1. Find the value of 5 + 8 x 2 divided by 4 - 11
2. Evaluate (a-y)^2 + 2y^3, if a =2 and y= -3
3. Evaluate -|a-3b|, if a=-2 and b = 6
4. The formula A= 180 (n-20 OVER N relates the measure A of an interior angle of a regular polygon to the number of sides. If an interior angle measures 120 degrees, find the number of sides.
5. Name the sets of numbers to which -28 belongs.
6. Simplify 1/2(6x+3) - 4 (3x-2)
7. The property illustrated by 7 x (9+1) = ( 9+1) x 7 is
8. Solve the equation 2/5y = 3/14
1. -7
1. To find the value of the expression 5 + 8 x 2 ÷ 4 - 11, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division - from left to right, and Addition and Subtraction - from left to right).
Step 1: Perform the multiplication first. 8 x 2 = 16.
Step 2: Perform the division. 16 ÷ 4 = 4.
Step 3: Perform the addition and subtraction from left to right. 5 + 4 - 11 = -2.
Therefore, the value of the expression is -2.
2. To evaluate the expression (a - y)^2 + 2y^3, given values a = 2 and y = -3, we substitute these values into the expression.
Substitute a = 2 and y = -3:
(2 - (-3))^2 + 2(-3)^3 = (2 + 3)^2 + 2(-27) = 5^2 - 54 = 25 - 54 = -29.
Therefore, the value of the expression is -29.
3. To evaluate the expression -|a-3b|, given values a = -2 and b = 6, we substitute these values into the expression.
Substitute a = -2 and b = 6:
-|-2 - 3(6)| = -|-2 - 18| = -|-20| = -20.
Therefore, the value of the expression is -20.
4. The formula A = 180(n-2) / n relates the measure A of an interior angle of a regular polygon to the number of sides. If an interior angle measures 120 degrees, the formula becomes:
120 = 180(n-2) / n.
To solve for n, we can cross multiply and solve for n:
120n = 180(n-2).
120n = 180n - 360.
360 = 180n - 120n.
360 = 60n.
n = 360 / 60.
n = 6.
Therefore, the number of sides of the regular polygon is 6.
5. The number -28 belongs to the set of Integers, Rational numbers, and Real numbers.
Integers: This set includes all whole numbers and their negatives, including zero (0).
Rational numbers: This set includes all numbers that can be expressed as a fraction of two integers, where the denominator is not zero.
Real numbers: This set includes all numbers on the number line, including integers, fractions, decimals, and irrational numbers.
6. To simplify the expression 1/2(6x + 3) - 4(3x - 2), we distribute the coefficients and combine like terms.
1/2(6x + 3) - 4(3x - 2) = 3x + 3/2 - 12x + 8.
Combine like terms:
-9x + 11/2.
Therefore, the simplified expression is -9x + 11/2.
7. The property illustrated by 7 x (9 + 1) = (9 + 1) x 7 is called the commutative property of multiplication. This property states that the order of multiplication does not affect the product. In other words, you can multiply two numbers in any order and still get the same result.
8. To solve the equation 2/5y = 3/14 for y, we can cross multiply and solve for y.
Cross multiplying:
(2/5)y = (3/14).
Multiply both sides by the reciprocal of (2/5), which is (5/2):
y = (3/14) x (5/2).
Multiply numerators and denominators:
y = (3 x 5) / (14 x 2).
Simplify:
y = 15/28.
Therefore, the solution to the equation is y = 15/28.