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What is a qualitative variable?

Examples of qualitative variables include things such as color, shape or pattern. For instance, if scientists were studying a group of people, they may want to record the skin color of the subjects. However, the various skin colors are not numerically related to each other. Similarly, the scientists may wish to record the race of the people; however, the various races are not related to each other numerically. By contrast, quantitative variables do have a natural order. For example, height, weight or density are all quantitative measurements. While quantitative variables offer the ability to o..

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Why do we study algebra?

Being proficient in algebra is important for students going to college because those without algebra proficiency often have to take additional remedial math courses before they can move onto college math. When someone is proficient in algebra, they will have an easier time grasping other types of math, such as higher-level algebra, calculus, geometry and trigonometry. Knowing this type of math is also critical for students who plan to take tests like the ACT and SAT.

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What is a "factor by grouping" solver?

To factor by grouping without a solver, the equation must be capable of being factored. There must be no common factors to all terms and the equation must be quadratic rather than trinomial. Group the first two and last two terms together, and look for a common factor to the first two terms and a common factor to the last two terms. If there is a common factor between the two sets of terms, the equation can be simplified using factor by grouping.

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What are the ways of reducing rational expressions to lowest terms?

Factoring by grouping involves rearranging the expressions by degree, grouping them into smaller parenthetical expressions and simplifying them. After removing common terms, the common terms are placed in their own group. For example, the expression x^4 + 3x^3 - x^2 + 5x simplifies to x^3(x + 3) - x(x + 5). In turn, this goes to (x^3 - x)(x + 3)(x + 5).\nFactoring with the distributive property works similarly. For example, the expression (6x^2 -12x + 9)/(3x - 6) reduces to 3(x - 1)(x - 3)/3(x - 2). The 3 cancels out, leaving (x - 1)(x - 3)/(x - 2). This expression can be placed on a graph, le..

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What are the names of some 3D shapes?

The sphere resembles a 3D circle. It is a perfectly symmetrical shape, and all points on its surface have the same distance from the center. It has no edges or corners, and it has the smallest surface area for a certain volume compared to the other shapes. In nature, spheres appear whenever a surface wants to be as small as possible, such as in bubbles and water drops.\nThe cylinder has three sides, two flat and one curved. The flat sides, as well as the space in between them, are the same. By unwrapping the middle curved section and laying it flat, the result is a rectangle.\nThe cone has a f..

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What are some good resources for learning fractions?

Khan Academy offers comprehensive sections on fractions that cover third-, fourth- and fifth-grade Common Core standards. Each section includes grade-appropriate concepts, beginning with basic recognition and progressing to multiplication and division with mixed numbers. The site uses a combination of video lessons and assessment questions to help students learn and review fractions.\nEnchanted Learning publishes a variety of printable resources for learning fractions, including worksheets that require students to color fractions of objects, fraction booklets and fraction comparison worksheets..

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How do you draw a plane in geometry?

Understand planesIn geometry, a plane is created by any three points that are not on a single line or more than three points that all exist within two dimensions of one another. A plane is a theoretical surface that has no thickness and extends outward infinitely, so there is no way to draw an entire plane. Instead, you can draw a segment of the plane and indicate with arrows that it will continue to extend.\n\nAn example of a plane is an x and y plot that you might find on graphing paper.Plot the parameters of your planeIf you were given points, lines or line segments that make up your plane,..

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What are block and schematic diagrams?

Schematic and block diagrams are used regularly in engineering. Block diagrams are efficient at providing a concise overview of a complicated system, while schematic diagrams provide the detailed explanations of the parts that the system holds. Together, block and schematic diagrams are used to explain circuits. Schematic diagrams can also resemble a blueprint, such as a drawn representation of a full circuit.

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How do you find the area of a cylinder?

The volume of any prism is calculated by multiplying the cross-sectional area by the height. The volume of a cube, for example, is equal to the area of the square base multiplied by the height of the cube. A cylinder is a circular prism, so its volume is the area of either the base or the top multiplied by the height of the cylinder.

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How do you change a quadratic function to vertex form?

Isolate x to one side of the equationA quadratic equation takes the form y = ax^2 + bx + c. Transpose the constant c to the other side to obtain y - c = ax^2 + bx.Separate the coefficientDivide all x-variables by a. Group the x-variables together, with the coefficient outside the parentheses. The new equation is y - c = a(x^2 + [b/a]x).Complete the squareDivide the coefficient of x by 2, then raise that value by the power of 2. Add that value inside the parentheses. Doing this step results in a perfect square trinomial. Remember that whatever you add to one side of the equation, you must also ..

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