Download Math 3 EXAM 1 FALL 2010 Solve the equation. Identify the equation

Math 3
EXAM 1
FALL 2010
Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.
x
9
-9 =11)
x+9
x+9
x+9
- 9 = 10
x+9
1 = 10
incomsistent
2)
x-9
1
-2=
x-4
2
3
6
x-9
1
x-46
-2 =
2
3
3 x - 9 - 12 = 2 x - 4
3x - 27 = 2x - 8
x = 31
31
conditional
Solve the absolute value equation.
3) - 2 x + 4 - 9 = 1
- 2 x + 4 = 10
x + 4 = -5
Solve the formula for the specified variable.
1 1 1
for r
4) = +
F r v
Frv
1
1 1
Frv
=
+
F
r v
rv = Fv + Fr
rv - Fr = Fv
r(v - F) = Fv
Fv
r=
v-F
1
Solve the problem. Write your answer as a complete sentence.
5) The perimeter of a rectangle is 44 m. If the width were doubled and the length were increased by 19 m, the
perimeter would be 96 m. What are the length and width of the rectangle?
44=2L + 2W
22 = L + W
22 - W = L
96 = 2(L + 19) + 2(2W)
48 = L + 19 + 2W
48 = (22 - W) + 19 + 2W
48 = 41 + W
7=W
22 - 7 = L
15 = L
The length is 15m and the width is 7m.
6) Jill normally commutes an average speed of 54mph, but this morning's heavy traffic held her to only 36mph.
She must determine whether she can drive home fast enough this evening in order to maintain her usual
round-trip speed. What speed would she need to drive home?
d
d = rt
t=
d = 36t
d = xT
2d = 54(t + T)
r
t=
d
36
T=
d
x
t+ T =
2d
54
d
d 2d
+ =
36 x
54
1
1
1
+ =
36 x 27
108x
1
1
1
+
=
108x
36 x
27
3x + 108 = 4x
108 = x
Jill will need to drive 108mph on her return trip.
7) If David plans to develop a circular race track 2.75 miles in circumference on a square plot of land, then what is
the minimum number of acres that he need?
( 1 acre = 43,560ft2 ; 1mi = 5280ft) round the final answer to two decimal places.
C = 2.75 = d
A = d2
5280ft
2.75mi
= 14520ft
1mi
d=
14520
A=
14520 2
1acre
43560ft2
=
(14520ft)2 1acre
210830400 1acre
=
2
2
43560ft 2
43560ft2
Divid will need approximately 490.39 acres.
2
490.39acres
8) Mardi earned $17,450 from two investments. She invested part at 7% which was $5000 more than the amount
invested at 11%. Find the total amount invested.
17450 = .07 x + 5000 + .11x
17450 = .07x + 350 + .11x
17100 = .18x
95000 = x
95000 + 5000 + 95000 = total
195000 = total
Mardi will invest a total of $195000.
Find the distance between the points, and find the midpoint of the line segment joining them. (10 points)
9) (-6, -5) and (2, -7)
distance
midpoint
- 6 + 2 -5 + (-7)
,
2
2
d=
2 - - 6 2 + -7 - (-5) 2
d=
8 2+ -22
- 4 - 12
,
2
2
d=
64 + 4
- 2, - 6
d=
68
d = 2 17
Find the real or imaginary solutions by completing the square. State the value of the discriminant and the number of
real solutions. (10 points)
10) 3x 2 + 12x = -2
x2 + 4x + 4 = -
2 12
+
3
3
10
x+22=
3
x+2=±
x=x=
6
±
3
-6 ±
3
10
·
3
3
=±
3
30
3
30
3
30
- 6 ± 30
3
discriminant = 122 - 4(3)(2) = 144 - 24 = 120
2 real solutions
3
Use the method of your choice to find all real solutions of the equation.
3-x
x+5
=
11)
x - 12 x + 16
3 - x x + 16 = x - 12 x + 5
3x + 48 - x 2 - 16x = x 2 + 5x - 12x - 60
- x 2 - 13x + 48 = x 2 - 7x - 60
0 = 2x 2 + 6x - 108
0 = x 2 + 3x - 54
0= x+9 x-6
x+9=0
x=- 9
x-6=0
x=6
-9, 6
Solve the absolute value inequality. Write the solution set using interval notation.
12) - 6 5x - 7 + 38 - 4
-6 5x - 7 < - 42
5x - 7
7
5x - 7 - 7
5x 0
x
0
-
,0 U
5x - 7 7
5x 14
14
x
5
14
,
5
Provide an appropriate response.
13) Write the equation of a line with an undefined slope.
x=5
(you can choose any number)
Find and identify the intercepts, and slope. Use the appropriate information to accurately graph the equation.
14) 2x + 9y = 16
16
= 8 (8,0) x-intercept
2
16
16
(0,
) y-intercept
9
9
4
m=-
2
9
Find the equation of the line through the given pair of points in standard form using only integers.
15) (-4, -2) and (2, 6)
m=
-2 - 6
-8
4
=
=
-4- 2 -6 3
y-6=
4
(x - 2)
3
3(y - 6) =
4
(x - 2)3
3
3y - 18 = 4(x - 2)
3y - 18 = 4x - 8
- 10 = 4x - 3y
Write an equation in standard form using only integers for the line described.
6
16) The line through (-6, 5), perpendicular to y = - x -1
5
y-5=
5
(x - -6)
6
6(y - 5) =
5
(x + 6)6
6
6y - 30 = 5(x + 6)
6y - 30 = 5x + 30
- 60 = 5x - 6y
Write an equation in standard form using only integers for the line described. Graph the equation.
17) The line parallel to y + 4 = 10 and containing (2, - 7)
y + 4 = 10
y=6
y=- 7
5
Write as a single interval and graph it.
18) (- , 16) (-12, )
- 12, 16
Solve the compound inequality. Write the solution set using interval notation and graph it.
3
17
3y - 5 <
y or -6y + 8 -5y + 4
19)
4
3
12
3
17
3y - 5 <
y(12)
4
3
9 3y - 5 < 17y(4)
27y - 45 < 68y
- 45 < 41y
45
<y
41
8
y+4
4
y
- ,
6