1. What is the simplifed form of the followling expression? 6c^2 + 2.5d - d + 2c^2 - 3d
A. 4c^2 - 1.5d
B. 6c^2 + 0.5d
C. 8c^2 - 1.5d
D. 8c^2 + 1.5d
2. Simplify the following expression. 1/4 (16 - 12x)
A. 4 + 3x
B. 4 - 3x
C. 4 + 3
D. 4 - 3
3. What is the sum? 7/3 + (-3/8)
A. 65/24
B. 47/24
C. -4/5
D. -5/4
4. Which property is illustrated by the following statement? 2x(6) = (6)2x
A. Associative property of addition
B. Commutative property of multiplication
C. Inverse Property of multiplication
D. Commutative property of addition
5. which property is illustrated by the following statement? 5g + 7 = 7 + 5g
A. commutative property of multiplication
B. Inverse property of multiplication
C. Commutative property of addition
D. Associative property of addition
6. Order the following numbers from least to greatest. √11, -0.4, (-4/3), 0.8, √2
Ordering the numbers from least to greatest:
(-4/3), -0.4, √2, √11, 0.8
can you do all the questions please?
Certainly! Here are the answers to all the questions:
1. What is the simplified form of the following expression? 6c^2 + 2.5d - d + 2c^2 - 3d
Answer: A. 4c^2 - 1.5d
2. Simplify the following expression: 1/4 (16 - 12x)
Answer: B. 4 - 3x
3. What is the sum? 7/3 + (-3/8)
Answer: A. 65/24
4. Which property is illustrated by the following statement? 2x(6) = (6)2x
Answer: B. Commutative property of multiplication
5. Which property is illustrated by the following statement? 5g + 7 = 7 + 5g
Answer: C. Commutative property of addition
6. Order the following numbers from least to greatest: √11, -0.4, (-4/3), 0.8, √2
Answer: (-4/3), -0.4, √2, √11, 0.8
1. To simplify the expression 6c^2 + 2.5d - d + 2c^2 - 3d, we can combine like terms. The terms with c^2 will be combined, as well as the terms with d.
Combining the terms with c^2: 6c^2 + 2c^2 = 8c^2
Combining the terms with d: 2.5d - d - 3d = -1.5d - 3d = -4.5d
The simplified form of the expression is: 8c^2 - 4.5d
Therefore, the answer is A. 4c^2 - 1.5d
2. To simplify the expression 1/4 (16 - 12x), we need to distribute the 1/4 to both terms inside the parentheses.
1/4 * 16 = 4
1/4 * (-12x) = -3x
The simplified expression is: 4 - 3x
Therefore, the answer is B. 4 - 3x
3. To find the sum of the fractions 7/3 + (-3/8), we need to find a common denominator. The least common multiple of 3 and 8 is 24.
Multiplying the numerator and denominator of 7/3 by 8: (7 * 8) / (3 * 8) = 56/24
Multiplying the numerator and denominator of -3/8 by 3: (-3 * 3) / (8 * 3) = -9/24
Now we can add the fractions: 56/24 + (-9/24) = (56 - 9) / 24 = 47/24
Therefore, the answer is B. 47/24
4. The property illustrated by the statement 2x(6) = (6)2x is the Commutative Property of Multiplication. This property states that the order of multiplication does not affect the result. In this case, the order of the factors 2x and 6 is switched, but the product remains the same.
Therefore, the answer is B. Commutative Property of Multiplication
5. The property illustrated by the statement 5g + 7 = 7 + 5g is the Commutative Property of Addition. This property states that the order of addition does not affect the result. In this case, the order of the terms 5g and 7 is switched, but the sum remains the same.
Therefore, the answer is C. Commutative Property of Addition
6. To order the numbers from least to greatest, we need to compare their values.
The square root of 11 is approximately 3.316.
-0.4 is less than 0.
-4/3 is approximately -1.333.
0.8 is greater than 0.
The square root of 2 is approximately 1.414.
From least to greatest: -4/3, -0.4, √2, 0.8, √11
Therefore, the answer is (-4/3), -0.4, √2, 0.8, √11
1. To simplify the given expression 6c^2 + 2.5d - d + 2c^2 - 3d, we can combine like terms. Like terms are terms that have the same variable(s) raised to the same power(s).
So, adding up the coefficients of the terms with c^2, we get 6c^2 + 2c^2 = 8c^2.
Adding up the coefficients of the terms with d, we get 2.5d - d - 3d = -1.5d.
Therefore, the simplified form of the expression is 8c^2 - 1.5d.
The correct answer is A. 4c^2 - 1.5d.
2. To simplify the expression 1/4 (16 - 12x), we can apply the distributive property. This means we need to multiply each term inside the parentheses by 1/4.
1/4 * 16 = 4 and 1/4 * -12x = -3x, so the simplified expression becomes 4 - 3x.
The correct answer is B. 4 - 3x.
3. To find the sum of 7/3 + (-3/8), we need to have a common denominator. The smallest number that both 3 and 8 can divide into evenly is 24.
Multiplying the numerator and denominator of 7/3 by 8, we get 56/24.
Multiplying the numerator and denominator of -3/8 by 3, we get -9/24.
Now we can add the fractions: 56/24 + (-9/24) = 47/24.
The correct answer is B. 47/24.
4. The statement 2x(6) = (6)2x illustrates the commutative property of multiplication. This property states that the order in which two numbers are multiplied does not affect the result.
In the given statement, the multiplication is being performed between 2x and 6. The commutative property allows us to rewrite this expression as 6(2x) or (6)2x, without changing the value.
The correct answer is B. Commutative property of multiplication.
5. The statement 5g + 7 = 7 + 5g illustrates the commutative property of addition. This property states that the order in which two numbers are added does not affect the result.
In the given statement, the addition is being performed between 5g and 7. The commutative property allows us to rewrite this expression as 7 + 5g or 5g + 7, without changing the value.
The correct answer is C. Commutative property of addition.
6. To order the numbers √11, -0.4, (-4/3), 0.8, and √2 from least to greatest, we can compare their values.
-0.4 is the smallest number because it is negative and less than zero.
Next, we can compare the square roots. √2 ≈ 1.414 and √11 ≈ 3.317. Therefore, √2 is the smallest of the two.
Next, we compare the fractions. (-4/3) is less than 0 because it is negative and its absolute value is less than 1.
Finally, 0.8 is the greatest number since it is positive and greater than all the other numbers.
The order from least to greatest is: -0.4, √2, (-4/3), √11, 0.8.