match the following.

1 .
trapezoid
any surface that is not a base
2 .
volume
the ratio of the circumference of a circle to its diameter; approximately 3.14
3 .
pi
three-dimensional figure with two parallel, congruent, polygonal faces and parallelograms for all other faces
4 .
surface area
geometric figure with three dimensions
5 .
lateral surface
point where three or more edges meet
6 .
pyramid
the unit of measure for area
7 .
vertex
the total area of all the faces or surfaces of a three-dimensional figure
8 .
solid figure
a quadrilateral with one pair of parallel sides
9 .
square units
the amount of space inside a three-dimensional figure

1.Trapezoids: Characteristics

Probably the TRAPEZOID is one of the most popular quadrilaterals when it comes to bridge construction. Numerous railroad trestles and wooden bridges of the nineteenth and early twentieth centuries were trapezoidal in shape.

The two parallel sides of a trapezoid are its bases while the legs are the nonparallel sides. The height of a trapezoid is a line segment that runs perpendicular to the bases. The median, or mid-segment, is a line that is parallel to the bases and connects the midpoints of each leg. The area is calculated with a formula using the lengths of each base and the height.

A parallelogram is usually defined as a trapezoid, although it has two pairs of parallel sides instead of just one. An isosceles trapezoid has congruent base angles and equal leg lengths.  

2.The circumference of a circle is the distance around the outside of the circle. ... The circumference of a circle can be found by multiplying pi ( π = 3.14 ) by the diameter of the circle. If a circle has a diameter of 4, its circumference is 3.14*4=12.56. If you know the radius, the diameter is twice as large.

3.a cube is a platonic solid because all six of its faces are congruent squares. ... A prism is a polyhedron whose bottom and top faces (known as bases) are congruent polygons and faces known as lateral faces are parallelograms (when the side faces are rectangles, the shape is known as right prism).

4.If a solid is composed of flat surfaces, such as the cube on the right, the surface area is simply the sum of the areas of the flat surfaces (called faces). So, for example, if a each edge of a cube has a length s, the area of one face is s2 since it is a square.

5.A pyramid is a polyhedron that has a base, which can be any polygon, and three or more triangular faces that meet at a point called the apex. These triangular sides are sometimes called the lateral faces to distinguish them from the base.

6.The surface area and the volume of pyramids, prisms, cylinders and cones. The surface area is the area that describes the material that will be used to cover a geometric solid. ... The volume is a measure of how much a figure can hold and is measured in cubic units.

7.A flat surface of a solid figure; A polygon that is a flat surface of a three-dimensional figure. Example: A face is one of the polygonal surfaces of a polyhedron.

8.RHOMBUS (all sides congruent/opposite angles congruent) PARALLELOGRAM (quadrilateral with 2 pairs of parallel lines.) POLYGON (closed figure made up of line segments) trapezoid. a quadrilateral with exactly one pair of parallel sides.

9.Three-dimensional figure with two circular, parallel and congruent bases. A cube whose edges are one unit long. The number of cubic units needed to fill the space inside a three-dimensional figure. The set of points in space that are the same distance from a given point called the center.

answer: learning objective(s)

·         describe the creation and use of systems of equations.

·         graph a system of linear equations on the coordinate plane and identify its solution.

introduction

sometimes graphing a single linear equation is all it takes to solve a mathematical problem. other times, one line just doesn’t do it, and a second equation is needed to model the situation. this is often the case when a problem involves two variables. solving these kinds of problems requires working with a system of equations, which is a set of two or more equations containing the same unknowns.

let’s take a look at systems of equations, and see what the graphs of individual equations within a system reveal about the mathematical relationship of the variables.

systems of equations

a system of equations contains two or more linear equations that share two or more unknowns. to find a solution for a system of equations, we must find a value (or range of values) that is true for all equations in the system.

the graphs of equations within a system can tell us how many solutions exist for that system. look at the images below. each show two lines that make up a system of equations (in the graph on the right the two lines are superimposed and look like a single line). how many points in common does each system of lines reveal?

one solution

no solutions

infinite solutions

if the graphs of the equations intersect, then there is one solution that is true for both equations.

if the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.

if the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations.

remember, the graph of a line represents every point that is a possible solution for the equation of that line. so when the graphs of two equations cross, the point of intersection lies on both lines, meaning that it is a possible solution for both equations. when the graphs of two equations never touch, there are no shared points and there are no possible solutions for the system. when the graphs of two equations lie on top of one another, they share all their points and every one is a possible solution.

graphing as a solution method

graphing equations in order to identify a specific point of intersection is usually not a precise way to solve systems because it is often difficult to see exactly where two lines intersect (unless you are using a computer-based graphing program that allows you to zoom in on a point). however, the graph of a system of equations can still give a good idea of what type of solution, if any, exists. let’s graph a system, and see how it works.

graph the system y = 3x and x + 2y = 4. how many solutions does this system have?

a graph of the two lines y = 3x and x + 2y = 4 shows us that the lines intersect, meaning that there is a single (x, y) value that satisfies both equations. looking at the graph does not tell us exactly where that point is, but we don’t need to know that information here, because the question only asks for the number of solutions.

so a system made of two intersecting lines has one solution. now let’s look at a different situation:

how many solutions exist for the system y -0.5x = 7 and 2y = x − 3?

plotting both equations, it looks like there is no solution—the lines are parallel. to check this finding, we can compare the slopes of the equations. to make that easy, we’ll rearrange the equations into slope-intercept form, or y = mx + b.   that gives us the equations y = 0.5x + 7 and y = 0.5x − 1.5.   yes, the slope of both lines is 0.5, which means the lines really are parallel. they never intersect, so there is no point that lies on both lines, and no solution to the system.

step-by-step explanation:

answer is the third choice:

3x^5+4x^4+x^3+2x^2-10x-7=0

step-by-step explanation: