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.
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
Apologies for the previous confusion. The accurate response is:
The product is rational.
The number sentence that represents the given number line is: 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
rational numbers
irrational numbers
whole numbers, integers, rational numbers
whole numbers, natural numbers, integers
The square root of seven belongs to the subset of real numbers known as irrational numbers.
Which sum or difference is equivalent to the following expression?
Start Fraction 2 x plus 3 over 4 End Fraction
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
The sum or difference that is equivalent to the expression Start Fraction 2 x plus 3 over 4 End Fraction is 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?
10g
4g + 6
4 g minus 6
StartFraction 4 g over 6 EndFraction
The algebraic expression for the word phrase "the sum of 4g and 6" is 4g + 6.
What is the algebraic expression for the following word phrase: the quotient of 8 and the sum of 3 and m?
StartFraction 8 over 3 plus m EndFraction
eight-thirds plus 8 m
8 left parenthesis 3 plus m right parenthesis
StartFraction 8 over 3 minus m EndFraction
The algebraic expression for the word phrase "the quotient of 8 and the sum of 3 and m" is StartFraction 8 over 3 plus m EndFraction.
What is the algebraic expression for the following word phrase: the quotient of x and 6y?
x over 6
x over 6y
6xy
x – 6y
The algebraic expression for the word phrase "the quotient of x and 6y" is x over 6y.
What is the difference?
nine-fourths minus one-seventh
negative three-eighths
fifty-nine-twenty-eighths
negative eight-thirds
sixty-seven-twenty-eighths
The difference between nine-fourths and one-seventh is sixty-seven-twenty-eighths.
What is the difference?
nine-fourths minus one-seventh
negative three-eighths
fifty-nine-twenty-eighths
negative eight-thirds
sixty-seven-twenty-eighths
The difference between nine-fourths and one-seventh is fifty-nine-twenty-eighths.
What is the simplified form of the following expression?
square root of one-one hundred forty-fourth
one-twelfth
one-two hundred eighty-eighth
12
two-one hundred forty-fourths
The simplified form of the expression "square root of one-one hundred forty-fourth" is 12.
Which property is illustrated by the following statement?
(3z)xy = 3(zx)y
Associative Property of Multiplication
Commutative Property of Multiplication
Inverse Property of Multiplication
Commutative Property of Addition
The property illustrated by the statement (3z)xy = 3(zx)y is the Associative Property of Multiplication.
Evaluate a over z + bw2 for a = 21, b = 3, w = 6, and z = 7.
111
108
301
1,771
To evaluate a over z + bw^2 for a = 21, b = 3, w = 6, and z = 7, we substitute the given values into the expression:
21 over 7 + 3 * 6^2
This simplifies to:
21/7 + 3 * 36
Next, we need to perform the multiplication:
21/7 + 108
Now we need to find a common denominator to add the fractions:
3 + 108
Lastly, we sum the two numbers:
111
Therefore, the evaluation is 111.
What is the product?
4.3(–2.9)
12.47
–12.47
7.74
–5.22
The product of 4.3 and -2.9 is -12.47.
What is the simplified form of the following expression?
three-fifths cubed
twenty-seven-one hundred twenty-fifths
152
3,375
one hundred twenty-five-twenty-sevenths
The simplified form of the expression "three-fifths cubed" is twenty-seven-one hundred twenty-fifths.
Which word phrase can you use to represent the algebraic expression 6y?
6 less than a number y
the sum of 6 and a number y
the product of 6 and a number y
the quotient of a number y and 6
To represent the algebraic expression 6y, the word phrase "the product of 6 and a number y" can be used.
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?
71 mph
106 mph
150 mph
85 mph
To find the rate at which you must travel to cover 212.5 miles in 2.5 hours, we can rearrange the formula r = d/t to solve for r.
We have d = 212.5 miles and t = 2.5 hours.
Plugging these values into the formula, we have:
r = 212.5 miles / 2.5 hours
Simplifying the expression, 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)
–8n + 5v
8n + 5v
8n – 5v
–8n – 5v
The simplified form of the expression –(8n – 5v) is –8n + 5v.
What is the simplified form of the following expression?
12[62 ÷ (52 – 42) + 7]
12.6
195
33.8
132
To simplify the expression 12[62 ÷ (52 – 42) + 7], we need to begin by evaluating the expression inside the parentheses.
52 – 42 simplifies to 10.
So the expression becomes 12[62 ÷ 10 + 7].
Next, we evaluate 62 ÷ 10, which is 6.2.
Therefore, the expression simplifies to 12[6.2 + 7].
Adding 6.2 and 7 gives us 13.2.
Finally, multiplying 12 by 13.2 gives us the simplified form of the expression:
12 * 13.2 = 158.4.
Thus, the simplified form of the expression 12[62 ÷ (52 – 42) + 7] is 158.4.
What is the simplified form of the following expression?
StartFraction 10 y z over negative 2 z EndFraction
negative 5 y z
negative 5 y
negative 5 y z squared
5y
The simplified form of the expression StartFraction 10 y z over negative 2 z EndFraction is negative 5 y.
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?
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 end of the day temperature of 64 degrees.
The total increase is 8 degrees + 4 degrees = 12 degrees.
Therefore, the expression that shows what the temperature was at the start of the day is:
64 - 12
This simplifies to:
52.
Hence, the temperature at the start of the day was 52 degrees.
What is the value of xy over w if x = –3, y = 4 and w = –6.
2
–2
one-half
–one-half
To find the value of xy over w, we substitute the given values for x, y, and w into the expression:
xy over w = (-3)(4) / (-6)
= -12 / -6
Simplifying the expression, the negative signs cancel out:
-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
The product is irrational.
The product is rational.
The product is neither rational nor irrational.
The nature of the product cannot be determined.
The statement "7.56 times 6.7 with a bar above 7" describes the multiplication of a decimal number with a recurring decimal representation.
The product of 7.56 and 6.7 with a bar above 7 is rational because it can be expressed as a fraction, with a terminating or recurring decimal representation.
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.
Which of the following results in a sum or a product that is rational? Choose all that apply.
4 + 9
pi times 5
3 point ModifyingAbove 45 with bar times 1.2
StartRoot 16 Endroot times StartRoot 4 EndRoot
StartRoot 7 EndRoot times StartRoot 2 EndRoot
The examples that result in a sum or a product that is rational are:
4 + 9 (sum)
StartRoot 16 EndRoot times StartRoot 4 EndRoot (product)
Molli purchased 8 apples for $2.96. While looking at her receipt, Molli divided $2.96 by 8. Why might Molli perform this calculation?
in order to find the total number of apples purchased
in order to find out how much she paid per apple
in order to calculate the total amount that she owes
in order to calculate how much money she has left
Molli might perform the calculation of dividing $2.96 by 8 in order to find out how much she paid per apple.
Short Answer
Note: Your teacher will grade your response to ensure that you receive proper credit for your answer.
A gym membership costs $25 to join and $14 each month. Write and use an algebraic expression to find the cost of the gym membership for 6 months.
The algebraic expression to find the cost of the gym membership for 6 months is:
Joining cost + Monthly cost * Number of months
Substituting the given values:
$25 + $14 * 6
Simplifying the expression:
$25 + $84
The cost of the gym membership for 6 months is $109.