Chapter 1 - Expressions, Equations, and Functions Flashcards
Write a verbal expression for the algebraic expression:
h - 7
Seven less than the number h
Write an algebraic expression for the verbal expression:
5 less than 4 times a number
4n - 5
A Christmas tree company charges $55 per Christmas tree and additional Christmas tree food is an extra 50 cents. If p is the number of Christmas tree food packets bought, which expression would give us the total amount spent at the Christmas tree company?
a. 55p + 50
b. 50p + 55
c. .50p + 55
c. .50p + 55
Evaluate the expression:
6 to the 4th power
or
6^4
6 x 6 x 6 x 6
1,296
Evaluate the expression:
7[42 - (5-3)^2]
7[42 - (5-3)^2]
= 7[42 - (2)^2]
= 7[42 - 4]
= 7[40]
= 280Evaluate 2n + (3y - 4) - 4m if:
n = 3 y = 5 m = 4
2n + (3y - 4) - 4m
= 2(3) + (3[5] - 4) - 4(4)
= 6 + (15 - 4) - 16
= 6 + (11) - 16
= 17 - 16
= 1Evaluate 4(6-2) + 7 x (1/7). Name the property used in each step.
4(6-2) + 7 + (1/7)
= 4(4) + 1 Distributive Property
= 16 + 1 Substitution
= 17 Substitution
Abby is getting a new puppy. She needs 4 things before she picks up the puppy:
Purina ProPlan Large Breed Puppy Food: $35
KONG Huggz Koala: $11
Food and Water Bowls: $39
Bully Sticks: $15
Find out how much these cost all together and name the properties used.
35 + 11 + 39 + 15
= 35 + 15 + 39 + 11 Communicative
= (35 + 15) + (39 + 11)
Associative
= (50) + (50)
Substitution
= 100
SubstitutionEvaluate 8 x 4 x 6 x 2 using the properties of numbers. Name the properties used in each step.
8 x 4 x 6 x 2
= 8 x 2 x 6 x 4 Communicative
= (8 x 2)(6 x 4) Associative
= (16)(24) Substitution
= 384 Substitution
Use the distributive property to rewrite 8 x 65. Then evaluate.
8 x 65
= 8(70 - 5)
= 560 - 40
= 520
Rewrite the expression using the distributive property. Then simplify.
8(11w + 4)
8(11w + 4)
= 88w + 32
Simplify 11w + 4w - 5w
11w + 4w - 5w
= 15w - 5w
= 10w
Use the expression four times the sum of 4w and 9 subtracted from the difference of 9w and 4 times 5
a. Write an algebraic expression for the verbal expression
b. Simplify the expression, and indicate the properties used
4(4w + 9) - 5(9w - 4)
= 16w + 36 - 45w - 20
= 29w + 16
Find the solution set of the equation 4n + 11 = 19 if the replacement set is {2,4,6,8,10}
n 4n + 11 = 19 True or False?
2 4(2) + 11 = 19 True 4 4(4) + 11 = 19 False 6 4(6) + 11 = 19 False 8 4(8) + 11 = 19 False 10 4(10) + 11 = 19 False
Solve 6(4 - 2) + 6(7-5)
6(4-2) + 6(7-5)
= 24 - 12 + 42 - 30
= 12 + 12
= 24
Solve each equation.
12 - (6^2 - 4) + x = 12
12 - (6^2 - 4) + x = 12
= 12 - (36 - 4) + x = 12
= 12 - (32) + x = 12
= -20 + x = 12
= x = 32Solve 2(n +3) = 2(n + 4)
2(n + 3) = 2(n + 4)
2n + 6 = 2n + 8
No Solution
Solve 2(5n + 5) = 10(n + 1)
2(5n + 5) = 10(n + 1)
10n + 10 = 10n + 10
n is equal to ALL REAL NUMBERS
Abby pays $12 every year for the Backyard Poultry magazine subscription. She also buys Chickens magazine for $3 per magazine. Let t equal total cost and m be the number of magazines bought separately. Find out how much the total cost would be if she bought 12 magazines separately.
t = 3m + 12 t = 3(12) + 12 t = 36 + 12 t = 48
Abby is buying balloons for her sisters birthday party. She bought regular and special balloons. A regular balloon costs 75 cents and a special ballon costs $2. Write an algebraic for regular balloons (r) and special balloons (s) and the total cost (t). Then identify the independent and dependent variables.
t = .75r + 2s
Independent Variable - # of balloons bought
Dependent Variable - total cost
Determine whether {(1,3),(4,2),(1,2),(2,7)} is a function.
No, there is 2 of the same domain
Determine whether {(2,4),(1,3),(3,5),(4,6)} is a function
Yes, because the x-values do not repeat
There are 4 chickens. One lays 3 eggs a week, one lays 5 eggs a week, one lays 4 eggs a week, and one lays 6 eggs a week.
{(1,3),(2,5),(3,4),(4,6)}
Determine the domain and range.
Domain: {1,2,3,4}
Range: {3,5,4,6}
Determine whether 3x + 3y = 6 is a function.
x 3x + 3y = 6 y
-2 3(-2) + 3y = 6 4 Yes
-1 3(-1) + 3y = 6 3
0 3(0) + 3y = 6 2
1 3(1) + 3y = 6 1
2 3(2) + 3y = 6 0
For f(x) = 2x + 4, find each value
a. f(3)
b. f(-2)
a. f(3) = 2(3) + 4
= 6 + 4
f(3) = 10
b. f(-2) = 2(-2) + 4
= -4 + 4
f(-2) = 0
For f(x) = -12x + 4x - 11, find the values
a. f(3)
b. f(-2)
a. f(3) = 12(3) + 4(3) + 11
= 36 + 12 + 11
= 48 +11
f(3) = 59
b. f(-2) = 12(-2) + 4(-2) + 11
= -24 -8 + 11
= -32 + 11
f(-2) = -21
