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
160 = 2 x 2 x 2 x 2 x 2 x 5 = 2^5 x 5
243 = 3 x 3 x 3 x 3 x 3 = 3^5
So
(160 * 243)^1/5
= 5th root of (160 * 243)
= 5th root of (2^5 * 5 * 3^5)
= 2 * 3 * (5th root of 5)
= 6 * (5th root of 5)
Answer is D. 6 * (5th root of 5)
12 is the number of $10 bills
20 is the number of $20 bills
<u><em>Step-by-step explanation:</em></u>
<u><em /></u>
Hello,
<u>Let's note</u>
a the number of $10 bills
b the number of $20 bills
The total value is $520 so we can write the first equation (1)
We know that there are 32 bills in total so we can write the second equation (2)
(1) - 10*(2) gives
10a + 20b - 10(a+b) = 520 - 320 = 200
10a + 20b - 10a - 10b = 10b = 200
So b = 200/10=20
and then from (2) a = 32 - 20 = 12
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
9-63x
Step-by-step explanation:
9(1-7x)
9-63x
Answer:
24cm
Step-by-step explanation:
The area of the rectangle is length × breadth. You already know the area and the breadth, so you can find the length.
288cm² = length × 12cm
length = 288cm² ÷ 12cm
= 24cm