Tutor profile: Noah O.
Simplify the following expression: 7x - 3y - 5x + 6y - 4z
To simplify the expression, we will need to group together the like variables, then add or subtract their coefficients. So, we can reorganize the expression by putting all the "x" terms together, then all the "y" terms together, then all the "z" terms together. The expression then becomes 7x - 5x - 3y + 6y - 4z. Now, we add or subtract the coefficients of the like variables. 7x - 5x = 2x, -3y + 6y = 3y, and we don't have anything to combine with -4z, so it stays the same. That makes the expression 2x - 3y - 4z
Subject: Basic Math
Solve the following expression: (8 - 3)^2 * 2 + 7
To find the answer, we will use the order of operation: parentheses, exponents, multiplication, division, addition, subtraction. So, we will start by simplifying the portion in the parentheses, (8 - 3), which is 5. So now we have (5)^2 * 2 + 7. Next, we will solve the exponents, (5)^2, which is 25. Now we have 25 * 2 + 7. From here, we move on to multiplication, which we have 25 * 2, or 50. That gives us 50 + 7. Last, we do the addition to get 57.
Solve the following polynomial equation for x: x^2 + 4x - 21 = 0
In order to solve this polynomial equation, we will first need to factor the equation, then solve each factor for x. To begin factoring, we must first find the factors of -21 that add together to equal 4. The factors of -21 are as follows: -1 and 21, 1 and -21, -3 and 7, and 3 and -7. Of these factors, only -3 and 7 will add together to equal 4, so those will be the factors we use for our factoring. This will give us (x + 7)(x -3) = 0 as our factored polynomial. Now, we need to solve each factor as being equal to 0 to find the solutions for x. First, to solve (x + 7) = 0, we subtract 7 from both sides of the equation, giving us x = -7. Second, to solve (x - 3) = 0, we add 3 to both sides of the equation, giving us x = 3. So, our solutions are x = 3 and x = -7.