Answer:
The missing term is 3x
Step-by-step explanation:
Given
-(x - 1) + 5 = 2(x + 3) - _
Required
Find _
For proper identification of the parameters, represent _ with Z
So, the equation becomes
-(x - 1) + 5 = 2(x + 3) - Z
Open bracket (start from the left hand side)
-x + 1 + 5 = 2(x + 3) - Z
-x + 1 + 5 = 2x + 6 - Z
Solve like terms
-x + 6 = 2x + 6 - Z
Subtract 6 from both sides
-x + 6 - 6 = 2x + 6 - 6 - Z
-x = 2x - Z
Subtract 2x from both sides
-x - 2x = 2x - 2x - Z
-3x = -Z
Multiply both sides by -1
-3x * -1 = -Z * -1
3x = Z
Reorder
Z = 3x
Hence, the missing term is 3x
Answer:
The student should have switched the direction of the inequality sign to
get –5 > x for a final answer.
Step-by-step explanation:
When multiplying or dividing an inequality by a negative "flip" the inequality sign
The student should have switched the direction of the inequality sign to
get –5 > x for a final answer.
---------------
Note:
For a more conventional appearance the entire inequality can be flipped to
–5 < x
Answer:
x = -2
y = 1
Step-by-step explanation:
-3x - 4y = 2
x = -2
y = 1
3x + 3y = -3
x = -2
y = 1
Answer:
Given radius (R) = 13
Diameter = 2R = 26
Circumference = 2πR
= 26π
= 81.681408993335
Area = πR2
= 169π
= 530.92915845668
Step-by-step explanation:
While a circle, symbolically, represents many different things to many different groups of people including concepts such as eternity, timelessness, and totality, a circle by definition is a simple closed shape. It is a set of all points in a plane that are equidistant from a given point, called the center. It can also be defined as a curve traced by a point where the distance from a given point remains constant as the point moves. The distance between any point of a circle and the center of a circle is called its radius, while the diameter of a circle is defined as the largest distance between any two points on a circle. Essentially, the diameter is twice the radius, as the largest distance between two points on a circle has to be a line segment through the center of a circle. The circumference of a circle can be defined as the distance around the circle, or the length of a circuit along the circle. All of these values are related through the mathematical constant π, or pi, which is the ratio of a circle's circumference to its diameter, and is approximately 3.14159. π is an irrational number meaning that it cannot be expressed exactly as a fraction (though it is often approximated as 22/7) and its decimal representation never ends or has a permanent repeating pattern. It is also a transcendental number, meaning that it is not the root of any non-zero, polynomial that has rational coefficients. Interestingly, the proof by Ferdinand von Lindemann in 1880 that π is transcendental finally put an end to the millennia-old quest that began with ancient geometers of "squaring the circle." This involved attempting to construct a square with the same area as a given circle within a finite number of steps, only using a compass and straightedge. While it is now known that this is impossible, and imagining the ardent efforts of flustered ancient geometers attempting the impossible by candlelight might evoke a ludicrous image, it is important to remember that it is thanks to people like these that so many mathematical concepts are well defined today.
Circle Formulas
D = 2R
C = 2πR
A = πR2
where:
R: Radius
D: Diameter
C: Circumference
A: Area
π: 3.14159
