Answer:
The measure of one angle of a regular convex 20-gon is 162°
Step-by-step explanation:
* Lets explain how to solve the problem
- A convex polygon is a polygon with all the measures of its interior
angles less than 180°
- In any polygon the number of its angles equal the number of its sides
- A regular polygon is a polygon that is all angles are equal in measure
and all sides are equal in length
- The rule of the measure of an angle of a regular polygon is
, where m is the measure of each interior
angle in the polygon and n is the numbers of the sides or the angles
of the polygon
* Lets solve the problem
- The polygon is convex polygon of 20 sides (20 angles)
- The polygon is regular polygon
∵ The number of the sides of the polygon is 20 sides
∴ n = 20
∵ The polygon is regular
∴ All angles are equal in measures
∵ The measure of each angle is
∴ 
∴ 
∴ 
∴ m = 162
∴ The measure of one angle of a regular convex 20-gon is 162°
Answer:
Below.
Step-by-step explanation:
2x+4 = (x²)²÷2
2x + 4 = x^4/2
x^4 = 4x + 8
x^4 - 4x - 8 = 0
We can try trial an error to solve this
Looks like x = 2 fits it:
2^4 - 4(2) - 8
= 16 -8 -8 = 0
so x = 2 is one solution.
I can't find any other solution among other integers.
To find the other solutions you can draw a graph manually or by using software.
There will be either 1 or 3 more real solutions.
I used software to draw the graph and found one other solution:
x = -1.296
Answer:
2.15
Step-by-step explanation:
Let g= cost of granola bars
b = cost of bottles of water
10g+12b =23
5g +4b = 10
I will solve this system by elimination
Multiply the second equation by -2
-2(5g +4b) = -2*10
-10g -8b = -20
Now we add this equation to the first equation to eliminate g
-10g -8b = -20
10g+12b =23
---------------------
4b = 3
b = 3/4
A bottle of water = $.75
Now we need to find g
5g+4b =10
5g +4(.75) = 10
5g +3 = 10
Subtract 3 from each side
5g +3-3 = 10-3
5g =7
Divide by 5
5g/5=7/5
g = 7/5
g = 1 2/5
g =1.40
We want the cost of one bottle of water and 1 granola bar
1g + 1b
1.4+.75
2.15
Answer:
The number is -6
The second operation is -60
Step-by-step explanation:
Let the number be x.
Solving (a): The value of x
Operations 1:
Multiply by 3: 3x
Add 40: 3x + 40
Operations 2:
Add 17: x + 17
Multiply by 2: (x + 17) * 2
To find x, equate both operations.
Collect like terms
Solving (b):
Operations:
Subtract 9: 
Multiply by 4: 
This gives:
