John Math Midterm Practice

Let Nathan's weight be x. Then, James's weight is x + 30. Together, they weigh 130 pounds: x + (x + 30) = 130. Solving gives 2x + 30 = 130, so 2x = 100, and x = 50. Thus, James weighs 50 + 30 = 80 pounds.

To factor 17abcd - 51ab, first factor out the common term ab. This gives us ab(17cd - 51), which matches the correct choice. The other options do not correctly represent the factored form.

To combine (3x - 4y + 5z) - (6z + 2y - 4x), distribute the negative sign: 3x - 4y + 5z - 6z - 2y + 4x. Combine like terms: (3x + 4x) + (-4y - 2y) + (5z - 6z) = 7x - 6y - z. Thus, the correct answer is 7x - 6y - z.

To combine (3x - 4y + 5z) + (6z + 2y - 4x), first group like terms: (3x - 4x) + (-4y + 2y) + (5z + 6z) = -x - 2y + 11z. Thus, the correct answer is -x - 2y + 11z.

The phrase '7 less than a number, n' means you subtract 7 from n. Therefore, the correct algebraic expression is n - 7.

The phrase "Four times a number, k, increased by 5 is 12" translates to the equation 4k + 5 = 12, where 4k represents four times the number k, and adding 5 gives the total of 12.

The phrase 'The sum of two numbers, a and b' directly translates to the mathematical operation of addition, which is represented as 'a + b'. Therefore, the correct expression is 'a + b'.

The phrase 'Twice the difference of two numbers, p and r' means you first find the difference (p - r) and then multiply it by 2. Thus, the expression is 2(p - r), making it the correct choice.

The phrase 'The product of 3 and a number, d, is 20' translates mathematically to 3 multiplied by d, which is expressed as 3d. Therefore, the correct equation is 3d = 20.

To express '6 more than three times a number, f', you first calculate three times the number, which is 3f, and then add 6. Thus, the correct expression is 3f + 6.