University:
North Central College
Course:
MATH 152 | Calculus II
Academic year:

2024
Views:

4

Pages:

2
Author:

nesikhiyawl0

Question 1 What is the constant in this algebraic expression 5a+2? Answer Explanation: A constant is a term in expression which contains only a number (positive, or negative) without any variables (letters). Here an expression is a sum of 2 smaller expressions. The term 5a contains a variable a, so it is not a constant. The term 2 does not contain any letters, so it is a constant. Result: The constant is 2. Question 2 What is the standard form of y = (-2/7x + 1/9 x^2)(7x-18)? Answer Explanation: y=(-2/7x + 1/9 x^2)(7x-18) y = (-2/7x)(7x-18) + (1/9 x^2) (7x-18) ⇒ -14/7x^2 + 36/7 x + 7/9 x^3 - 18/9 x^2 ⇒ -2x^2 + 36/7x + 7/9x^3 - 2x^2 ⇒7/9x^3-2x^2-2x^2 +36/7x ⇒7/9x^3-4x^2 +36/7x y = 7/9x³ - 4x² + 36/7x Question 3 How do you solve -15x-40=9-8x? Answer 1 Explanation: Given -15x-40=9-8x Add 8x+40 (=40 + 8x) to both sides in order to isolate the variable term on the left and the constant term on the right: -15x-40=9-8x +8x+40=+40+8x -7x=49 Divide both sides by (-7) x=-7 Answer 2 Explanation: First, add 15x and subtract 9 from each side of the equation to isolate the x term while keeping the equation balanced: -15x-40+15x-9=9-8x+15x-9 -15x+15x-40-9=9-9-8x+15x 0-49=0+7x -49=7x Now, divide each side of the equation by 7 to solve for x while keeping the equation balanced: -49/7=7x/7 -7=x x=-7 Question 4 How do you multiply monomials by polynomials? Answer Since each term in a polynomial is a monomial, multiplying polynomials becomes multiplying monomials. When multiplying monomials, use the product rule for exponents. The factors are regrouped, and then multiplied. Notice the product rule for exponents at work [when the bases are the same, add the exponents]. Question 5 How do you write the equation y=2x-5 in standard form? Answer Explanation: The standard form of a linear equation is: Ax+By=C Where, if at all possible, A,B, and C are integers, and A is non-negative, and, A,B, and C have no common factors other than l First, we need to move the x term to the left side of the equation by subtracting 2x from each side of the equation: -2x+y=-2x+2x-5 -2x+y=0-5 -2x+y=-5 Another requirement is for the x coefficient to be non-negative. Therefore, we must multiply each side of the equation by -1: -1(-2x+y)=-1*-5 (-1*-2x)+(-1*y)=5 2x-y=5 2x-1y=5