How to Turn a Mixed Fraction Into an Improper Fraction
To convert a mixed fraction into an improper fraction, you can follow a simple process. A mixed fraction consists of a whole number and a proper fraction. For example, in the mixed number 2 ½, ‘2’ is the whole number and ‘½’ is the proper fraction. Here’s how to make the conversion: Multiply the whole […]
Find the number of permutations of 8 things taken 5 at a time
To find the number of permutations of 8 things taken 5 at a time, we can use the formula for permutations, which is: P(n, r) = n! / (n – r)! Where n is the total number of items, and r is the number of items to choose. In this case, we have: n = […]
What is the third term of a sequence that has a first term of 3 and a common ratio of 3?
To find the third term of a geometric sequence, we can use the formula for the nth term of a geometric sequence, which is: an = a1 × r(n-1) Where: an is the nth term of the sequence. a1 is the first term of the sequence. r is the common ratio. n is the term […]
How to Solve the System of Equations by Substitution: y = x² – 3x + 7 and 3x + y = 2
To solve the system of equations using substitution, we start with the equations: Equation 1: y = x² – 3x + 7 Equation 2: 3x + y = 2 Since Equation 1 is already solved for y, we can substitute the expression for y in Equation 2. Substituting y from Equation 1 into Equation 2 […]
If the volume of the triangular prism is 54 cubic units, what is the value of x?
To find the value of x for a triangular prism with a volume of 54 cubic units, we can use the formula for the volume of a triangular prism: Volume = Base Area × Height The base area of the triangular prism can further be calculated using the formula for the area of a triangle: […]
What is the remainder when x³ + 3x² + 13x + 78 is divided by x – 4?
To find the remainder when a polynomial is divided by a linear binomial, we can use the Remainder Theorem. This theorem states that the remainder of the division of a polynomial f(x) by x – c is equal to f(c). In this case, our polynomial is: f(x) = x³ + 3x² + 13x + 78 […]
Given that ABC EFG, if FG = 76, what is the length of BC?
To find the length of BC, we need to understand the context of the given problem. In geometry, the letters usually represent points in a figure, where ABC might refer to a triangle and EFG to another line or segment related to it. However, without additional information about the relationships between these points or any […]
A Rectangular Piece of Paper Folded into a Cylinder
To find the volume of the cylinder formed by folding a rectangular piece of paper measuring 11 cm by 4 cm without overlapping, we first need to determine the dimensions of the cylinder. The height of the cylinder is given as 4 cm. Since the paper is folded along the longer side, we can assume […]
What are the dimensions of a rectangle if the length is 97cm more than 4 times the width and the perimeter is 914cm?
Let the width of the rectangle be represented as w. According to the problem, the length l can be expressed as: l = 4w + 97 The perimeter P of a rectangle can be calculated using the formula: P = 2(l + w) Substituting the given perimeter value: 914 = 2(l + w) We can […]
Find the fifth root of 243cos 260 i sin 260
To find the fifth root of the complex number given by 243cos(260°) + i sin(260°), we can first express the number in polar form. The general form of a complex number is represented as r(cos θ + i sin θ), where r is the modulus and θ is the argument. Here, we see that the […]