Answer:
Step-by-step explanation:
15 x 7 = 105
The gap is either 9 x 7 =63 or 12 x 7 = 84
105 - 84 = 21
105 - 63 = 42
So the shaded area is either is 21 or 42
Any geometric sequence can be expressed as:
a(n)=ar^(n-1), a=initial term, r=common ratio, n=term number
We are given that a(5)=1/16 and r=1/4 so we can say:
1/16=a(1/4)^(5-1)
1/16=a(1/4)^4
1/16=a/256
256/16=a
16=a
So the initial term is 16 so our formula is:
a(n)=16(1/4)^(n-1)
Given :
a-b = c-d ...1)
b = d-1 ...2)
c = 6
To Prove :
a = 5
Solution :
Adding equation 1 and 2, we get :
(a-b) + (b) = (c-d) + (d-1)
a = c -1 ...3)
Putting given value of c = 6 in above equation, we get :
a = 6 - 1
a = 5
Hence, proved.
Answer: (7, 20)
Concept:
There are three general ways to solve systems of equations:
- Elimination
- Substitution
- Graphing
Since the question has specific requirements, we are going to use <u>substitution </u>to solve the equations.
Solve:
<u>Given equations</u>
y = 3x - 1
2x + 6 = y
<u>Substitute the y value since both equations has isolated [y]</u>
2x + 6 = 3x - 1
<u>Add 1 on both sides</u>
2x + 6 + 1 = 3x - 1 + 1
2x + 7 = 3x
<u>Subtract 2x on both sides</u>
2x + 7 - 2x = 3x - 2x

<u>Find the value of y</u>
y = 3x - 1
y = 3(7) - 1
y = 21 - 1

Hope this helps!! :)
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