Hello,
Penny==>a*10 (a is an integer)
Kenny==>b*18 (b is an integer)
a*10=b*18==>a=9*b/5 ==>b=5+n*5
a=9*(5+5*n)/5=9*(1+n)=9+9n
If n=0 then a=9 and b=5 :Number od cards: 9*10=10, 5*18=90
if n=1 then a=19 and b=10: Number of cards: 19*10=190>100 to exclude.
So number of cards=90
ANSWER
Frequency=2
Midline =3
Amplitude =5
Period =π
EXPLANATION
We have:
![f(x) = 5 \cos(x) + 3](https://tex.z-dn.net/?f=f%28x%29%20%3D%205%20%5Ccos%28x%29%20%20%2B%203)
The given function is of the form;
![f(x) = a\cos(bx) + c](https://tex.z-dn.net/?f=f%28x%29%20%3D%20a%5Ccos%28bx%29%20%20%2B%20c)
where
a=|5| =5 is the amplitude
and b=2 is the frequency.
and 2π/b=2π/2=π
The range of the given function is
8≤y≤-2
The midline is
![\frac{8 + - 2}{2} = \frac{6}{2} = 3](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%20%20%2B%20-%202%7D%7B2%7D%20%20%3D%20%20%5Cfrac%7B6%7D%7B2%7D%20%20%3D%203)
4. Using the given formula, replace t with 8 seconds and multiply:
343 x 8 = 2,744 meters.
5. Domain is the X value, replace x with 1/4 and solve:
1/4^2 + 2 = 2 1/8
y= 2 1/8
Answer:
11
Step-by-step explanation: