9 y 7
a.
b.
2x 3 y 2
x 3 y 2
2
14y
14x 12 y 9
2x 3 y 2
c. 2x 3 y 2 14y
d. none of these
55. Write the equation in logarithmic form.
6 4 = 1, 296
a. log 6
1, 296 = 4
b. log 1, 296 = 4
c. log 1, 296 = 4 ⋅ 6
d. log 4
1, 296 = 6
56. Suppose that x and y vary inversely, and x = 7 when
y = 11. Write the function that models the inverse
variation.
a. y = 1.57x
b. y = 77
x
c. y = 4 x
d. y = 18
x
57. Is the relationship between the variables in the table
a direct variation, an inverse variation, or neither
If it is a direct or inverse variation, write a function
to model it.
x 6 10 11 15
y 84 140 154 210
a. direct variation; y = 14x
b. inverse variation; y = 504
x
c. neither
58. Describe the combined variation that is modeled by
the formula or equation.
y =
w
2x 2
a. y varies directly as w and inversely as x.
b. y varies directly as w and inversely as the
square of 2x.
c. y varies directly as the square of x and inversely
as w.
d. y varies directly as w and inversely as the
square of x.
59. Describe the combined variation that is modeled by
the formula or equation.
a = F m
a. a varies directly as F and inversely as m.
b. a varies directly as m and inversely as F.
c. a varies directly as F and m.
d. y varies inversely as F and m.
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