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Answer: choice 4. f(x) and g(x) have a common x-intercept</h3>
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Explanation:
For me, it helps to graph everything on the same xy coordinate system. Start with the given graph and plot the points shown in the table. You'll get what you see in the diagram below.
The blue point C in that diagram is on the red parabola. This point is the x intercept as this is where both graphs cross the x axis. Therefore, they have a common x intercept.
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Side notes:
- Choice 1 is not true due to choice 4 being true. We have f(x) = g(x) when x = 2, which is why f(x) > g(x) is not true for all x.
- Choice 2 is not true. Point B is not on the parabola.
- Choice 3 is not true. There is only one known intersection point between f(x) and g(x), and that is at the x intercept mentioned above. Of course there may be more intersections, but we don't have enough info to determine this.
Hey there!
For Part A, because the amount earned on Sunday isn't specified, we can call this additional income x. Because we're writing an expression, we don't need an equal sign. The expression will be (x + 14).
For Part B, "2 less than" will mean "– 2" and "twice than" will mean the amount of dogs that Alicia walked times 2. We can call the amount that Alicia walked y to avoid confusion with the last expression (though you could use whatever variable here) and your expression will be (2y – 2).
Hope this helped you out! :-)
Answer: 1
Step-by-step explanation: It is 1 because according to order of operations we have to do what is inside the parentheses first, so we do 2x2 + 2x2, which equals 4+4=8, finally do 8/8 to get 1.
Hope this helps! :)
9514 1404 393
Answer:
£592 for 16 boxes
Step-by-step explanation:
The classroom floor area is ...
A = LW = (8.8 m)(2.2 m) = 19.36 m²
The cupboard floor area is ...
A = (2.3 m)(2.1 m) = 4.83 m²
Then the total area to be covered is ...
19.36 m² +4.83 m² = 24.19 m²
At 1.6 m² per box, the number of boxes required is ...
(24.19 m²)/(1.6 m²/box) = 15.12 boxes
If we assume we can only purchase whole boxes, we need to purchase 16 boxes to cover the floor. The cost will be ...
(16 boxes)(£37/box) = £592 . . . . cost of laminate to replace the floor
Answer:
17) MC(x) = 35 − 12/x²
18) R(x) = -0.05x² + 80x
Step-by-step explanation:
17) The marginal average cost function (MC) is the derivative of the average cost function (AC).
AC(x) = C(x) / x
MC(x) = d/dx AC(x)
First, find the average cost function:
AC(x) = C(x) / x
AC(x) = (5x + 3)(7x + 4) / x
AC(x) = (35x² + 41x + 12) / x
AC(x) = 35x + 41 + 12/x
Now find the marginal average cost function:
MC(x) = d/dx AC(x)
MC(x) = 35 − 12/x²
18) x is the demand, and p(x) is the price at that demand. Assuming the equation is linear, let's use the points to find the slope:
m = (40 − 50) / (800 − 600)
m = -0.05
Use point-slope form to find the equation of the line:
p(x) − 50 = -0.05 (x − 600)
p(x) − 50 = -0.05x + 30
p(x) = -0.05x + 80
The revenue is the product of price and demand:
R(x) = x p(x)
R(x) = x (-0.05x + 80)
R(x) = -0.05x² + 80x
