Answer:
Step-by-step explanation:
We know that for any two function f(x) and g(x) ,
Given functions : 
and 
Then, 
At x= 6 , we get
The , The expression is equivalent to
When we further simplify it , we get 
Answer:
The domain is (-∞ , ∞)
The domain is continuous
Step-by-step explanation:
Here, we want to identify the domain of the linear function
The domain in this case can be represented by the set of all real numbers.
When we talk of the domain of a function, we are simply referring to the the range of values between the smallest value on the x-axis and the largest number on the x-axis
Hence, mathematically, we are simply considering the smallest value of b up to the largest value of b in this case. Where b simply represents the number of books
Thus, the domain here will be (-∞ , ∞)
On if the domain is discrete or continuous, we can see that the domain is continuous.
The domain is continuous simply because, the domain we have contains all the values and not some in the set of real numbers. If it had contain only some, then it would have been discrete. But since it contains all, it is continuous
(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
Answer:
$26
Step-by-step explanation:
In the picture attached, the table, the plot and the line of best fit are shown. There we can see the next equation:
y = 0.177x + 25.936
where x is the total dollar amount of her customers’ bills and then y is her total daily wages.
This means that even if she serves no customers (x = 0) she will earn $26 ($25.936 rounded to the nearest dollar) for each day of work.
Answer:
The radius of the scoop is r = 3.1 cm
Step-by-step explanation:
Since 3 gallons yields 90 scoops, and 1 gallon = 3785 cm³.
3 gallons = 3 × 3785 cm³ = 11355 cm³
So we have 11355 cm³ in 3 gallons which is also the volume of 90 scoops.
Since 90 scoops = 11355 cm³, then
1 scoop = 11355 cm³/90 = 126.2 cm³
Now, if each scoop is a sphere, the volume is given by V = 4πr³/3 where r is the radius of the scoop. Since we need to find the radius of the scoop, r, making r subject of the formula, we have
r = ∛(3V/4π)
Substituting V = 126.2 cm³, we have
r = ∛(3× 126.2 cm³/4π)
= ∛(378.6 cm³/12.57)
= ∛30.13 cm³
= 3.1 cm
So, the radius of the scoop is r = 3.1 cm
