Shortest side (a) = 58
middle side (b) = 64
longest side (c) = 77
the 3 sides a + b + c = 199
b = a + 6
c = a + 19
substitute your new values for b & c into your original formula, so:
a + (a+6) + (a+19) = 199
3a + 25 = 199
3a = 174
a = 58
then substitute 58 into your b & c formulas to figure out the rest
b = a + 6 = 58 + 6 = 64
c = a + 19 = 58 + 19 = 77
Answer:
The correct options are;
1) Write tan(x + y) as sin(x + y) over cos(x + y)
2) Use the sum identity for sine to rewrite the numerator
3) Use the sum identity for cosine to rewrite the denominator
4) Divide both the numerator and denominator by cos(x)·cos(y)
5) Simplify fractions by dividing out common factors or using the tangent quotient identity
Step-by-step explanation:
Given that the required identity is Tangent (x + y) = (tangent (x) + tangent (y))/(1 - tangent(x) × tangent (y)), we have;
tan(x + y) = sin(x + y)/(cos(x + y))
sin(x + y)/(cos(x + y)) = (Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y) - sin(x)·sin(y))
(Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y) - sin(x)·sin(y)) = (Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y))/(cos(x)·cos(y) - sin(x)·sin(y))/(cos(x)·cos(y))
(Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y))/(cos(x)·cos(y) - sin(x)·sin(y))/(cos(x)·cos(y)) = (tan(x) + tan(y))(1 - tan(x)·tan(y)
∴ tan(x + y) = (tan(x) + tan(y))(1 - tan(x)·tan(y)
The
value is multiplied by 3 when n increases by 1. The only expression that does that is the one that has 3 as the base of the exponential term.
The appropriate selection is ...
![a_n=\dfrac{1}{3}(3)^{n-1}](https://tex.z-dn.net/?f=a_n%3D%5Cdfrac%7B1%7D%7B3%7D%283%29%5E%7Bn-1%7D)
1st number = x
2nd number = 3x
3rd number = 2x-10
x +3x + 2x-10 =92
6x - 10 = 92
6x =102
x = 102/6
x = 17
1st number = 17
2nd number = 17*3 = 51
3rd number = 17 *2 = 34-10 = 24
17 + 51 + 24 = 92
3 numbers are 17, 51 and 24
Answer: Area = 389.5cm^2
Explanation:
Area = 104.5cm^2
Width = 9.5cm
Find Length:
L = A/W
L = 104.5/9.5
L = 11cm
Find the enlargement:
let x be the enlargement:
9.5cm + x = 19cm
x = 19 - 9.5
x = 9.5cm
Thus, the enlargement is 9.5cm.
L (after enlarging) = 11 + 9.5 = 20.5cm
W (after enlarging) = 19cm
Find area after enlarging:
A = 20.5 x 19
A = 389.5cm^2