What is 9c-c equal when u combined like terms
1 answer:
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Answer:
r=
Step-by-step explanation:
The sum to infinity of a geometric series is calculated as
S∞ = ; | r | < 1
where a₁ is the first term and r the common ratio
here a₁ = 15 and S∞ = 45 , then
45 = ( multiply both sides by (1 - r ) )
45(1 - r) = 15 ( divide both sides by 45 )
1 - r = =
( subtract 1 from both sides )
- r = - 1 = -
( multiply both sides by - 1 )
r =
Answer:
The area of the parallelogram is;
32 square units
Step-by-step explanation:
The given parameters are;
The coordinates of the parallelogram RSTU = R(-4, 4), S(2, 6), T(6, 2), and U(0, 0)
We note that the area of a parallelogram = Base length × Height
From the drawing of the parallelogram RSTU, we have;
The base length = The length of = The length of
= √((2 - (-4))² + (6 - 4)²) = 2·√10
The height of a parallelogram is perpendicular to its base length = The line
∴ Where, the slope of the base length = m, the slope of the height = -1/m
The slope, 'm' of = (6 - 4)/(2 - (-4)) = 1/3
Therefore, the slope of the height = -1/(1/3) = -3
We note that a point on the height is the point 'T', therefore, the equation of the line in point and slope form is therefore;
y - 0 = -3·(x - 0)
∴ y = -3·x
Therefore, the coordinates of the point 'V' is given by the simultaneous solution of the equations of and
The equation of the line in point and slope form from the point 'R' and the slope 'm = 1/3' is given as follows;
y - 4 = (1/3) × (x - (-4)) = (1/3) × (x + 4)
y = x/3 + 4/3 + 4 = x/3 + 16/3
y = x/3 + 16/3
We then have the coordinate at the point 'V' (x, y) is given as follows;
-3·x = x/3 + 16/3
-9·x = x + 16
-10·x = 16
x = -16/10 = -1.6
x = -1.6
∴ y = -3·x = -3 × -1.6 = -4.8
y = 4.8
The coordinate at the point, V = (-1.6, 4.8)
The length of the line = The height of the parallelogram = √((-1.6 - 0)² + (4.8 - 0)²) = 8/5·√10
The height of the parallelogram = 8/5·√10
The area of the parallelogram, A = Base length × Height
∴ A = 2·√(10) × 8/5·√(10) = (16/5) × 10 = 32
The area of the parallelogram, A = 32 square units.
There are 6 other positions in the string, each with 26 choices. So if you fix BO as the first two letters, there are 
possible strings that you can make.
If BO is at the end of the string, you still have possible strings.
Together, then, you have
possible strings.
If BO is at the end of the string, you still have
Together, then, you have