Answer:
Let's talk through this a one step at a time.
*Since f(x) is concave-up with its vertex on the x-axis, we know f(x) ≥ 0.
*We also know that when we shift a function's domain by a positive number, we shift the function left and when we shift a function's domain by a negative number, we shift the function right. So f(x-5) is f(x) shifted to the right by 5.
*At this point, f(x-5) has its vertex at (5,0).
*When we negate f(x-5), the parabola becomes concave down yet the vertex remains at (5,0). Now we're at -f(x-5). At this point we have -f(x-5)≤0 with a range (-∞,0]
*If we add 2 to create g(x)=2-f(x-5), then we have a concave down parabola with its vertex shifted up by 2, at (5,2). So, g(x) is concave down with its vertex at (5,2). Hence
Answer:
You can model a data using a linear function when the dependent variable is a multiple of the independent formula plus another constant by the y-intercept. The constant multiple is represented by the slope. In real life problems, linear function is applied when you want to determine the cost given with a slope which is represented by cost per unit time. For example, the cost of wifi connection is $10/month plus $2 inclusive for phone charges. The linear function would be:
C = 10t + 2
where C is the cost and t is time in months
Step-by-step explanation:
12x + 16y = 96
Subtract 12x from both sides
16y = 96 - 12x
Divide each side by 16
y = 6 - 0.75x
Answer: $24.19
Step-by-step explanation:
From the question, we are informed that Mai bought gas for her car which cost $2.95 per gallon and that she bought 8.2 gallons.
The total cost for Mai's gas will be:
= $2.95 × 8.2
= $24.19
Answer: 22.5 . The weight of the elephant is "22.5 times greater" than the weight of the lion.
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Explanation:
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(weight of lion) * (x) = (eight of the elephant) ; Solve for "x" .
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→ Divide each side of the equation by "(weight of lion)" ;
to isolate "x" on one side of the equation ; and to solve for "x" ;
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→ (weight of lion)*(x) / (weight of lion) = (weight of the elephant) /
(weight of lion) ;
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→ x = (weight of the elephant) / (weight of lion) ;
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→ Plug in our "given values" ; and solve for "x" ;
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→ x = (<span>9*10</span>³) / (4*10²) = (9*10⁽³⁻²⁾) / 4 = (9*10¹) / 4 ;
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→ x = 90 /4 = 25/2 = 22.5 ; which is our answer.
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