The correct answer is 35º.. The correct answer is 36º.. The correct answer is 24.The tangent is perpendicular to the radius at the point of tangency.. The correct answer is .Let radius o
Trang 12 T he correct answer is (A).
logb x = 1+c
b1+c = x
3 The correct answer is (D) log 2xy = log 2 + log x + log y
4 The correct answer is (C) From the graph, 20 = 1, 21 = 2, 22 = 4 and 23 = 8 where y is the exponent and x is the power of 2.
Thus, 2y = x or y = log2x
5 The correct answer is (4 and 5) Let log3 92= x, then 3x = 92.
Since 34 = 81 and 35 = 243, x is between 4 and 5
6 The correct answer is (D) P = K10 -xt
7 The correct answer is (B) If logr 6 = S, log r 3 = T, then
1 The correct answer is (9) x2 + 6x + c = 0
2 The correct answer is (3).
Trang 23 The correct answer is
4 The correct answer is (4).
5 The correct answer is (3).
Check both values in original equation
x = 3 is the only root
Trang 36 The correct answer is (0) x2 + y2 = 4 graphs as a circle of radius 2 with center at the origin.
y = 4 graphs as a horizontal line 4 units above the x-axis.
There are no intersections
6r – s = 10 or s = 6r –10 Substitute this value of s in original equation.
8 The correct answer is
Trang 49 The correct answer is ( ).
Substitute a = 1, b = –6, c = 7.
10 The correct answer is (8,4) x + y = 12 or y = 12 – x
x 2 + y2 = 80 Substitute y = 12 – x.
8 INEQUALITIES
1 The correct answer is (x > 3).
Trang 52 The correct answer is
When q = 90°,
When q = 180 °, x = 10
When 90° <q <180 ° , < x < 10
4 The correct answer is (D).
5 The correct answer is (p < –3).
6 The correct answer is (D).
If x > y, in (A), (B), and (C), we are adding, dividing, and subtracting z from both sides of the
inequality; none of these operations affects the inequality when z is a positive number In (E), since x > y and they are both positive numbers, must be greater than 1 In (D), we wrote the
reciprocal of the two fractions in (B), and this changes the inequality
Trang 67 The correct answer is (B).
Since t > 0, y > x
8 The correct answer is (A).
(B), (C), (D), and (E) all show increases as t increases when t > 1 In (A), t is in the
denomina-tor, and decreases as t increases beyond 1.
9 VERBAL PROBLEMS
1 The correct answer is (20) Let x = no of liters of water to be evaporated.
2 The correct answer is (24) Let x = no of hours to fill the tank.
r mph (r + 155)mph 5r mi 0 5(r + 15)mi
Trang 74 The correct answer is (46) Let t = ten’s digit of original number
u = unit’s digit of original number
10t + u = original number
10u + t = number with reversed digits
t + u = 10
(from the given information)
The original number is 46
5 The correct answer is (53,55).
6 The correct answer is ($4000 at 5%, $8000 at 7%).
Let x = amount invested at 5%
y = 2x = amount invested at 7%
Trang 810 GEOMETRY
1 The correct answer is (35º).
Let PT be a diameter of Circle O.
2 The correct answer is (36º) Let 2x = smallest angle in degrees, 3x and 5x = other two angles
in degrees
3 The correct answer is (120º).
m (alernate interior angles), and m
Angle x is an exterior angle of ∆DEF and is
equal to the sum of the measures of the two remote interior angles
x= 50º + 70º = 120º
Trang 94 The correct answer is (240).
5 The correct answer is (150).
Trang 106 The correct answer is (24).
The tangent is perpendicular to the radius
at the point of tangency
In right triangle OTP
7 The correct answer is (96 - 16 π).
Trang 118 The correct answer is
Let radius of circle be 1
Side of square is 1 + 1 =2
9 The correct answer is (130º).
From noon to 4:00 PM., the hour hand has moved from 12 to 4: of 360º = 120º In the next 20 minutes it moves of the distance from 4:00 to 5:00: of 30º = 10º
120º + 10º = 130º
10 The correct answer is (125).
Trang 1211 The correct answer is (6).
12 The correct answer is (56).
13 The correct answer is (3).
14 The correct answer is
Cross-multiply
Trang 1315 The correct answer is (108 °).
16 The correct answer is (2).
The locus of points 10 ft from T is a
circle of radius 10 The locus of points
12 ft from F consists of two parallel
lines 12 ft from F on each side The
circle and one parallel line intersect in
two points
17 The correct answer is (C) The only statement that has the same truth value as the given statement is
the contrapositive of the original statement This is the converse of the inverse of the original statement.
18 The correct answer is (4).
The locus of points 4 units from P is a circle
of radius 4 with center at P The locus
of points 3 units from the given line consists
of two parallel lines 3 units from the
line The two parallel lines intersect the
Trang 1419 The correct answer is (1).
The locus of points 8 cm from P consists
of two planes parallel to P and 8 cm from
it The locus of points 12 cm from Q is a sphere of radius 12 and center at Q The
sphere intersects one of the parallel planes
in one point (point of tangency)
20 The correct answer is (1080°) The sum of the interior angles of an n-sided polygon is (n – 2) 180°
= 720° Divide by 180
The second polygon has 6 + 2 = 8 sides
Sum of the measures of its interior angles = 180(8 – 2)
= 180(6) = 1080°
11 TRIGONOMETRY
1 The correct answer is (C).
Trang 152 The correct answer is (2) cos x(cos x – 2) = 0
3 The correct answer is (I and III) Curves intersect in Quadrants I and III.
4 The correct answer is Let x = arc tan
tan sin
x
x
=
= ⋅ =
2 2 2
3 3
6 3
5 The correct answer is
Trang 166 The correct answer is
7 The correct answer is (90 °, 210°, 330°).
8 The correct answer is (1) Let x = arc sin 1, y = arc cos 1.
sin x = 1, x = 90°
cos y = 1, y = 0°
Trang 179 The correct answer is (B).
cos A
10 The correct answer is (A) Use the law of sines to find angle B.
Thus B may be acute or obtuse.
11 The correct answer is (cot θθθθθ).
Trang 1812 The correct answer is
13 The correct answer is
14 The correct answer is
Square both sides
Trang 1915 The correct answer is (15).
16 The correct answer is (cot 28°) cot x is positive in Quadrant III, so that cot 208° is positive.
cot 208° = cot (208° - 180°) = cot 28°
17 The correct answer is (2).
Graph y = 2 sin x and y = cos 2x on same set of axes in interval - π ≤ x ≤π Graph shows 2 values.
18 The correct answer is
Trang 2019 The correct answer is (B) Use law of sines.
B may have two values, one acute or one obtuse Also, since a < b, two triangles may be constructed.
20 The correct answer is
12 GRAPHS AND COORDINATE GEOMETRY
1 The correct answer is (20).
In ∆∆∆∆∆PQR, use QR = 8 as base and PH = 5 as altitude.