The area is given by f(x) = 10x² + 31x + 15.
The function is a rectangle's area function.
Rectangle Area = Length * Width
The length of fabric scrap is 5x. So, the rectangular patchwork's length will be 5x + 3.
Since the width of the fabric scrap will be 2x, the rectangular patchwork's width will be 2x + 5.
Then area = f(x) = (5x + 3)(2x + 5) = 10x² + 25x + 6x + 15 = 10x² + 31x + 15
Therefore the area is given by f(x) = 10x² + 31x + 15.
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Answer:
y = 3.2
Step-by-step explanation:
8/y = 10/4
10y = 32
y = 32 / 10
y = 3.2
The correct answer is D. x=9
The angles of a square are right angles (90 degrees) so it would be set up as 90=11x-9. Then you would combine like terms and solve.
<h3>
Answer: 100 meters</h3>
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Explanation:
If you draw out the diagram, then you'll find that a 45-45-90 triangle forms. The nice thing about this type of triangle is that the two legs are always the same length. The horizontal leg is 100 meters, so the vertical leg must also be 100 meters.
Side note: this type of triangle is an isosceles right triangle.
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You could use the tangent rule to get the same thing
tan(angle) = opposite/adjacent
tan(45) = 100/x
1 = 100/x
1*x = 100
x = 100
In this case, the opposite leg is the vertical leg since it is furthest from the angle of elevation.
I took the liberty of finding for the complete question.
And here I believe that the problem asks for the half life of Curium. Assuming
that the radioactive decay of Curium is of 1st order, therefore the
rate equation is in the form of:
A = Ao e^(-kt)
where,
A = amount after t years = 2755
Ao = initial amount = 3312
k = rate constant
t = number of years passed = 6
Therefore the rate constant is:
2755/3312 = e^(-6k)
-6k = ln (2755/3312)
k = 0.0307/yr
The half life, t’, can be calculated using the formula:
t’ = ln 2 / k
Substituting the value of k:
t’ = ln 2 / 0.0307
t’ = 22.586 years
or
t’ = 22.6 years
