Geometry and Graphs - GED Math

The radius is half of the diameter, or 11.

If two angles are complementary, that means the sum of their degrees of measure will add up to 90. In order to find the measure of angle B, subtract angle A from 90 like shown:

This gives us a final answer of 37 degrees for angle B.

If two angles are complementary, that means the sum of their degrees of measure will add up to 90. In order to find the measure of angle B, subtract angle A from 90 like shown:

This gives us a final answer of 81 degrees for angle B.

Two angles are classified as complementary if an only if the sum of the angles equals to exactly 90 degrees.

Since we know the measurement of one angle, and we know the rule about complementary angles, let's find the other angle:

The other angle is simply the total sum of both angles minus the given angle.
The total sum of the angles is , and the given angle is .

So, we will subtract from .

Other angle=

The other angle has a measurement of degrees.

First, we need to find the slope of the above line.

The slope of a line. given two points can be calculated using the slope formula:

Set :

A line parallel to this line also has slope . Since it passes through the origin, its -intercept is , and we can substitute into the slope-intercept form of the equation:

We find the slope of each line by putting each equation in slope-intercept form, , and examining the coefficient of .

is already in slope-intercept form; its slope is .

To get in slope-intercept form we solve for :

The slope of this line is .

The slopes are not equal so we can eliminate both "parallel" and "identical" as choices.

Multiply the slopes together:

The product of the slopes of the lines is not , so we can eliminate "perpendicular" as a choice.

The correct response is "neither".

We find the slope of each line by putting each equation in slope-intercept form and examining the coefficient of .

is already in slope-intercept form; its slope is .

To get into slope-intercept form we solve for :

The slope of this line is .

The slopes are not equal so we can eliminate both "parallel" and "one and the same" as choices.

Multiply the two slopes together:

The product of the slopes of the lines is , making the lines perpendicular.

Recall that at a point of intersection of two lines, they will have the same x and y-coordinates.

Thus, we can set the two equations equal to each other and solve for to find the x-coordinate.

To find the y-coordinate, plug the back into either of the equations.

First we need to recall that whenever we add up all 3 angles of any given triangle, the sum will always be .

In an isosceles triangle two of the angles are congruent. Since we are told that one of the angles of our triangle is we know that this is an obtuse triangle, since 120 is greater than 90.

We need to subtract 120 from 180 to find the remainder of the triangle which is

Since we are working with an isosceles triangle, we know that the remaining two angles are going to be congruent. To find the degree of the angles we simply divide 60 by 2. Our answer is; both angles are

The inscribed rectangle is a 20 by 20 square. Since opposite sides of the square are parallel, the corresponding angles of the two smaller right triangles are congruent; therefore, the two triangles are similar and, by definition, their sides are in proportion.

The small top triangle has legs 10 and 20; the blue triangle has legs 20 and , where can be calculated with the following proportion:

The legs of the blue triangle are 20 and 40; half their product is the area:

The area of a triangle is half the product of its baselength and its height.

To find the area of , we can use the lengths of the legs and :

To find the area of , we can use the hypotenuse , the length of which is 30, and the altitude perpendicular to it:

In terms of area, is

of .

Complementary angles must add up to ninety.

Subtract the given angle from 90 to find the other angle.

The answer is:

Two angles are complementary when they add up to .

The area of a circle, given its radius , can be found using the formula

The radius is half the diameter - that is, - so, substituting,

or

The diameter of the given circle is 7, so set in the above formula:

,

the correct area.

To find the area of a circle, we will use the following formula:

where r is the radius of the circle.

Now, we know . We also know the diameter is 12in. We know the diameter is two times the radius, so the radius is 6in. Now, we can substitute. We get

The base of a square pyramid is, as the name suggests, a square which has edges and vertices. The vertices of the square each have edges that meet at a single point, adding an additional vertex and additional edges. Together, a square pyramid has edges and vertices.

An octagonal pyramid has a base with eight vertices, each of which is a vertex of the pyramid. There is one more vertex, or the apex, which is connected to each of the vertices of the base by an edge. Nine is the correct choice.

The pool can be seen as a cylinder with depth (or height) 2.5 meters and a base with diameter 18 meters - and radius half this, or 9 meters.

The bottom of the pool - the base of the cylinder - is a circle with radius 9 meters, so its area is

square meters.

Its side - the lateral face of the cylinder - has area

square meters.

Their sum - the total area to be painted - is square feet. Since one can of paint covers 40 square meters, divide:

Nine cans of paint and part of a tenth will be required, so the correct response is ten.

The area of an equilateral triangle is given by the formula

.

Since there are twenty equilateral triangles that comprise the surface of the icosahedron, the total surface area is

.

Substitute :

square inches.