Order the following numbers from least to greatest.
square root of eleven, –0.4, negative four-thirds, 0.8, square root of two
(1 point)
Responses
0.8, square root of two, negative four-thirds, square root of eleven, –0.4
0.8, Image with alt text: square root of two , Image with alt text: negative four-thirds , Image with alt text: square root of eleven , –0.4
square root of eleven, square root of two, 0.8, negative four-thirds, –0.4
Image with alt text: square root of eleven , Image with alt text: square root of two , 0.8, Image with alt text: negative four-thirds , –0.4
negative four-thirds, –0.4, 0.8, square root of two, square root of eleven
Image with alt text: negative four-thirds , –0.4, 0.8, Image with alt text: square root of two , Image with alt text: square root of eleven
–0.4, 0.8, square root of two, square root of eleven, negative four-thirds
–0.4, 0.8, Image with alt text: square root of two , Image with alt text: square root of eleven , Image with alt text: negative four-thirds
50 answers
–0.4, 0.8, square root of two, square root of eleven, negative four-thirds
Which number sentence does the following number line represent?
A number line is shown from negative 6 to 6. There are dots at negative 3 and 2. Above the dots are small vertical lines. An arrow that points to the left connects these two small lines.
(1 point)
Responses
3 + 2 = 5
3 + 2 = 5
negative 3 plus 5 equals 2
Image with alt text: negative 3 plus 5 equals 2
2 plus left parenthesis negative 3 right parenthesis equals 5
Image with alt text: 2 plus left parenthesis negative 3 right parenthesis equals 5
2 plus left parenthesis negative 5 right parenthesis equals negative 3
A number line is shown from negative 6 to 6. There are dots at negative 3 and 2. Above the dots are small vertical lines. An arrow that points to the left connects these two small lines.
(1 point)
Responses
3 + 2 = 5
3 + 2 = 5
negative 3 plus 5 equals 2
Image with alt text: negative 3 plus 5 equals 2
2 plus left parenthesis negative 3 right parenthesis equals 5
Image with alt text: 2 plus left parenthesis negative 3 right parenthesis equals 5
2 plus left parenthesis negative 5 right parenthesis equals negative 3
2 plus left parenthesis negative 3 right parenthesis equals 5
To which subset of real numbers does the following number belong?
square root of seven
(1 point)
Responses
rational numbers
rational numbers
irrational numbers
irrational numbers
whole numbers, integers, rational numbers
whole numbers, integers, rational numbers
whole numbers, natural numbers, integers
whole numbers, natural numbers, integers
square root of seven
(1 point)
Responses
rational numbers
rational numbers
irrational numbers
irrational numbers
whole numbers, integers, rational numbers
whole numbers, integers, rational numbers
whole numbers, natural numbers, integers
whole numbers, natural numbers, integers
irrational numbers
Which sum or difference is equivalent to the following expression?
Start Fraction 2 x plus 3 over 4 End Fraction
(1 point)
Responses
start fraction x over 2 end fraction + three-fourths
Image with alt text: start fraction x over 2 end fraction + Image with alt text: three-fourths
start fraction x over 2 end fraction – three-fourths
Image with alt text: start fraction x over 2 end fraction – Image with alt text: three-fourths
start fraction 3 x over 4 end fraction+ three-fourths
Image with alt text: start fraction 3 x over 4 end fraction + Image with alt text: three-fourths
8x + 24
Start Fraction 2 x plus 3 over 4 End Fraction
(1 point)
Responses
start fraction x over 2 end fraction + three-fourths
Image with alt text: start fraction x over 2 end fraction + Image with alt text: three-fourths
start fraction x over 2 end fraction – three-fourths
Image with alt text: start fraction x over 2 end fraction – Image with alt text: three-fourths
start fraction 3 x over 4 end fraction+ three-fourths
Image with alt text: start fraction 3 x over 4 end fraction + Image with alt text: three-fourths
8x + 24
start fraction x over 2 end fraction + three-fourths
What is the algebraic expression for the following word phrase: the sum of 4g and 6?
(1 point)
Responses
10g
10 g
4g + 6
4 g + 6
4 g minus 6
Image with alt text: 4 g minus 6
StartFraction 4 g over 6 EndFraction
(1 point)
Responses
10g
10 g
4g + 6
4 g + 6
4 g minus 6
Image with alt text: 4 g minus 6
StartFraction 4 g over 6 EndFraction
4g + 6
What is the algebraic expression for the following word phrase: the quotient of 8 and the sum of 3 and m?
(1 point)
Responses
StartFraction 8 over 3 plus m EndFraction
Image with alt text: StartFraction 8 over 3 plus m EndFraction
eight-thirds plus 8 m
Image with alt text: eight-thirds plus 8 m
8 left parenthesis 3 plus m right parenthesis
Image with alt text: 8 left parenthesis 3 plus m right parenthesis
StartFraction 8 over 3 minus m EndFraction
(1 point)
Responses
StartFraction 8 over 3 plus m EndFraction
Image with alt text: StartFraction 8 over 3 plus m EndFraction
eight-thirds plus 8 m
Image with alt text: eight-thirds plus 8 m
8 left parenthesis 3 plus m right parenthesis
Image with alt text: 8 left parenthesis 3 plus m right parenthesis
StartFraction 8 over 3 minus m EndFraction
StartFraction 8 over 3 plus m EndFraction
What is the algebraic expression for the following word phrase: the quotient of x and 6y?
(1 point)
Responses
x over 6
Image with alt text: x over 6
x over 6y
Image with alt text: x over 6y
6xy
6 xy
x – 6y
(1 point)
Responses
x over 6
Image with alt text: x over 6
x over 6y
Image with alt text: x over 6y
6xy
6 xy
x – 6y
x over 6y
What is the difference?
nine-fourths minus one-seventh
(1 point)
Responses
negative three-eighths
Image with alt text: negative three-eighths
fifty-nine-twenty-eighths
Image with alt text: fifty-nine-twenty-eighths
negative eight-thirds
Image with alt text: negative eight-thirds
sixty-seven-twenty-eighths
nine-fourths minus one-seventh
(1 point)
Responses
negative three-eighths
Image with alt text: negative three-eighths
fifty-nine-twenty-eighths
Image with alt text: fifty-nine-twenty-eighths
negative eight-thirds
Image with alt text: negative eight-thirds
sixty-seven-twenty-eighths
negative eight-thirds
What is the simplified form of the following expression?
square root of one-one hundred forty-fourth
(1 point)
Responses
one-twelfth
Image with alt text: one-twelfth
one-two hundred eighty-eighth
Image with alt text: one-two hundred eighty-eighth
12
12
two-one hundred forty-fourths
square root of one-one hundred forty-fourth
(1 point)
Responses
one-twelfth
Image with alt text: one-twelfth
one-two hundred eighty-eighth
Image with alt text: one-two hundred eighty-eighth
12
12
two-one hundred forty-fourths
12
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
(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
Associative Property of Multiplication
Evaluate a over z + bw2 for a = 21, b = 3, w = 6, and z = 7.
(1 point)
Responses
111
111
108
108
301
301
1,771
1,771
(1 point)
Responses
111
111
108
108
301
301
1,771
1,771
To evaluate the expression, substitute the given values into the expression:
a/z + bw^2 = 21/7 + 3(6^2)
= 21/7 + 3(36)
= 3 + 108
= 111
Therefore, the value of the expression is 111.
a/z + bw^2 = 21/7 + 3(6^2)
= 21/7 + 3(36)
= 3 + 108
= 111
Therefore, the value of the expression is 111.
What is the product?
4.3(–2.9)
(1 point)
Responses
12.47
12.47
–12.47
–12.47
7.74
7.74
–5.22
4.3(–2.9)
(1 point)
Responses
12.47
12.47
–12.47
–12.47
7.74
7.74
–5.22
To find the product of 4.3 and -2.9, simply multiply these two numbers:
4.3 * (-2.9) = -12.47
Therefore, the product is -12.47.
4.3 * (-2.9) = -12.47
Therefore, the product is -12.47.
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
To simplify the expression (three-fifths) cubed, you need to raise the numerator, 3, to the power of 3, and the denominator, 5, to the power of 3.
(3/5)^3 = (3^3)/(5^3) = 27/125
Therefore, the simplified form of the expression is twenty-seven-one hundred twenty-fifths.
(3/5)^3 = (3^3)/(5^3) = 27/125
Therefore, the simplified form of the expression is twenty-seven-one hundred twenty-fifths.
Which word phrase can you use to represent the algebraic expression 6y?
(1 point)
Responses
6 less than a number y
6 less than a number y
the sum of 6 and a number y
the sum of 6 and a number y
the product of 6 and a number y
the product of 6 and a number y
the quotient of a number y and 6
(1 point)
Responses
6 less than a number y
6 less than a number y
the sum of 6 and a number y
the sum of 6 and a number y
the product of 6 and a number y
the product of 6 and a number y
the quotient of a number y and 6
the product of 6 and a number y
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, we need to rearrange the formula:r = d/t
Given:
d = 212.5 miles
t = 2.5 hours
Substituting these values into the formula:
r = 212.5 miles / 2.5 hours = 85 mph
Therefore, you must travel at a rate of 85 mph to cover 212.5 miles in 2.5 hours.
Given:
d = 212.5 miles
t = 2.5 hours
Substituting these values into the formula:
r = 212.5 miles / 2.5 hours = 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
To simplify the expression –(8n – 5v), you distribute the negative sign to each term inside the parentheses:
–(8n – 5v) = –8n + 5v
Therefore, the simplified form of the expression is –8n + 5v.
–(8n – 5v) = –8n + 5v
Therefore, the simplified form of the expression 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], follow the order of operations (PEMDAS/BODMAS), which states to simplify expressions inside parentheses first, then perform any multiplication or division from left to right, and finally perform addition or subtraction from left to right.
Inside the parentheses:
52 – 42 = 10
Now substitute the simplified value back into the expression:
12[62 ÷ 10 + 7]
Next, perform the division:
62 ÷ 10 = 6.2
Now substitute the simplified value back into the expression:
12[6.2 + 7]
Perform the addition:
6.2 + 7 = 13.2
Now substitute the simplified value back into the expression:
12 * 13.2
Perform the multiplication:
12 * 13.2 = 158.4
Therefore, the simplified form of the expression 12[62 ÷ (52 – 42) + 7] is 158.4.
Inside the parentheses:
52 – 42 = 10
Now substitute the simplified value back into the expression:
12[62 ÷ 10 + 7]
Next, perform the division:
62 ÷ 10 = 6.2
Now substitute the simplified value back into the expression:
12[6.2 + 7]
Perform the addition:
6.2 + 7 = 13.2
Now substitute the simplified value back into the expression:
12 * 13.2
Perform the multiplication:
12 * 13.2 = 158.4
Therefore, the simplified form of the expression 12[62 ÷ (52 – 42) + 7] is 158.4.
the 2s by the 4 and 5 are exponents
Apologies for the confusion. To simplify the expression 12[62 ÷ (52 – 42) + 7], we need to follow the order of operations, taking into account the exponents.
Inside the parentheses:
52 – 42 = 10
Now substitute the simplified value back into the expression:
12[62 ÷ 10 + 7]
Next, perform the division:
62 ÷ 10 = 6.2
Now substitute the simplified value back into the expression:
12[6.2 + 7]
Perform the addition:
6.2 + 7 = 13.2
Now substitute the simplified value back into the expression:
12 * 13.2
Perform the multiplication:
12 * 13.2 = 158.4
Therefore, the simplified form of the expression 12[62 ÷ (52 – 42) + 7] is 158.4.
Inside the parentheses:
52 – 42 = 10
Now substitute the simplified value back into the expression:
12[62 ÷ 10 + 7]
Next, perform the division:
62 ÷ 10 = 6.2
Now substitute the simplified value back into the expression:
12[6.2 + 7]
Perform the addition:
6.2 + 7 = 13.2
Now substitute the simplified value back into the expression:
12 * 13.2
Perform the multiplication:
12 * 13.2 = 158.4
Therefore, the simplified form of the expression 12[62 ÷ (52 – 42) + 7] is 158.4.
all of the 2 in this equation are exponents
Apologies for the previous incorrect responses.
To simplify the expression 12[62 ÷ (52 – 42) + 7], we need to consider the exponents first.
Inside the parentheses:
52 – 42 = 5
Now substitute the simplified value back into the expression:
12[62 ÷ 5^2 + 7]
Next, perform the exponentiation:
5^2 = 25
Now substitute the simplified value back into the expression:
12[62 ÷ 25 + 7]
Next, perform the division:
62 ÷ 25 = 2.48
Now substitute the simplified value back into the expression:
12[2.48 + 7]
Perform the addition:
2.48 + 7 = 9.48
Now substitute the simplified value back into the expression:
12 * 9.48
Perform the multiplication:
12 * 9.48 = 113.76
Therefore, the simplified form of the expression 12[62 ÷ (52 – 42) + 7] is 113.76.
To simplify the expression 12[62 ÷ (52 – 42) + 7], we need to consider the exponents first.
Inside the parentheses:
52 – 42 = 5
Now substitute the simplified value back into the expression:
12[62 ÷ 5^2 + 7]
Next, perform the exponentiation:
5^2 = 25
Now substitute the simplified value back into the expression:
12[62 ÷ 25 + 7]
Next, perform the division:
62 ÷ 25 = 2.48
Now substitute the simplified value back into the expression:
12[2.48 + 7]
Perform the addition:
2.48 + 7 = 9.48
Now substitute the simplified value back into the expression:
12 * 9.48
Perform the multiplication:
12 * 9.48 = 113.76
Therefore, the simplified form of the expression 12[62 ÷ (52 – 42) + 7] is 113.76.
that's still wrong
Apologies for the misunderstanding. Let's simplify the expression again, considering the 2 as exponents.
Inside the parentheses:
52 - 42 = 10
Now substitute the simplified value back into the expression:
12[62 ÷ (10) + 7]
Perform the division:
62 ÷ 10 = 6.2
Now substitute the simplified value back into the expression:
12[6.2 + 7]
Perform the addition:
6.2 + 7 = 13.2
Now substitute the simplified value back into the expression:
12 * 13.2
Perform the multiplication:
12 * 13.2 = 158.4
Therefore, the simplified form of the expression 12[62 ÷ (52 – 42) + 7] is 158.4.
Inside the parentheses:
52 - 42 = 10
Now substitute the simplified value back into the expression:
12[62 ÷ (10) + 7]
Perform the division:
62 ÷ 10 = 6.2
Now substitute the simplified value back into the expression:
12[6.2 + 7]
Perform the addition:
6.2 + 7 = 13.2
Now substitute the simplified value back into the expression:
12 * 13.2
Perform the multiplication:
12 * 13.2 = 158.4
Therefore, the simplified form of the expression 12[62 ÷ (52 – 42) + 7] is 158.4.
158.4 is not one of the options the options are 12.6, 195, 33.8, 132
Apologies for the confusion. Let's simplify the expression again, considering the 2 as exponents.
Inside the parentheses:
52 - 42 = 10
Now substitute the simplified value back into the expression:
12[6^2 ÷ 10 + 7]
Perform the exponentiation:
6^2 = 36
Now substitute the simplified value back into the expression:
12[36 ÷ 10 + 7]
Perform the division:
36 ÷ 10 = 3.6
Now substitute the simplified value back into the expression:
12[3.6 + 7]
Perform the addition:
3.6 + 7 = 10.6
Now substitute the simplified value back into the expression:
12 * 10.6
Perform the multiplication:
12 * 10.6 = 127.2
Therefore, the simplified form of the expression 12[62 ÷ (52 – 42) + 7] is 127.2.
Inside the parentheses:
52 - 42 = 10
Now substitute the simplified value back into the expression:
12[6^2 ÷ 10 + 7]
Perform the exponentiation:
6^2 = 36
Now substitute the simplified value back into the expression:
12[36 ÷ 10 + 7]
Perform the division:
36 ÷ 10 = 3.6
Now substitute the simplified value back into the expression:
12[3.6 + 7]
Perform the addition:
3.6 + 7 = 10.6
Now substitute the simplified value back into the expression:
12 * 10.6
Perform the multiplication:
12 * 10.6 = 127.2
Therefore, the simplified form of the expression 12[62 ÷ (52 – 42) + 7] is 127.2.
What is the simplified form of the following expression?
12[6^2 ÷ (5^2 – 4^2) + 7]
(1 point)
Responses
12.6
12.6
195
195
33.8
33.8
132
12[6^2 ÷ (5^2 – 4^2) + 7]
(1 point)
Responses
12.6
12.6
195
195
33.8
33.8
132
To simplify the expression 12[6^2 ÷ (5^2 - 4^2) + 7], we need to calculate the exponents and perform the operations within the parentheses first.
Inside the parentheses:
5^2 - 4^2 = 25 - 16 = 9
Now substitute the simplified value back into the expression:
12[6^2 ÷ 9 + 7]
Perform the exponentiation:
6^2 = 36
Now substitute the simplified value back into the expression:
12[36 ÷ 9 + 7]
Perform the division:
36 ÷ 9 = 4
Now substitute the simplified value back into the expression:
12[4 + 7]
Perform the addition:
4 + 7 = 11
Now substitute the simplified value back into the expression:
12 * 11 = 132
Therefore, the simplified form of the expression 12[6^2 ÷ (5^2 - 4^2) + 7] is 132.
Inside the parentheses:
5^2 - 4^2 = 25 - 16 = 9
Now substitute the simplified value back into the expression:
12[6^2 ÷ 9 + 7]
Perform the exponentiation:
6^2 = 36
Now substitute the simplified value back into the expression:
12[36 ÷ 9 + 7]
Perform the division:
36 ÷ 9 = 4
Now substitute the simplified value back into the expression:
12[4 + 7]
Perform the addition:
4 + 7 = 11
Now substitute the simplified value back into the expression:
12 * 11 = 132
Therefore, the simplified form of the expression 12[6^2 ÷ (5^2 - 4^2) + 7] is 132.
What is the simplified form of the following expression?
StartFraction 10 y z over negative 2 z EndFraction
(1 point)
Responses
negative 5 y z
Image with alt text: negative 5 y z
negative 5 y
Image with alt text: negative 5 y
negative 5 y z squared
Image with alt text: negative 5 y z squared
5y
5 y
StartFraction 10 y z over negative 2 z EndFraction
(1 point)
Responses
negative 5 y z
Image with alt text: negative 5 y z
negative 5 y
Image with alt text: negative 5 y
negative 5 y z squared
Image with alt text: negative 5 y z squared
5y
5 y
To simplify the expression StartFraction 10yz over negative 2z EndFraction, we can cancel out the common factors in the numerator and denominator.
10yz ÷ -2z = 5y
Therefore, the simplified form of the expression is 5y.
10yz ÷ -2z = 5y
Therefore, the simplified form of the expression is 5y.
The temperature at the end of the day was 64 degrees. The temperature had increased twice during the day, once by 8 degrees and another time by 4 degrees.
Which expression shows what the temperature was at the start of the day?
(1 point)
Responses
64 – 8 – 4
64 – 8 – 4
64 + 8 – 4
64 + 8 – 4
64 – 8 + 4
64 – 8 + 4
78 + 5 + 7
Which expression shows what the temperature was at the start of the day?
(1 point)
Responses
64 – 8 – 4
64 – 8 – 4
64 + 8 – 4
64 + 8 – 4
64 – 8 + 4
64 – 8 + 4
78 + 5 + 7
To find the temperature at the start of the day, we need to subtract the total increase in temperature from the temperature at the end of the day.
Given:
Temperature at the end of the day = 64 degrees
Increase in temperature during the day = 8 degrees + 4 degrees = 12 degrees
To find the temperature at the start of the day:
64 - 12 = 52 degrees
Therefore, the expression that shows what the temperature was at the start of the day is 64 - 8 - 4.
Given:
Temperature at the end of the day = 64 degrees
Increase in temperature during the day = 8 degrees + 4 degrees = 12 degrees
To find the temperature at the start of the day:
64 - 12 = 52 degrees
Therefore, the expression that shows what the temperature was at the start of the day is 64 - 8 - 4.
What is the value of xy over w if x = –3, y = 4 and w = –6.
(1 point)
Responses
2
2
–2
–2
one-half
Image with alt text: one-half
–one-half
(1 point)
Responses
2
2
–2
–2
one-half
Image with alt text: one-half
–one-half
To find the value of xy over w, substitute the given values into the expression:
xy / w = (-3)(4) / (-6) = -12 / -6 = 2
Therefore, the value of xy over w is 2.
xy / w = (-3)(4) / (-6) = -12 / -6 = 2
Therefore, the value of xy over w is 2.
Which statement about the product is true?
7.56 times 6 point ModifyingAbove 7 with bar
(1 point)
Responses
The product is irrational.
The product is irrational.
The product is rational.
The product is rational.
The product is neither rational nor irrational.
The product is neither rational nor irrational.
The nature of the product cannot be determined.
The nature of the product cannot be determined.
7.56 times 6 point ModifyingAbove 7 with bar
(1 point)
Responses
The product is irrational.
The product is irrational.
The product is rational.
The product is rational.
The product is neither rational nor irrational.
The product is neither rational nor irrational.
The nature of the product cannot be determined.
The nature of the product cannot be determined.