The Recursive formula for an Arithmetic Sequence is a1 = -3, an = an-1 + 6.
<h3>What is Arithmetic sequence ?</h3>
An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k.
Given:
an = -3 + 6(n – 1)
a1= -3
a2= 3
a3 = 9
Here the common difference is 6 and first term is -3
Hence, the recursive formula is a1 = -3, an = an-1 + 6.
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We are given : Cost of a gallon of milk = $2.50.
Cost of a cup of yogurt = $1.20.
Total money Monica has = $20.
Number of cups of yogurt Monica can buy = x.
And inequality made is also correct
1.20x + 2.5 ≤ 20.
Now, we need to solve it for x.
Subtracting 2.5 from both sides, we get
1.20x + 2.5 -2.5 ≤ 20 - 2.5.
1.20x ≤ 17.5
Dividing both sides by 1.20, we get
1.20x/1.20 ≤ 17.5/1.20.
x ≤ 14.5833...
Because it's less than 15, so final answer is : 14 is greatest number of cups of yogurt Monica can buy.
Let us say that the numbers are x and y. The given clues
are:
1. x – y = 16 (so
x is the larger number)
2. y / x = 5 / 7
rewriting eqtn 2 in terms of y:
y = (5/7) x
combining 1 and 2:
x – (5/7) x = 16
(2/7) x = 16
x = 56
y = (5/7) x = 40
So the two numbers are 56 and 40.
The value of the length DF is 1/4 of that of CD because of the Angle Bisector Theorem for triangles.
<h3>
What is the Angle Bisector Theorem?</h3>
The Angel Bisector Theorem states that if a ray bisects an angle of a triangle, it dissects the side of the triangle that is opposite to the dissected angle into parts that are proportionate to the adjacent sides.
Note that the angle that has been dissected here is ∠CBD. Thus,
= 
See the link below for more about Angle Bisector Theorem of the Triangle:
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Answer:
136000 cm
Step-by-step explanation:
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