What is 19 5 as a mixed number?
To convert the improper fraction 19/5 into a mixed number, we start by dividing the numerator (19) by the denominator (5). 19 divided by 5 equals 3, which is the whole number part of the mixed number. Next, we calculate the remainder: 19 – (5 x 3) = 19 – 15 = 4. This remainder […]
What is the reciprocal of 3/5?
The reciprocal of a fraction is obtained by flipping it, which means switching its numerator and denominator. For the fraction 3/5, the numerator is 3 and the denominator is 5. Therefore, the reciprocal is 5/3. In other words, if you have a fraction a/b, its reciprocal is b/a. So in this case: Original Fraction: 3/5 […]
How do you subtract a fraction from a whole number?
Subtracting a fraction from a whole number is a straightforward process once you understand how to handle the two types of terms. Here’s how you can do it step by step: Convert the Whole Number to a Fraction: The whole number you’re working with can be expressed as a fraction. For instance, if you have […]
Find the exact values of cos 150 and sin 150
To find the exact values of cos 150° and sin 150°, we can use the properties of trigonometric functions and the unit circle. First, note that 150° is in the second quadrant. In the second quadrant, the cosine function is negative, and the sine function is positive. We can express 150° as follows: 150° = […]
How to Integrate ln x²?
To integrate the function ln x², we can use integration by parts. The integration by parts formula is: ∫u dv = uv – ∫v du First, we need to select our u and dv. Let’s choose: u = ln x² (thus, we will differentiate this) dv = dx (and we will integrate this) Next, we […]
Are 4, 6, and 8, 12 Equal?
No, the numbers 4, 6, 8, and 12 are not equal. To clarify, equality means that two or more numbers have the same value. In this case: 4 is a whole number that represents a quantity of four. 6 is a whole number that represents a quantity of six. 8 is a whole number that […]
Which equation has no solution: 4x + 2 = 6 – 2x + 9 + 3x – 6 – 2x + 8 = 0?
To determine which equation has no solution, let’s first simplify the expression you provided: We have: 4x + 2 = 6 – 2x + 9 + 3x – 6 – 2x + 8 Combining like terms on the right side, we get: Constant terms: 6 – 6 + 9 + 8 = 17 Variable terms: […]
The Legs of a Right Triangle Have Lengths of 4 and 5 Units. Find the Length of the Hypotenuse.
To find the length of the hypotenuse in a right triangle when the lengths of the legs are given, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the […]
How do you express 3 power 3 by 2 in radical form?
To express 3 raised to the power of 3/2 in radical form, we start by breaking it down: First, we can rewrite the exponent 3/2 as follows: 3/2 = 1.5, which can also be interpreted as: 3/2 = 3^(1) * 3^(1/2) Now, applying the exponent of 3/2, we have: 3^(3/2) = (3^3)^(1/2) Which simplifies to: […]
Find the First Three Common Multiples of a 6 and 8, and 12 and 18
To find the first three common multiples of the numbers, we need to first determine the least common multiple (LCM) of each pair. Common Multiples of 6 and 8 1. The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, … 2. The multiples of 8 are: 8, 16, 24, 32, 40, 48, […]