Algebra I Semester Exam

To solve the equation 2(n - 3) = -14, we first distribute the 2 to both terms inside the parentheses, giving us 2n - 6 = -14. Then, we isolate the variable by adding 6 to both sides of the equation, resulting in 2n = -8. Finally, we divide both sides by 2 to solve for n, giving us n = -4. Therefore, the correct answer is n = -4.

By distributing the 8 to both terms inside the parentheses, the equation becomes 8x - 40 = -40. Adding 40 to both sides of the equation, we get 8x = 0. Finally, dividing both sides by 8, we find that x = 0.

The phrase "the quotient of n and 6" means dividing n by 6. Therefore, the algebraic expression for this phrase would be n/6.

The given expression can be simplified by combining like terms. 2b and b can be combined to give 3b, and -3a and a can be combined to give -2a. Therefore, the equivalent expression is 3b - 2a.

To simplify (2n^4)^3, we need to raise both the coefficient and the exponent inside the parentheses to the power of 3. The coefficient 2 raised to the power of 3 is 8. The exponent n^4 raised to the power of 3 is 12, since we multiply the exponents. Therefore, the simplified expression is 8n^12.

The opposite of a fraction is obtained by changing the sign of the numerator while keeping the denominator the same. In this case, the opposite of 3/2 would be -3/2, as the numerator is changed to its opposite sign while the denominator remains unchanged.

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To solve the equation 3x + 9 = 24, we need to isolate the variable x. First, we subtract 9 from both sides of the equation to get 3x = 15. Then, we divide both sides by 3 to solve for x, which gives us x = 5. Therefore, the correct answer is x = 5.

The given expression can be simplified by combining like terms. The fractions -5/4 and 5/4 are like terms because they have the same denominator. When we subtract -5/4 from 5/4, we get 10/4. Similarly, the fractions -4/5 and 4/5 are like terms. When we subtract -4/5 from 4/5, we get 8/5. Therefore, the simplified expression is 10/4 - 8/5.

The expression follows the order of operations, which states that we should first simplify within parentheses, then perform any exponents, and finally perform any multiplication or division from left to right. In this case, within the parentheses, 5 - 3 equals 2. Then, we have 10 multiplied by 2 squared, which equals 40. Finally, we add 4 to 40, resulting in 44.

To find the value of 5x + 2y when x = -1 and y = 4, we substitute the given values into the expression. Plugging in x = -1 and y = 4, we get 5(-1) + 2(4) = -5 + 8 = 3. Therefore, the value of 5x + 2y when x = -1 and y = 4 is 3.

To solve the equation 3(x + 2) - 5 = 16, we first distribute the 3 to the terms inside the parentheses: 3x + 6 - 5 = 16. Then, we combine like terms by subtracting 5 from both sides of the equation: 3x + 1 = 16. Next, we isolate the variable by subtracting 1 from both sides: 3x = 15. Finally, we solve for x by dividing both sides by 3: x = 5.

The given expression cannot be simplified any further because there are no common factors or like terms that can be combined. Therefore, the expression 2x^2 + 3x + 15 is already in its simplest form.

The reciprocal of a number is obtained by dividing 1 by that number. In this case, the reciprocal of -40 would be -1/40, since -40 divided by 1 is -1/40.

The given expression is a multiplication of two binomials, (x + 6) and (x + 3). To multiply these binomials, we use the distributive property. We multiply the first terms of each binomial, which gives us x * x = x^2. Then, we multiply the outer terms, which gives us x * 3 = 3x. Next, we multiply the inner terms, which gives us 6 * x = 6x. Finally, we multiply the last terms, which gives us 6 * 3 = 18. Combining all these terms, we get x^2 + 9x + 18, which is the correct answer.

The expression 6(12 - 3) = 6(12) - 6(3) demonstrates the Distributive Property. This property states that when multiplying a number by the sum or difference of two other numbers, we can distribute the multiplication to each term inside the parentheses. In this case, the 6 is being multiplied by the difference (12 - 3), and we can distribute the multiplication to both terms inside the parentheses, resulting in 6(12) - 6(3).

The expression -20 - (-5) can be simplified by removing the parentheses and applying the rule of subtracting a negative number, which is equivalent to adding the positive number. So, -20 - (-5) becomes -20 + 5, which equals -15. However, none of the given answer options match the correct answer of -15, so the correct answer is not available.

To solve the equation, we first distribute the 4 to the terms inside the parentheses on the right side of the equation, resulting in 5(x - 1) = 2x + 8x + 4. Then, we distribute the 5 to the term inside the parentheses on the left side of the equation, giving us 5x - 5 = 2x + 8x + 4. Next, we combine like terms on both sides of the equation, resulting in 5x - 5 = 10x + 4. To isolate the variable, we subtract 10x from both sides, giving us -5x - 5 = 4. Finally, we add 5 to both sides and divide by -5 to solve for x, which gives us x = -9/5.

The numbers in the set are arranged in ascending order, from least to greatest. The first number, -3.4, is the smallest, followed by -3, then 0, and finally 5.3, which is the largest.

The expression can be simplified by following the order of operations. First, we need to perform the addition inside the parentheses: 3 + 7 = 10. Then, we multiply 5 by 10: 5 * 10 = 50. Next, we need to divide 9 by 3: 9 / 3 = 3. Finally, we subtract 3 from 50: 50 - 3 = 47. Therefore, the correct order of operations to simplify the expression is add, multiply, divide, subtract.