QC Algebra Worksheet

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DETAILS
LARCOLALG10 6.1.008.MI.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Solve the system by the method of substitution. Check your solution(s) graphically.
Fx – 4y = -13
1x + 3y =
1
(x, y) =
) =(
y
20
16
12
8
4
X
12 16 20
8
-20 -16 – 12 -8 -4
-4
-8
-12
-16
-20
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3. [-70.76 Points]
DETAILS
LARCOLALG10 6.1.015.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Solve the system by the method of substitution. (If there is no solution, enter NO SOLUTION.)
I x – y =
5
6x – 5y = 33
(x, y) =
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DETAILS
LARCOLALG10 6.1.017.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Solve the system by the method of substitution. (If there is no solution, enter NO SOLUTION.)
2x – y + 6 = 0
4x + y – 9 = 0
(x, y) =
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5. [-70.76 Points]
DETAILS
LARCOLALG10 6.1.019.
MY NOTES
ASK YOUR TEACHER
Solve the system by the method of substitution. (If there is no solution, enter NO SOLUTION.)
(1.5x + 0.8y = 2.3
0.3x – 0.2y = 0.1
(x, y) =
=(
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6. [-70.76 Points]
DETAILS
LARCOLALG10 6.1.024.MI.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Solve the system by the method of substitution. (If there is no solution, enter NO SOLUTION.)
2x + y =
8
9
2x – 9y = 18
(x, y) =
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7. [-70.76 Points]
DETAILS
LARCOLALG10 6.1.055.
MY NOTES
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PRACTICE ANOTHER
Use the equations for the total cost C and total revenue R to find the number x of units a company must sell to break even. (Round to the nearest whole unit.)
C = 8900x + 250,000, R = 9602x
units
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DETAILS
LARCOLALG10 6.1.064.
MY NOTES
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Use a system of equations to find the dimensions of the rectangle meeting the specified conditions.
The perimeter is 28 inches and the width is three-fourths the length.
width
in
length
in
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DETAILS
LARCOLALG10 6.2.013.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Solve the system by the method of elimination and check any solutions algebraically. (If there is no solution, enter NO SOLUTION. If the system is dependent, express x and y in terms of the parameter a.)
Sx + 2y = 8
1x – 2y = 4
(x, y) = (
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DETAILS
LARCOLALG10 6.2.015.
MY NOTES
ASK YOUR TEACHER
Solve the system by the method of elimination and check any solutions algebraically. (If there is no solution, enter NO SOLUTION. If the system is dependent, express x and y in terms of the parameter a.)
5x + 3y = 6
3x – y = 5
(x, y) =
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MY NOTES
11. [-70.76 Points] DETAILS LARCOLALG10 6.2.019.
Solve the system by the method of elimination and check any solutions algebraically. (If there is no solution, enter NO SOLUTION. If the system is dependent, express x and y in terms of the parameter a.)
3x + 2y = 25
2x + 5y = 13
(x, y) =
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DETAILS
LARCOLALG10 6.2.026.MI.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Solve the system by the method of elimination and check any solutions algebraically. (If there is no solution, enter NO SOLUTION. If the system is dependent enter a for x and enter y in terms of
a.)
5-6x + 4y = 7
15x – 10y = -18
(x, y) =
=(
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13. [-70.88 Points]
DETAILS
LARCOLALG10 6.2.043.
MY NOTES
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Two cheeseburgers and one small order of fries contain a total of 1270 calories. Three cheeseburgers and two small orders of fries contain a total of 2030 calories. Find the caloric content of each
item.
cheeseburger
calories
fries
calories
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2. [-/14.28 Points]
DETAILS
LARCOLALG10 P.1.017.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Consider the following.
X36
(a) Give a verbal description of the subset of real numbers represented by the interval.
The inequality is the set of all real numbers.
The inequality is the set of all real numbers greater than or equal to 6.
O The inequality is the set of all real numbers less than or equal to 6.
The inequality is the set of all real numbers less than 6.
O The inequality is the set of all real numbers greater than 6.
(b) Sketch the subset on the real number line.
Use the tools to enter your answer.
+
+
0
1
2
3
4
5
6
7
8
9
10
O O O O ]
NO
SOL
WebAssign NumberLine
өHelp
(c) State whether the interval is bounded or unbounded.
O The interval is unbounded.
The interval is bounded.
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DETAILS
LARCOLALG10 P.1.010.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Determine which numbers in the set are natural numbers, whole numbers, integers, rational numbers, and irrational numbers. (Select all that apply.)
{14, -19, – 4, V7,3.92, – 1, 8, -6.2, 23}
—
14
-19
14
3.92
일
8
-6.2
23
4
(a) natural numbers
o
U
U
O
O
O
O
0
(b) whole numbers
C
O
U
O
O
(c) integers
ооо
0 0
O
o o o
0 0
(d) rational numbers
0
(e) irrational numbers
o
O
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LARCOLALG10 P.2.045.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Simplify each radical expression.
(a)
V 96×3
(b)
8xy8
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DETAILS
LARCOLALG10 P.2.024.
MY NOTES
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PRACTICE ANOTHER
Simplify each expression.
درو
(a)
x6
(b)
21(x + y)
12(x + y)
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LARCOLALG10 P.2.017.
MY NOTES
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PRACTICE ANOTHER
Evaluate the expression for the given value of x.
6×0, x = 10
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6x°, x = 10
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DETAILS
RCOLALG10 P.2.025.
MYN
ASK YOUR TEACHER
PRACTICE ANOTHER
Simplify each expression.
(a)
‘)
(b)
( * )*)*
b
-8
a
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2. [-76.66 Points]
DETAILS
LARCOLALG10 P.4.020.
MY NOTES
ASK YOUR TEACHER
Factor the perfect square trinomial.
4t2 + 4t + 1
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3. [-76.66 Points]
DETAILS
LARCOLALG10 P.4.027.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Factor the sum or difference of cubes.
6473
– 1
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DETAILS
LARCOLALG10 P.5.013.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Find the domain of the expression.
12-X
O all real numbers
O all real numbers x satisfying x 22
O all real numbers x satisfying x < 2 O all real numbers x satisfying x > 2
O all real numbers x satisfying x 5 2
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DETAILS
LARCOLALG10 P.5.004.
MY NOTES
ASK YOUR TEACHER
Fill in the blank.
Two algebraic expressions that have the same domain and yield the same values for all numbers in their domains are —Select— v
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6. [-76.66 Points]
DETAILS
LARCOLALG10 P.5.009.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Find the domain of the expression.
x + 2
5x + 6
O all positive real numbers
O all real numbers
O all real numbers x such that x # 6/5 and x = -6/5
O all real numbers x such that x = -6/5
O all real numbers x such that x # 6/5
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DETAILS
LARCOLALG10 P.5.012.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Find the domain of the expression.
x² 4
x2 + x – 30
O all real numbers x such that x = -5, 6
O all real numbers x such that x = -2,2
O all real numbers
O all real numbers x such that x = 5, -6
O all real numbers x such that x + 30
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O all real numbers x such that x # 5, -6
O all real numbers x such that x 30
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DETAILS
LARCOLALG10 P.5.034.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Perform the division and simplify.
2
r – 5 2 – 25
5+
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DETAILS
LARCOLALG10 P.6.032.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Consider the following.
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DETAILS
LARCOLALG10 P.6.032.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Consider the following.
(2, 15), (10,0)
(a) Plot the points.
Graph Layers
17
16
16
After you add an object to the graph you
can use Graph Layers to view and edit its
properties
14
13
Fill
12
10
.
NO
Solution
14 15
16 17 18
Help
WebAssign. Graphing Tool
(b) Find the distance between the points.
units
(c) Find the midpoint of the line segment joining the points.
(x, y) =
=(
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10. [-/6.66 Points]
DETAILS
LARCOLALG10 P.6.005.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Plot the points in the Cartesian plane.
(7,5), (1, -4), (-3, 7), (-5,0),(-4,-2), (4.5, -1.5)
10
10
-5
10
– 10
10
-101
-10
o
10
10
– 10
-5
• 5
10
– 10
-5
5
10
0
-10
o
– 10
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PREVIOUS ANSWERS
LARCOLALG10 P.6.001.
MY NOTES
ASK YOUR TEACHER
COL
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12. [-16.66 Points]
DETAILS
LARCOLALG10 P.6.024.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Consider the following graph.
у
8
(14,7)
4
(2,2)
(14,2)
X
16
4
8
12
(a) Find the length of each side of the right triangle.
distance between (2, 2) and (14, 2) di =
distance between (14, 2) and (14,7) d2 =
distance between (2, 2) and (14,7) dz =
(b) Show that these lengths satisfy the Pythagorean Theorem.
0,2 =
d₂2=
d12 + d22 =
d32
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13. [-76.66 Points]
DETAILS
LARCOLALG10 P.6.014.MI.
MY NOTES
ASK YOUR TEACHER
Determine the quadrant(s) in which (x, y) is located so that the condition is satisfied. (Select all that apply.)
xy > 0
O Quadrant I
O Quadrant II
O Quadrant III
Quadrant IV
none of these
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14. [-76.66 Points]
DETAILS
LARCOLALG10 P.4.019.
MY NOTES
ASK YOUR TEACHER
Factor the perfect square trinomial.
x2 – 4x + 4
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Factor the perfect square trinomial.
x2 – 4x + 4
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DETAILS
LARCOLALG10 P.4.040.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Factor the trinomial.
2×2 + 13x + 15
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2. [0/0.47 Points]
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PREVIOUS ANSWERS
LARCOLALG10 1.4.007.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Solve the quadratic equation by factoring. (Enter your answers as a comma-separated list.)
4×2 + 2x = 0
x =
x
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3. [0.47/0.47 Points]
DETAILS
PREVIOUS ANSWERS
LARCOLALG10 1.4.010.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Solve the quadratic equation by factoring. (Enter your answers as a comma-separated list.)
x2 + 6x + 9 = 0
X =
-3
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PREVIOUS ANSWERS
LARCOLALG10 1.4.014.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Solve the quadratic equation by factoring. (Enter your answers as a comma-separated list.)
x2 – 3x – 18 = 0
x =
x
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5. [-70.47 Points]
DETAILS
LARCOLALG10 1.4.019.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Solve the equation by extracting the square roots. List both the exact solution and its approximation rounded to two decimal places.
x2 = 81
X =
(smaller value)
X =
(larger value)
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DETAILS
LARCOLALG10 1.4.025.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Solve the equation by extracting the square roots. List both the exact solution and its approximation rounded to two decimal places.
(x – 7)2 = 64
X =
(smaller value)
x =
(larger value)
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PREVIOUS ANSWERS
LARCOLALG10 1.4.052.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Consider the following equation.
y = (x – 9)2 – 1
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New window
Ctrl+N
7. 10. 2/0.47 Points)
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LARCOLALG10 1.4.052
Ctrl+Shift+N
New Incognito window
Consider the following equation.
y-x-9-1
(a) Use a graphing utility to graph the equation
у
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(b) Use the graph to approximate any x-intercepts of the graph
Exit
(smaller x-value
(x,y)-(
(larger x-value)
(c) Sety- and solve the resulting equation. (Enter your answers as a comma-separated list.)
c) Compare the result of art (c) with the x-intercepts of the graph.
The x-values are the same.
The values are reciprocals.
The x-values are unrelated
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LARCOLALG10 1.4.071
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Use the Quadratic Formula to solve the equation. (Enter your answers as a comma-separated list.)
15x + x – 3-0
X-
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LARCOLALG10 1.4.071.
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Use the Quadratic Formula to solve the equation. (Enter your answers as a comma-separated list.)
15×2 + 4x – 3 = 0
X=
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LARCOLALG10 1.4.105.
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The floor of a one-story building is 14 feet longer than it is wide (see figure). The building has 1320 square feet of floor space.
W
W + 14
(a) Write a quadratic equation for the area of the floor in terms of w.
(b) Find the length / and width w of the floor.
ft
ft
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LARCOLALG10 1.5.012.
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Write the complex number in standard form.
4 +-36
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LARCOLALG10 1.5.013.MI.
MY NOTES
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Write the complex number in standard form.
5-V-63
DNE
X
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LARCOLALG10 1.5.029.
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Perform the operation and write the result in standard form.
111 – (16 – 71)
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LARCOLALG10 1.5.032.MI.
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Perform the operation and write the result in standard form.
(6 – 5)(2 – 21)
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LARCOLALG10 1.5.049.
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Write the quotient in standard form.
6 +
6 – i
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LARCOLALG10 1.5.063.
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Write the complex number in standard form.
-32 + -8
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LARCOLALG10 1.5.071.
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Use the Quadratic Formula to solve the quadratic equation. (Enter your answers as a comma-separated list.)
4×2 + 16x + 19 = 0
X =
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LARCOLALG10 1.6.056.
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Solve the equation. Check your solutions. (Enter your answers as a comma-separated list.)
19 6
7 =
x2
+
+
X
X =
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LARCOLALG10 1.7.013.
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Solve the inequality. Then graph the solution set.
2x < 14 Use the tools to enter your answer. -10 -8 -6 -4 -2 0 2 4 6 8 10 O O O O ] NO SOL WebAssign. NumberLine Help Need Help? Read It Watch It COL O 9:53 AM 2/11/2022 8 All apps | Micro x WebAssign: M, X >
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LARCOLALG10 1.7.019.
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Solve the inequality. Then graph the solution set.
3x + 8< 4 + 5x Use the tools to enter your answer. -10 -8 -6 -2 0 2 4 6 8 10 15 O [ ] NO SOL WebAssign NumberLine Help Need Help? Read It Watch It 20 L-10 47 Points! DETAILS I ARCOL ALG101 7022 MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 9:53 AM 2/11/2022 COL o 8 o >
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LARCOLALG10 1.7.022.
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Solve the inequality. Then graph the solution set.
4x – 2 3 13 + 9x
Use the tools to enter your answer.
+
-10
-8
-6
-4
-2
0
2
4
6
8
10
o o O [ ]
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LARCOLALG10 1.7.032.
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COL
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LARCOLALG10 1.7.032.
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Solve the inequality. Then graph the solution set.
-93-4x – 5 < 3 - 15x -10 -8 -6 -4 -2 0 2 4 6 8 10 0 0 0 NO SOL WebAssign NumberLine Help Need Help? Read It COL o 9:53 AM 2/11/2022 8