1.) Use the distributive Property to simplify the expression .
(-1)(4 - c)
A. 4 - c
B. -4 + c
C. 4 + c
D.-4 - c
2.)Use the distributive Property to simplify the expression
4(2x - 4)
A.8x + 4
B.8x - 4
C.8x - 16
D.4x - 16
3.) Use the distributive Property to simplify the expression
(10 + 4y) 1/2
A. 5 + 2y
B. 20 + 8y
C. 5 + 4y
D. 10 +2y
4.) To which subsets of real numbers does the number - 22 belong ? Choose all that apply (2 points)
A.Whole numbers
B.Rational numbers
C. Integers
D. Irrational numbers
E. Natural numbers
5.)What is an algebraic expression for the following word phrase: "6 times the difference of b and p" ?
A. 6b - p
B. 6(b - p)
C. 6 - bp
D. 6bp
6.)What is the simplified form of the expression ?
5(14 - 2)^2
------------------
2
A. 60
B. 30
C. 72
D. 360
7.) Evaluate u + xy, if u = 18, x = 10, and y = 8
A.188
B.36
C.98
D.224
8. A square field has an area of 479 ft^2 . What is the approximate length of a side of the field ? Give your answer to the nearest foot . Explain your response .
9. Simplify the expression (7 + 5) + 4 x 13 - 2 Show work .
1.) Use the distributive Property to simplify the expression (-1)(4 - c)
Distributing -1:
-1 * 4 = -4
-1 * (-c) = c
So the simplified expression is: -4 + c
The correct answer is B. -4 + c
2.) Use the distributive Property to simplify the expression 4(2x - 4)
Distributing 4:
4 * 2x = 8x
4 * (-4) = -16
So the simplified expression is: 8x - 16
The correct answer is C. 8x - 16
3.) Use the distributive Property to simplify the expression (10 + 4y) 1/2
Distributing 1/2:
1/2 * 10 = 5
1/2 * 4y = 2y
So the simplified expression is: 5 + 2y
The correct answer is A. 5 + 2y
4.) To which subsets of real numbers does the number -22 belong? Choose all that apply.
A. Whole numbers - No, because whole numbers are non-negative integers.
B. Rational numbers - Yes, because -22 can be expressed as a fraction (-22/1).
C. Integers - Yes, because -22 is an integer.
D. Irrational numbers - No, because -22 is a rational number.
E. Natural numbers - No, because natural numbers are positive integers.
The correct answers are B. Rational numbers and C. Integers.
5.) What is an algebraic expression for the following word phrase: "6 times the difference of b and p"?
To find the difference of b and p, we subtract p from b: b - p
Now, we multiply this difference by 6: 6 * (b - p)
So the algebraic expression is B. 6(b - p).
6.) What is the simplified form of the expression 5(14 - 2)^2 / 2?
Simplifying the expression inside the parentheses:
14 - 2 = 12
Squaring the result:
12^2 = 144
Now, multiplying by 5:
5 * 144 = 720
Lastly, dividing by 2:
720 / 2 = 360
So the simplified form of the expression is D. 360.
7.) Evaluate u + xy, if u = 18, x = 10, and y = 8
Substituting the given values:
18 + 10 * 8 = 18 + 80 = 98
So the value of u + xy is C. 98.
8.) A square field has an area of 479 ft^2. What is the approximate length of a side of the field? Give your answer to the nearest foot. Explain your response.
To find the length of a side of a square, we need to take the square root of the area.
√479 ≈ 21.91
Rounding to the nearest foot, the length of a side is approximately 22 feet.
The approximate length of a side of the field is 22 feet.
9.) Simplify the expression (7 + 5) + 4 × 13 - 2. Show work.
Using the order of operations (PEMDAS):
(7 + 5) + 4 × 13 - 2
12 + 4 × 13 - 2
12 + 52 - 2
64 - 2
62
So the simplified expression is 62.
1.) To simplify the expression (-1)(4 - c) using the distributive property, we need to distribute the -1 to each term inside the parentheses.
(-1)(4 - c)
= -1 * 4 - (-1) * c
= -4 + c
So the simplified form is B. -4 + c.
2.) To simplify the expression 4(2x - 4) using the distributive property, we need to distribute the 4 to each term inside the parentheses.
4(2x - 4)
= 4 * 2x - 4 * 4
= 8x - 16
So the simplified form is C. 8x - 16.
3.) To simplify the expression (10 + 4y) 1/2 using the distributive property, we need to distribute the 1/2 to each term inside the parentheses.
(10 + 4y) 1/2
= 10 * 1/2 + 4y * 1/2
= 5 + 2y
So the simplified form is A. 5 + 2y.
4.) The number -22 belongs to the subsets of real numbers:
B. Rational numbers
C. Integers.
Rational numbers include integers, and since -22 can be expressed as the fraction -22/1, it is a rational number. Integers consist of positive and negative whole numbers, including 0, so -22 is also an integer.
5.) The algebraic expression for the word phrase "6 times the difference of b and p" is B. 6(b - p).
6.) To simplify the expression 5(14 - 2)^2 / 2, we first calculate the value inside the parentheses, then square it, and finally divide by 2.
5(14 - 2)^2 / 2
= 5 * 12^2 / 2
= 5 * 144 / 2
= 720 / 2
= 360
So the simplified form is D. 360.
7.) To evaluate u + xy, given u = 18, x = 10, and y = 8, we substitute the values into the expression and perform the operations.
u + xy = 18 + 10 * 8
= 18 + 80
= 98
So the value of u + xy is C. 98.
8.) To find the approximate length of a side of a square field with an area of 479 ft^2, we need to find the square root of the area.
√(479 ft^2) ≈ 21.907 ft
Rounded to the nearest foot, the approximate length of a side of the field is 22 feet.
Explanation: The area of a square is equal to the length of one side squared. To find the side length, we need to find the square root of the area.
9.) Simplify the expression (7 + 5) + 4 x 13 - 2.
(7 + 5) + 4 x 13 - 2
= 12 + 4 x 13 - 2
= 12 + 52 - 2
= 64 - 2
= 62
So the simplified value of the expression is 62.
@Reiny
(Although this is old) It is not the beginning, it is Unit 2. As a freshman, you are supposed to be more independent. Benchmarks are what test students to see if they are ready. What may be easy for you, is not easy for others.
This looks like a test a teacher would give his/her students on the first day of a basic algebra course to evaluate if the student is ready to continue. Anything less than 90% should disqualify the student. I would not undermine the teacher's effort by doing the student's work for them.
I will check your answers if you state them.