Please help, (AP is arithemtic progression)
1 answer:
Answer:
p = 8
Step-by-step explanation:
The n th term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₉ = 4 + 5p and d = 5, then
a₁ + 8d = 4 + 5p, that is
a₁ + 8(5) = 4 + 5p
a₁ + 40 = 4 + 5p ( subtract 40 from both sides )
a₁ = 5p - 36
a₂ = 5p - 36 + 5 = 5p - 31
a₃ = 5p - 31 + 5 = 5p - 26
a₄ = 5p - 26 + 5 = 5p - 21
Given that the sum of the first 4 terms = 7p - 10, then
5p - 36 + 5p - 31 + 5p - 26 + 5p - 21 = 7p - 10, that is
20p - 114 = 7p - 10 ( subtract 7p from both sides )
13p - 114 = - 10 ( add 114 to both sides )
13p = 104 ( divide both sides by 13 )
p = 8
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Answer: The expressions for the length and width of the new patio are
And the area of the new patio is 384 sq. feet.
Step-by-step explanation: Given that Stephen has a square brick patio. He wants to reduce the width by 4 feet and increase the length by 4 feet.
The length of one side of the square patio is represented by x.
We are to write the expressions for the length and width of the new patio and then to find the area of the new patio if the original patio measures 20 feet by 20 feet.
Since Stephen wants to reduce width of the patio by 4 feet, so the width of the new patio will be
The length of the patio is increased by 4 feet, so the length of the new patio will be
Now, if the original patio measures 20 feet by 20 feet, then we must have
and
Therefore, the area of the new patio is given by
Thus, the expressions for the length and width of the new patio are
And the area of the new patio is 384 sq. feet.