C. Action: Divide both sides by 3.
In geometry, definitions are formed using known words or terms to describe a new word. There are three words in geometry that are not formally defined. These three undefined terms are point, line and plane.
<span>POINT (an undefined term) </span>
<span>In geometry, a point has no dimension (actual size). Even though we represent a point with a dot, the point has no length, width, or thickness. A point is usually named with a capital letter. In the coordinate plane, a point is named by an ordered pair, (x,y). </span>
<span>LINE (an undefined term) </span>
<span>In geometry, a line has no thickness but its length extends in one dimension and goes on forever in both directions. A line is depicted to be a straight line with two arrowheads indicating that the line extends without end in two directions. A line is named by a single lowercase written letter or by two points on the line with an arrow drawn above them. </span>
<span>PLANE (an undefined term) </span>
<span>In geometry, a plane has no thickness but extends indefinitely in all directions. Planes are usually represented by a shape that looks like a tabletop or wall. Even though the diagram of a plane has edges, you must remember that the plane has no boundaries. A plane is named by a single letter (plane m) or by three non-collinear points (plane ABC). </span>
<span>Undefined terms can be combined to define other terms. Noncollinear points, for example, are points that do not lie on the same line. A line segment is the portion of a line that includes two particular points and all points that lie between them, while a ray is the portion of a line that includes a particular point, called the end point, and all points extending infinitely to one side of the end point. </span>
<span>Defined terms can be combined with each other and with undefined terms to define still more terms. An angle, for example, is a combination of two different rays or line segments that share a single end point. Similarly, a triangle is composed of three noncollinear points and the line segments that lie between them. </span>
<span>Everything else builds on these and adds more information to this base. Those added things include all the theorems and other "defined" terms like parallelogram or acute angle. </span>
Answer:
A) 33
Step-by-step explanation:
Complementary angles mean they add up do 90. SO x+57 = 90
so then x=33 the correct answer is A)
Answer:
1/6 sqrt(3) + 1/2
Step-by-step explanation:
(1 + sqrt(3))
------------------
sqrt(12)
Multiply the top and bottom by sqrt(12)
(1 + sqrt(3)) * sqrt(12)
------------------
sqrt(12)*sqrt(12)
sqrt(12) + sqrt(3) * sqrt(12)
------------------
12
Simplify
sqrt(4)sqrt(3) + 6
------------------------
12
2 sqrt(3) +6
--------------------
12
1/6 sqrt(3) + 1/2
Answer:
We would use 12 hours assembly and 6 hours sanitization in a maximization problem
Step-by-step explanation:
Let us make a system of inequalities to solve the problem
Each good requires two steps, assembly(x) and sanitization (y)
∵ Face masks take 2 hours to assemble and 1 hour to sanitize
- Multiply x by 2 and y by 1, then add the products
∴ The face masks take 2x + y hours
∵ You have up to 30 hours to make face masks
∴ 2x + y ≤ 30
∵ Gloves take 1 hour to assemble and 2 hours to sanitize
- Multiply x by 1 and y by 2, then add the products
∴ The gloves take x + 2y hours
∵ You have up to 24 hours to make gloves
∴ x + 2y ≤ 24
Lets solve the system as equations to find the maximum values of x and y
∵ 2x + y = 30 ⇒ (1)
∵ x + 2y = 24 ⇒ (2)
- Multiply (2) by -2
∴ -2x - 4y = -48 ⇒ (3)
- Add (1) and (3)
∴ -3y = -18
- Divide both sides by -3
∴ y = 6
- Substitute the value of y in equation (2) to find x
∵ x + 2(6) = 24
∴ x + 12 = 24
- Subtract 12 from both sides
∴ x = 12
Look to the attached graph of the two inequalities to check the maximum values of x and y
We would use 12 hours assembly and 6 hours sanitization in a maximization problem
