Answer:
{x ∈ R: x<6}
Step-by-step explanation:
Given
- x is a real number
- x is less than 6
Required
Write the set using set builder notation
The very first thing to do is to list out the range of x, using inequalities;
x is less than 6 implies that -infiniti < x < 6
The next step is to translate this to set builder. This is done as follows
x ∈ R - > This means that x is a real number
x < 6 -> where x is less than 6.
Bringing these two together, it gives:
{x ∈ R: x<6}
Hence, the set of real numbers x less than 6 is equivalent to {x ∈ R: x<6} using set builder notation
Answer:
1. Different
2. More
3. Greater too
Step-by-step explanation:
I'm not completely sure I'm not good with graphs but i hope its right!
Answer:
A) -2/5
Step-by-step explanation:
Note that for a slope, the slope of the line is found by using the equation:
slope = (rise/run).
In this case, find two points. For example, i will use:
(0, 2) & (5, 0). (x = 0, y = 2) ; (x = 5, y = 0)
Note that "rise" = y, and "run" = x. Plug in the corresponding numbers for the corresponding points.
(2 - 0)/(0 - 5) = slope
Simplify
(2)/(-5) = slope
-(2/5) is your answer.
Note that it does not matter where the negative sign is placed.
~
Answer:
x = -5, and y = -6
Step-by-step explanation:
Suppose that we have two equations:
A = B
and
C = D
combining the equations means that we will do:
First we multiply both whole equations by constants:
k*(A = B) ---> k*A = k*B
j*(C = D) ----> j*C = j*D
And then we "add" them:
k*A + j*C = k*B + j*D
Now we have the equations:
-x - y = 11
4*x - 5*y = 10
We want to add them in a given form that one of the variables cancels, so we can solve it for the other variable.
Then we can take the first equation:
-x - y = 11
and multiply both sides by 4.
4*(-x - y = 11)
Then we get:
4*(-x - y) = 4*11
-4*x - 4*y = 44
Now we have the two equations:
-4*x - 4*y = 44
4*x - 5*y = 10
(here we can think that we multiplied the second equation by 1, then we have k = 4, and j = 1)
If we add them, we get:
(-4*x - 4*y) + (4*x - 5*y) = 10 + 44
-4*x - 4*y + 4*x - 5*y = 54
-9*y = 54
So we combined the equations and now ended with an equation that is really easy to solve for y.
y = 54/-9 = -6
Now that we know the value of y, we can simply replace it in one of the two equations to get the value of x.
-x - y = 11
-x - (-6) = 11
-x + 6 = 11
-x = 11 -6 = 5
-x = 5
x = -5
Then:
x = -5, and y = -6
Step 1
Find the area of one equilateral triangle
Applying the law of sines
in this problem
a=b=7 cm
C=60 degrees
so
cm²
Step 2
To calculate the area of the hexagon multiply the area of one equilateral triangle by 
![Area Hexagon=6*[49*\frac{\sqrt{3}}{4}] \\ Area Hexagon=73.5*\sqrt{3}](https://tex.z-dn.net/?f=%20Area%20Hexagon%3D6%2A%5B49%2A%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B4%7D%5D%20%20%5C%5C%20Area%20Hexagon%3D73.5%2A%5Csqrt%7B3%7D%20%20)
cm²
therefore
the answer is the option
73.5 sqrt 3cm²
