The problem above can be modelled as shown in the graph below
At
, the height of the water from the ground is
Answers:
4; 20; 3x² - 4x + 3; 52; 17
Step-by-step explanation:
f(-1): replace x in f(x) = x² + 3 with -1: f(-1) = (-1)² + 3 = 4
f(-4) + g(-1) = (-4)² + 3 + <em>2(-1) + 3</em> = 16 + 3 <em>- 2 + 3</em> = 20 <em>(since g(x) = 2X + 3)</em>
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3f(x) - 2g(x) = 3[x² +3] - 2[2x + 3} = 3x² + 9 - 4x - 6 = 3x² - 4x + 3
f(g(2)): First, evaluate g(2). It is g(2) = 2(2) + 3 = 7. Next, use this output, 7, as the input to f(x): f(g(x)) = (7)² + 3 = 49 + 3 = 52
g(f(2)): First, evaluate f(x) at x = 2: f(2) = (2)² + 3 = 7. Next, use this 7 as the input to g(x): g(f(2)) = g(7) = 2(7) + 3 = 17
Answer:
No, it's not a right triangle.
Step-by-step explanation:
1. The Pythagorean Theorem states that the area of the square whose side is the hypotenuse (longest side of a right triangle) is equal to the sum of the area of the squares from the two other sides.
2. The longest side in this "triangle" has 18 centimeters, and the other 2 sides are 5 and 12 centimeters.
3. Let's apply the Pythagorean Theorem to see if 5^2 + 12^2 = 18^2
4. Okay, so the sum of the area of the squares from the two other sides is not equal to the hypotenuse squared, therefore, it's not a right triangle.
(Plus, it's not even a triangle because 7 < x < 17, and the third "side", 18, is not between 7 and 17.)
Answer:
5.5 Hours
Step-by-step explanation:
Currently, the equation is 60=8.50h+13.25 and h stands for the hours that Sammie worked. So, you need to solve for h by first subtracting 13.25 (his tips) and getting the amount that he received for the hours that he worked.
You should now have 46.75=8.50h
Our final step, is to divide 46.75 by 8.50 to get h by itself and determine the total hours that Sammie worked.
In the end, you should come out with h=5.5, which means that Sammie worked 5.5 hours.
