Answer:
Slope is positive for all x, so always increasing
Step-by-step explanation:
Increasing/decreasing depends on the slope of the function, which is f'
f'(x) = 9x² + 18x + 25
If f'(x) > 0 for all x, then his claim is correct (increasing for all x)
If there's even 1 x-value for which f'(x) is not positive, his claim is incorrect
f'(x) is a quadratic function.
9x² + 18x + 25
9(x² + 2x) + 25
9(x² + 2(x)(1) + 1² - 1²) + 25
9(x + 1)² - 9 + 25
9(x + 1)² + 16
Since the minimum value of f' is 16, it's always positive.
Hence, the claim is correct
Answer:
Step-by-step explanation:
The addition of angles ABD and DBC make up the larger angle ABC. We know that angle ABD = 65 and DBC = 60, therefore
angle ABC = 65 + 60 and
angle ABC = 125 degrees
Answer:
£38.48
Step-by-step explanation:
First, we have to find what 4% of 37 is, so our equation is:
37 x 0.04 = 1.48
Then we have to add that 4% to the original cost:
1.48 + 37 = 38.48
So the total price of the theatre ticket is £38.48
The partial products would be 10 multiply 40, 10 multiply 3, 7 multiply 40, and 7 multiply 3.
Set it up like a regular equation. I used:

As you can see, however, I inserted the "less than" symbol rather than the equal sign because values greater than a certain value can also equal "x". Solve it like a normal equation and you will arrive at:
<u>
</u>

This means that, as long as x is greater than 45, "6x" will be greater than "3x+135". Thus, if you bring 46 students, the Science Center will cost less.