Answer:
Step-by-step explanation:
We are given the following in the question:
There are three pieces of a wood.
Length of longest piece =
Length of shortest piece =
Let x be the length of the third piece.
Since the length of third piece lies between the length of the longest and the shortest piece of wood, thus, we use the following inequality to represent the length of the third piece.
Inequality:
The second one if im not wrong
Answer: it will take 36 years for the account balance to reach $1,200.
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 70
A = 1200
r = 1.5% = 1.5/100 = 0.015
n = 1 because it was compounded once in a year.
Therefore,.
1200 = 700(1 + 0.015/1)^1 × t
1200/700 = (1.015)^t
1.714 = 1.015^t
Taking log of both sides,
Log 1.714 = log 1.015^t
0.234 = tlog 1.015 = t × 0.0065
t = 0.234/0.0065
t = 36 years
Answer:
Step-by-step explanation:
–3 is a valid solution because substituting it into the original equation gives a true statement.
<h3>
Answer: 14x - 8</h3>
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Explanation:
I'll use the quadratic formula to find the roots or x intercepts. This slight detour allows us to factor without having to use guess-and-check methods.
The equation is of the form ax^2+bx+c = 0
This leads to...
Now use those roots to form these steps
Refer to the zero product property for more info.
Therefore, the original expression factors fully to (4x-5)(3x+1)
Use the FOIL rule to expand it out and you should get 12x^2-11x-5 again.
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We did that factoring so we could find the side lengths of the rectangle.
I'm using the fact that area = length*width
- L = length = 4x-5
- W = width = 3x+1
The order of length and width doesn't matter.
From here, we can then compute the perimeter of the rectangle
P = 2(L+W)
P = 2(4x-5+3x+1)
P = 2(7x-4)
P = 14x - 8