Answer:
Tn = 64-4n
Step-by-step explanation:
The nth term of an AP is expressed as:
Tn = a+(n-1)d
a is the common difference
n is the number of terms
d is the common difference
Given the 6th term a6 = 40
T6 = a+(6-1)d
T6 = a+5d
40 = a+5d ... (1)
Given the 20th term a20 = -16
T20 = a+(20-1)d
T20 = a+19d
-16 = a+19d... (2)
Solving both equation simultaneously
40 = a+5d
-16 = a+19d
Subtracting both equation
40-(-16) = 5d-19d
56 = -14d
d = 56/-14
d = -4
Substituting d = -4 into equation
a+5d = 40
a+5(-4) = 40
a-20 = 40
a = 20+40
a = 60
Given a = 60, d = -4, to get the nth term of the sequence:
Tn = a+(n-1)d
Tn = 60+(n-1)(-4)
Tn = 60+(-4n+4)
Tn = 60-4n+4
Tn = 64-4n
A number without denominator such is equal to number with denominator 1.
So, 24 is equal to 24/1
5/8 x 24
= 5/8 x 24/1
= (5x24) / (8x1)
= 120/8
= 15
Answer:
2/3, 1,2,4
Step-by-step explanation:
The number of pieces of 1/3 foot tall to make a 6 feet skyscraper is 18 pieces.
The model of a skyscraper comes in pieces and each piece is 1/3 feet tall.
After all the pieces are put together the skyscraper is 6 feet tall.
We have to calculate how many pieces were put together to make the 6 feet skyscraper.
Let X be the number of pieces put together to make a 6 feet skyscraper.
Now,
Each piece = 1/3 feet tall.
Since all the pieces together make 6 feet tall, we can write the number of pieces needed to make 6 feet tall as:
X x (1/3) = 6
X = 6 x 3 = 18
Thus, we need 18 pieces of 1/3 foot tall to make a 6 feet skyscraper.
Learn more about multiplication word problems here:
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Answer:
The answer to your question is letter D
Step-by-step explanation:
We know that the sum of the internal angles in a triangle equals 180°.
So, B = 30°, C = 90° and A = ?
A + B + C = 180°
Substitution
A + 30 + 90 = 180
Solve for A
A = 180 - 30 - 90
A = 180 - 120
A = 60°
To find "b". use the trigonometric function sine
sin B = 
sin B x hypotenuse = Opposite side
Opposite side = sin 30 x 10
Opposite side = 0.5 x 10
Opposite side = b = 5.0
To find "a" use the trigonometric function cosine
Cos A = adjacent side / hypotenuse
Adjacent side = a = cos A x hypotenuse
Adjacent side = a = cos 60 x 10
a = 0.866 x 10
a = 8.66
