It represents equal parts of a whole or a collection?
2 answers:
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Answer:
Angle 1 = 108°
Angle 2 = 72°
Angle 3 = 120°
Angle 4 = 96°
Angle 5 = 144°
Step-by-step explanation:
We need to find the measures of the interior angles in a pentagon if the measure of each consecutive angle is in the ratio 9:6:10:8:12.
Let x be the common ratio
So, we can write:
Angle 1 = 9x
Angle 2 = 6x
Angle 3 = 10x
Angle 4 = 8x
Angle 5 = 12x
We know that the <em>sum of all angles of pentagon = 540</em>
So, adding all angles and equal them to 540, we can find value of x
So, we get the value of x: x=12
Now, calculating the angles by putting x=12:
Angle 1 = 9x = 9(12) = 108°
Angle 2 = 6x = 6(12) = 72°
Angle 3 = 10x = 10(12) = 120°
Angle 4 = 8x = 8(12) = 96°
Angle 5 = 12x= 12(12) = 144°
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Answer:
"complete the square" to put in vertex form
Step-by-step explanation:
It may be helpful to consider the square of a binomial:
(x +a)² = x² +2ax +a²
The expression x² +x +1 is in the standard form of the expression on the right above. Comparing the coefficients of x, we see ...
2a = 1
a = 1/2
That means we can write ...
(x +1/2)² = x² +x +1/4
But we need x² +x +1, so we need to add 3/4 to the binomial square in order to make the expressions equal:
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Another way to consider this is ...
x² +bx +c
= x² +2(b/2)x +(b/2)² +c -(b/2)² . . . . . . rewrite bx, add and subtract (b/2)²*
= (x +b/2)² +(c -(b/2)²)
for b=1, c=1, this becomes ...
x² +x +1 = (x +1/2)² +(1 -(1/2)²)
= (x +1/2)² +3/4
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* This process, "rewrite bx, add and subtract (b/2)²," is called "completing the square"—especially when written as (x-h)² +k, a parabola with vertex (h, k).