What is the simplified form of the following expression?
6c2 + 2.5d – d + 2c2 – 3d
(1 point)
Responses
4c2 – 1.5d
4 c 2 – 1.5 d
6c2 + 0.5d
6 c 2 + 0.5 d
8c2 – 1.5d
8 c 2 – 1.5 d
8c2 + 1.5d
Yup thats what I thought
4c2 – 1.5d
Simplify the following expression.
one-fourth(16 – 12x)
(1 point)
Responses
4 + 3x
4 + 3 x
4 – 3x
4 – 3 x
4 + 3
4 + 3
4 – 3
4 - 3x
What is the sum?
seven-thirds plus negative three-eighths
(1 point)
Responses
sixty-five-twenty-fourths
Image with alt text: sixty-five-twenty-fourths
forty-seven-twenty-fourths
Image with alt text: forty-seven-twenty-fourths
negative four-fifths
Image with alt text: negative four-fifths
negative five-fourths
negative five-fourths
I'm pretty sure you did that one wrong, can you explain your steps to finding that answer?
Apologies for the incorrect response. Let's go through the steps to find the correct answer.
To add fractions, we need to have a common denominator. In this case, the common denominator is 24.
The sum of seven-thirds and negative three-eighths is:
(7/3) + (-3/8)
To find a common denominator of 24, we need to multiply the numerator and denominator of the first fraction by 8, and the numerator and denominator of the second fraction by 3:
(7/3) * (8/8) + (-3/8) * (3/3)
This becomes:
(56/24) + (-9/24)
Now that we have a common denominator, we can simply add the numerators:
56 + (-9) = 47
Therefore, the correct sum is forty-seven-twenty-fourths.
Apologies for the confusion earlier. Thank you for bringing it to my attention. If you have any further questions, feel free to ask.
What is the algebraic expression for the following word phrase: the quotient of 8 and the sum of 3 and m?
(1 point)
To express the given word phrase as an algebraic expression, we can use the division symbol to represent "the quotient of" and the addition symbol to represent "the sum of."
The word phrase "the quotient of 8 and the sum of 3 and m" can be represented algebraically as:
8 / (3 + m)
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
To find the difference between two fractions, we need to have a common denominator. In this case, the common denominator is 28.
The difference between nine-fourths and one-seventh is:
(9/4) - (1/7)
To find a common denominator of 28, we need to multiply the numerator and denominator of the first fraction by 7, and the numerator and denominator of the second fraction by 4:
(9/4) * (7/7) - (1/7) * (4/4)
This becomes:
(63/28) - (4/28)
Now that we have a common denominator, we can simply subtract the numerators:
63 - 4 = 59
Therefore, the correct difference is fifty-nine-twenty-eighths.
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
The property illustrated by the following statement is the Associative Property of Multiplication. The property states that the grouping of factors in a multiplication expression does not affect the final result. In this case, we can see that the factors (3z), x, and y are grouped differently, but the final result remains the same.
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
To evaluate the expression a/z + bw^2 for a = 21, b = 3, w = 6, and z = 7, we can substitute these values into the expression and simplify:
a/z + bw^2 = 21/7 + 3(6)^2
= 21/7 + 3(36)
= 21/7 + 108
= 3 + 108
= 111
Therefore, the expression evaluates to 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
–5.22
The product of 4.3 and -2.9 is:
4.3 * (-2.9) = -12.47
Therefore, the correct response 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
The simplified form of "three-fifths cubed" can be found by cubing the fraction three-fifths.
To cube a fraction, we raise both the numerator and denominator to the power of 3.
(3/5)^3 = (3^3) / (5^3) = 27 / 125
Therefore, the simplified form of three-fifths cubed 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
the quotient of a number y and 6
The word phrase that can be used to represent the algebraic expression 6y is "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
To find the rate at which you must travel to cover 212.5 miles in 2.5 hours, we can use the formula r = d / t, where r is the rate, d is the distance, and t is the time.
Plugging in the given values:
r = 212.5 miles / 2.5 hours
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?
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 need to follow the order of operations, which is parentheses -> multiplication/division -> addition/subtraction.
First, let's simplify the expression within the parentheses:
52 - 42 = 10
Now, we can divide 62 by the result of the subtraction:
62 ÷ 10 = 6.2
Next, we add 7 to the result of the division:
6.2 + 7 = 13.2
Finally, we multiply the entire expression by 12:
12 * 13.2 = 158.4
Therefore, the simplified form of the expression is 158.4.
Oh no I'm so sorry I made a mistake in my typing! I meant to say: 12[6^2÷ (5^2 - 4^2)+7]
No problem! Let's simplify the corrected expression:
First, let's simplify the expression within the parentheses:
5^2 - 4^2 = 25 - 16 = 9
Now, we can divide 6^2 by the result of the subtraction:
6^2 ÷ 9 = 36 ÷ 9 = 4
Next, we add 7 to the result of the division:
4 + 7 = 11
Finally, we multiply the entire expression by 12:
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
The simplified form of the expression,
StartFraction 10 y z over negative 2 z EndFraction,
can be found by cancelling out the common factor of z in the numerator and denominator:
StartFraction 10y cancel(z) over negative 2 cancel(z) EndFraction
This simplifies to:
StartFraction 10y over negative 2 EndFraction
which further simplifies to:
-5y
Therefore, the correct simplified form is negative 5y.
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
To find the value of xy over w with x = -3, y = 4, and w = -6, we substitute these values into the expression:
xy / w = (-3 * 4) / (-6)
= -12 / -6
When dividing two negative numbers, the result is positive:
-12 / -6 = 2
Therefore, the value of xy over w is 2.