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What are the factors of 75?

The number 75 can be derived from the multiplication of these three possible combinations: 1 and 75, 3 and 25, and 5 and 15.\nAny whole number has at least two factors, the most basic being 1 and the number itself. One practical way of determining the factors of a number is to write them in ascending order, with the number 1 at the leftmost side of the row and the number itself at the rightmost. The next step is to divide the number by 2 to check if the quotient is a whole number. If so, the two factors should be written next to 1 and the number. The process is repeated by using 3, 4, and so o..

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Why is one column in a hundredths grid equal to one column in a tenths grid?

In a hundredths grid, there is a total of 100 equally sized blocks arranged in a 10-by-10 format. One column (or one row, for that matter) has 10 of these blocks. The fraction 10/100 is the same proportion as one-tenth, as both are equal to 10 percent.\nIn the case of the tenths grid, there are 10 columns of just one block each, leading to 10 blocks in total. Selecting one of those columns is choosing one-tenth of the space in the grid, which is the same fraction as the 10 blocks that comprise the column in the hundredths grid. In a tenths grid, each column is said to have a value of 10, thoug..

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What are negative and fractional exponents?

A negative exponent is equivalent to the reciprocal of the of the same number taken to the opposite positive exponent. For example, 5^(-3) is equal to 1/(5^3). A fractional exponent can be solved by taking the root of the denominator to the power of the numerator. For example, 4^(2/3) is equal to the square of the cube root of 4. The root of a negative exponent with an even number in the denominator does not exist.

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What is a real-life example where slope is used?

If the account starts out with no money and has $1200 at month 12, the formula to calculate slope is used to show the account's rate of change. The formula reads (y2-y1)/(x2-x1); when the numbers are plugged in, it reads (1200-0)/(12-0), which equals 1200/12. When 1200/12 is simplified, it equals $100. The rate of change for the account is $100 per month, which means this is how much the account owner saves on average each month.

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How do you find the area of a pentagon?

A regular pentagon means that all of the sides are identical and all angles are the same as each other. To calculate the area, the length of one side needs to be known. Also, the length of a line from the middle of a side to the middle of the pentagon is needed. This line is known as the apothem, which is also the radius of the intercircle that can be drawn within the pentagon.

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How are rational functions graphed?

With rational functions, the value of X generally expands. Numbers in the chain of values may be positive or negative, and should increase in value. When numbers begin as negatives, this process involves the values of X moving from negative charges to positive charges. Graphs with rational functions generally contain two intercepts: a y-intercept and an x-intercept. Graphs of rational functions exist as two separate parts, but are connected by the two intercepts. Although they exist on the same plane, the x and y axes never overlap, and are solved separately. Ideally, rational functions reduce..

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How do you find the area of a parallelogram?

Draw lines separating the parallelogramThe lines should run from the vertex of the triangle perpendicular to the top and bottom sides of the parallelogram. At this point, there should be two triangles and a quadrilateral.Measure the lengthsTake the measurements of the bases of the triangles, the height of the triangles and the length of the quadrilateral.Determine the areas of the trianglesUse the formula a = 1/2bh, where b is the base of the triangle and h is the height.Find the area of the center part of the parallelogramMultiply the length by the height. Add the results of all the areasThe ..

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How many diagonals does a heptagon have?

A heptagon is a type of polygon, which is a closed plane figure bounded by seven straight edges containing seven angles. When all the sides and angles are equilateral and equiangular, respectively, the heptagon is said to be a regular heptagon. Other types of polygons are triangles, quadrilaterals, pentagons, hexagons and octagons.

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What are piecewise defined functions?

There are an infinite number of examples of piecewise functions, varying in complexity. The absolute value function is one of the simplest of these functions. Its formula is written f(x) = |x|. The subfunctions that define this function are f(x) = x if x > 0 and f(x) = -x if x < 0. The graph of this function is two rays, originating at the point (0,0), both at a 45-degree angle to the horizon.\nThe floor function forms an infinite number of steps and is a piecewise-defined function. In this function, f(x) is the integer greater than or equal to x.\nPiecewise functions join functions of varying..

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How do you find the magnitude of a complex number?

For example, in the complex number z = 3 + 4i, the magnitude is sqrt(3^2 + 4^2) = 5. Similarly, in the complex number z = 3 - 4i, the magnitude is sqrt(3^2 + (-4)^2) = 5.\nSeveral corollaries come from the formula |z| = sqrt(a^2 + b^2). First, if the magnitude of a complex number is 0, then the complex number is equal to 0. It is also true that the magnitude of the product of two complex numbers is equal to the product of the magnitudes of both complex numbers. In other words, |z1 * z2| = |z1| * |z2|. This rule also applies to quotients; |z1 / z2| = |z1| / |z2|.

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