Which property is illustrated by the following statement?
(3z)xy = 3(zx)y
(1 point)
Responses
Associative Property of Multiplication
Associative Property of Multiplication
Commutative Property of Multiplication
Commutative Property of Multiplication
Inverse Property of Multiplication
Inverse Property of Multiplication
Commutative Property of Addition
Commutative Property of Addition
11 answers
Associative Property of Multiplication
Evaluate a over z + bw2 for a = 21, b = 3, w = 6, and z = 7.
To evaluate a over z + bw2 for a = 21, b = 3, w = 6, and z = 7, we substitute these values into the expression:
a over z + bw2 = 21 over 7 + 3 * 6^2
First, we simplify the exponent:
6^2 = 6 * 6 = 36
Then, we simplify the expression further:
21 over 7 + 3 * 36 = 21 over 7 + 108 = 3 + 108 = 111
Therefore, a over z + bw2, when a = 21, b = 3, w = 6, and z = 7, equals 111.
a over z + bw2 = 21 over 7 + 3 * 6^2
First, we simplify the exponent:
6^2 = 6 * 6 = 36
Then, we simplify the expression further:
21 over 7 + 3 * 36 = 21 over 7 + 108 = 3 + 108 = 111
Therefore, a over z + bw2, when a = 21, b = 3, w = 6, and z = 7, equals 111.
What is the simplified form of the following expression?
three-fifths cubed
(1 point)
Responses
twenty-seven-one hundred twenty-fifths
Image with alt text: twenty-seven-one hundred twenty-fifths
152
152
3,375
3,375
one hundred twenty-five-twenty-sevenths
three-fifths cubed
(1 point)
Responses
twenty-seven-one hundred twenty-fifths
Image with alt text: twenty-seven-one hundred twenty-fifths
152
152
3,375
3,375
one hundred twenty-five-twenty-sevenths
The simplified form of (three-fifths) cubed is:
three-fifths cubed = (3/5)^3 = 27/125
Therefore, the simplified form is twenty-seven-one hundred twenty-fifths.
three-fifths cubed = (3/5)^3 = 27/125
Therefore, the simplified form is twenty-seven-one hundred twenty-fifths.
Using the formula r equals d over t, where d is the distance in miles, r is the rate, and t is the time in hours, at which rate must you travel to cover 212.5 miles in 2.5 hours?
(1 point)
Responses
71 mph
71 mph
106 mph
106 mph
150 mph
150 mph
85 mph
(1 point)
Responses
71 mph
71 mph
106 mph
106 mph
150 mph
150 mph
85 mph
To find the rate at which you must travel to cover 212.5 miles in 2.5 hours, we use the formula r = d/t.
d = 212.5 miles
t = 2.5 hours
Substituting the values into the formula, we have:
r = 212.5 miles / 2.5 hours
Simplifying the division, we get:
r = 85 mph
Therefore, you must travel at a rate of 85 mph to cover 212.5 miles in 2.5 hours.
d = 212.5 miles
t = 2.5 hours
Substituting the values into the formula, we have:
r = 212.5 miles / 2.5 hours
Simplifying the division, we get:
r = 85 mph
Therefore, you must travel at a rate of 85 mph to cover 212.5 miles in 2.5 hours.
What is the simplified form of the following expression?
–(8n – 5v)
(1 point)
Responses
–8n + 5v
–8 n + 5 v
8n + 5v
8 n + 5 v
8n – 5v
8 n – 5 v
–8n – 5v
–8 n – 5 v
–(8n – 5v)
(1 point)
Responses
–8n + 5v
–8 n + 5 v
8n + 5v
8 n + 5 v
8n – 5v
8 n – 5 v
–8n – 5v
–8 n – 5 v
The simplified form of –(8n – 5v) is –8n + 5v.
Therefore, the correct response is –8n + 5v.
Therefore, the correct response is –8n + 5v.
What is the simplified form of the following expression?
12[62 ÷ (52 – 42) + 7]
(1 point)
Responses
12.6
12.6
195
195
33.8
33.8
132
12[62 ÷ (52 – 42) + 7]
(1 point)
Responses
12.6
12.6
195
195
33.8
33.8
132
To simplify the expression 12[62 ÷ (52 – 42) + 7], we start by evaluating the expression inside the parentheses first:
52 – 42 = 10
Next, we calculate the division:
62 ÷ 10 = 6.2
Then, we add 7 to this result:
6.2 + 7 = 13.2
Finally, we multiply this sum by 12:
12 * 13.2 = 158.4
So, the simplified form of the expression is 158.4.
Therefore, the correct response is 158.4.
52 – 42 = 10
Next, we calculate the division:
62 ÷ 10 = 6.2
Then, we add 7 to this result:
6.2 + 7 = 13.2
Finally, we multiply this sum by 12:
12 * 13.2 = 158.4
So, the simplified form of the expression is 158.4.
Therefore, the correct response is 158.4.
15 answers