(9,40,41) is a Pythagorean Triple, farther down the list than teachers usually venture.
Answer: D. 41 cm
There's a subset of Pythagorean Triples where the long leg is one less than the hypotenuse,
a^2+b^2 = (b+1)^2
a^2 + b^2 = b^2 + 2b +1
a^2=2b+1
So we get one for every odd number, since the square of an odd number is odd and the square of an even number is even.
b = (a^2 - 1)/2
a=3, b=(3^2-1)/2=4, c=b+1=5
a=5, b=(5^2-1)/2 =12, c = 13
a=7, b=24, c=25
a=9, b=40, c=41
a=11, b=60, c=61
a=13, b=84, c=85
It's good to be able to recognize Pythagorean Triples when we see them.
Otherwise we'd have to work the calculator:
√(9² + 40²) = √1681 = 41
The possible answers are A C and D because they all have at least a half pint of paint.
Answer:
(a) 
(b) 100
Step-by-step explanation:
Solving (a):
Given
Shape: Rectangle
Required
Calculate the perimeter.
Area is calculated as:
Where
and 
Substitute 64.8 for Area
Make L the subject:
Perimeter is calculated as:
Substitute 64.8/W for L
To solve further, we take the derivative of P and set it to 0, afterwards.
Set to 0
Collect Like Terms
Cross Multiply:
Divide through by 2
Take square roots
Recall that:
So:
The perimeter is:
Solving (b):
Given
((1 Group of 10 tenths) and (1 group of 8 tenths))/(6 groups of 3 tenths)
Required
Solve
So, the expression becomes:
((1 Group of 
) and (1 group of 
))/(6 groups of 
)
This gives:
((1 Group of 
) and (1 group of 
))/(6 groups of 
)
Group means product, so the expression becomes:
And, as used here means addition
Simplify:
Answer:
a)
b) number of flowers.
c) 2830
Step-by-step explanation:
We are given the following in the question:
The number of flowers bloomed is given by the function:
where s is the s is the number of seeds she planted.
The number of seeds planted per week is given by
where w represents the number of weeks.
a) composite function that represents how many flowers Lily can expect to bloom over a certain number of weeks.
The composite function can be written as:
where f(w) gives the number of flowers that bloomed in w weeks.
b) units of measurement for the composite function
The composite functions gives the number of flower that will bloom in w weeks. Thus, the unit of measurement is number of flowers.
c) Number of flowers in 35 weeks.
We put w = 35 in the composite function.
2830 flowers will bloom in 35 weeks.
Thanks
Step-by-step explanation:
<span>Answer:
Q3 represents 75%, meaning a z of ~0.67
80 - 70 is 10, so the standard deviations is ~14.9.
10 / 0.67 = 14.9
now find the z that represents a score of 90
90 - 70 is 20
20 / 14.9 = 1.34
from a z-table, a z of 1.34 represents a probability of ~90.99% meaning that there is about a 9.01% chance of getting a 90 or better.</span>
