Tutor profile: Regan K.
Evaluate and simplify the following expression (division of mixed numbers): [2 (3/7)] / [1 (1/3)]
First, the mixed numbers must be converted to improper fractions, by multiplying the whole number by the denominator of the fraction for each. This value is then added the the numerator of the fraction to obtain the numerator of the improper fraction, and the denominator remains the same: [17/7] / [4/3] In order to divide fractions, the division is changed to multiplication, and the second fraction is inverted: 17/7 * 3/4 To multiply fractions, the numerators are multiplied together to find the numerator of the answer, and the same is done with the denominators: 17/7 * 3/4 = (17*3)/(7*4) = 51/28 To simplify, the improper fraction is converted to a mixed number: 51/28 = 1 (23/28) Since the fraction 23/28 cannot be further simplified, the answer is reported as 1 (23/28).
Subject: Basic Math
What is the greatest common factor of 48 and 112?
The greatest common factor of 48 and 112 is 16. This can be obtained by listing all the factors for each number, and choosing the greatest common value. It can also be found via prime factorization, by multiplying together the common prime factors for one of the numbers.
Find the value of x for the function below when f(x) = -23: f(x) = 3(x - 7) + 4
To solve for x, plug in -23 for f(x) in the above equation: -23 = 3(x - 7) + 4 To solve the equation, first distribute the 3 in the parentheses: -23 = 3x - 21 + 4 Simplify by combining like terms: -23 = 3x - 17 Add 17 to both sides to isolate the term with the x: -23 + 17 = 3x - 17 + 17 -6 = 3x Finally, divide both sides by 3 to solve for x: -6/3 = 3x/3 -2 = x Thus, the value of x that satisfies the function when f(x) = -23 is x = -2.
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