Solutions
Name __________________________
Block ____ Date ____________
Algebra: 10.2.5: Mixed Practice
Bell Work:
6 𝑥
a.
6
+
Eliminate the Fractions in each equation and then Solve.
15 𝑥
2𝑥
=5
3
b.
𝑥 + 4𝑥 = 30
3
−
𝑥 2
=
5 3
x 𝑥
c.
5𝑥 − 3𝑥 = 10
5𝑥 = 30
7𝑥 = 17
2𝑥 = 10
𝒙=𝟔
17
𝑥
𝑥
𝑥 + 6𝑥 = 17
+6=
𝒙=𝟓
𝒙=
10-81. Use square roots to find two solutions to each equation.
a.
x2 − 81 = 0.
b.
x2 − 37 = 0.
c.
x2 − 49 = 0.
d.
2x2 − 10 = 0
a.
b.
𝑥 2 = 81
𝒙 = ±𝟗
c.
𝟏𝟏
𝟕
d.
2
𝑥 = 49
𝑥 2 = 37
𝒙 = ±𝟕
𝒙 = ±√𝟑𝟑
2𝑥 2 = 10
𝑥2 = 5
𝒙 = ±√𝟓
10-82. Identify each sum or product as a rational number or an irrational number.
rational
a.
irrational
b.
irrational
c.
rational
d.
10-83. Solve each equation by first rewriting it in a more useful form.
a.
b.
−2 −2𝑥
4
𝑥 𝑥 2 −2𝑥
𝑥
−2
c.
d.
15
252 = 125𝑥+1
𝑥
5
+
𝑥−1
3
=2
2
𝑥 − 4𝑥 + 4 = 25
𝑥
1 𝑥+3
9 =� �
3
a. (52 )2 = (53 )𝑥+1
54 = 53𝑥+3
4 = 3𝑥 + 3
1 = 3𝑥
b. 3𝑥 + 5(𝑥 − 1) = 30
𝟏
3𝑥 + 5𝑥 − 5 = 30
=𝒙
𝟑
8𝑥 − 5 = 30
8𝑥 = 35
𝒙=
𝟑𝟑
𝟖
c. (𝑥 − 2)2 = 25
𝑥 − 2 = ±5
𝑥 = 2±5
𝒙 = 𝟕 and 𝒙 = −𝟑
d. (32 )𝑥 = (3−1 )𝑥+3
32𝑥 = 3−𝑥−3
2𝑥 = −𝑥 − 3
3𝑥 = 3
𝒙=𝟏
10-84. Write in vertex form and graph: f(x) = x2 − 6x + 5.
a.
What is the vertex?
b.
Describe the domain and range of this function.
c.
What is the maximum or minimum value of the
function? (Identify which)
−3 −3𝑥
𝑥 𝑥
2
𝑥
9
-9
−3𝑥 +5
−3
𝒇(𝒙) = (𝒙 − 𝟑)𝟐 − 𝟒
10-85. The Mountain Bike Club has $475 in the treasury. Sarah, the president, plans to buy hats or
T-shirts for the members. If hats cost $5 and T-shirts cost $8, write an inequality to represent the
possible number of hats and T-shirts that she could purchase. Be sure to define your variables.
10-86. Chad is entering a rocket competition. He needs to program his rocket so that when it is launched
from the ground, it lands 20 feet away. In order to qualify, it must be 100 feet off the ground at its
highest point.
a.
b.
c.
What type of equation should be used to model
the path of the rocket? Quadratic
Let x represent the distance from the launch
pad in feet and y represent the height of the
rocket in feet. Create a table of at least three
solutions
x
y
0
0
10
100
20
0
y
(10, 100)
What equation should he program into his rocket
launcher to win?
x
0
d.
Draw a sketch of the rocket’s path.
20
10-87. Complete a table and graph the piecewise function.
y
x
y
-3
9
6
-2
4
4
-1
1
8
2
x
−8
−6
−4
−2
2
0
3
1
4
−4
2
5
−6
3
6
4
6
8
−2
−8
PARCC Practice
1. The graph shows y as a function of x.
For which intervals is the function decreasing?
Select all that apply.
2. Graph the solution set of 3𝑥 − 4𝑦 ≤ 24.
•
•
•
•
y
8
Solve for y.
Select the correct line style
Graph the line
Shade the desired region.
6
4
2
x
−8
−4𝑦 ≤ −3𝑥 + 24
𝒚≥
3.
−6
−4
−2
2
4
6
8
−2
𝟑
𝒙−𝟔
𝟒
−4
−6
−8
Graph each system of inequalities:
Dotted, Shade above
a.
𝑦 > −𝑥 + 3
2𝑥 − 3𝑦 ≤ 6
−3𝑦 ≤ −2𝑥 + 6
y
𝒚≥
8
6
b.
𝟐
𝒙−𝟐
𝟑
𝑦 ≥ 4𝑥 − 2 Solid, Shade above
𝑦 < −𝑥 2 − 3𝑥 + 4 Dotted, Shade below
y
8
6
Solid
Shade
Above
4
2
4
2
x
−8
−6
−4
−2
2
4
6
x
8
−8
−6
−4
−2
2
−2
−2
−4
−4
−6
−6
−8
−8
4
6
8
Circle each point that is a solution to the system of inequalities that is graphed.
Shade the solution set for each system.
Shade Above
Shade Below
Shade Below
Shade Above
Shade Above
Shade Below