Answer:
2
Step-by-step explanation:
x+16=9x
x-9x=-16
-8x=-16
x=2
Yes, Vicki's statement is true.
The fruit tart was split into 6 pieces and to find what 1/3 of 6 is, you'd have to divide 6/3 which equals 2. So, 1/3 of 6 is 2 and each girl took home 2 pieces (1/3) of the tart home
Answer:
Ok, we have:
d(t) = 3*t^2 + 5*t - 2.
The first interval is:
(2, 3)
and remember that, for an interval (a,b), the difference quotient is:
D = (f(b) - f(a))/(b -a)
Then in this first interval we have:
![d = \frac{d(3) - d(2)}{3-2} = \frac{3*3^2 + 5*3 - 2 - (3*2^2 + 5*2 - 2)}{1} = 20](https://tex.z-dn.net/?f=d%20%3D%20%5Cfrac%7Bd%283%29%20-%20d%282%29%7D%7B3-2%7D%20%20%3D%20%5Cfrac%7B3%2A3%5E2%20%2B%205%2A3%20-%202%20-%20%283%2A2%5E2%20%2B%205%2A2%20-%202%29%7D%7B1%7D%20%3D%2020)
So the average rate of change in (2,3) is 20.
now, in (2, 2.5) we have:
![d = \frac{d(2.5) - d(2)}{3-2} = \frac{3*2.5^2 + 5*2.5 - 2 - (3*2^2 + 5*2 - 2)}{1} = 9.25](https://tex.z-dn.net/?f=d%20%20%3D%20%5Cfrac%7Bd%282.5%29%20-%20d%282%29%7D%7B3-2%7D%20%20%3D%20%5Cfrac%7B3%2A2.5%5E2%20%2B%205%2A2.5%20-%202%20-%20%283%2A2%5E2%20%2B%205%2A2%20-%202%29%7D%7B1%7D%20%3D%209.25)
So here the rate of change is 9.25
And in the interval (2, 2.1) we have:
![d = \frac{d(2.1) - d(2)}{3-2} = \frac{3*2.1^2 + 5*2.1 - 2 - (3*2^2 + 5*2 - 2)}{1} = 1.73](https://tex.z-dn.net/?f=d%20%3D%20%5Cfrac%7Bd%282.1%29%20-%20d%282%29%7D%7B3-2%7D%20%20%3D%20%5Cfrac%7B3%2A2.1%5E2%20%2B%205%2A2.1%20-%202%20-%20%283%2A2%5E2%20%2B%205%2A2%20-%202%29%7D%7B1%7D%20%3D%201.73)
So in this interval the rate of change is 1.73
No. Because sides JM and KL have different slopes from sides AD and BC .
The formula of a slope:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
For AD:
We have the points A(2, -2) and D(1, -4). Substitute:
![m=\dfrac{-4-(-2)}{1-2}=\dfrac{-2}{-1}=2](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B-4-%28-2%29%7D%7B1-2%7D%3D%5Cdfrac%7B-2%7D%7B-1%7D%3D2)
For JM:
We have the points J(4, -4) and M(2, -9). Substitute:
![m=\dfrac{-9-(-4)}{2-4}=\dfrac{-5}{-2}=2.5](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B-9-%28-4%29%7D%7B2-4%7D%3D%5Cdfrac%7B-5%7D%7B-2%7D%3D2.5)
![2\neq2.5](https://tex.z-dn.net/?f=2%5Cneq2.5)
----------------------------------------
Another argument.
No. Because the MJ is not twice as long as AD.
The formula of the length of a segment:
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
The length of AD:
![|AD|=\sqrt{(1-2)^2+(-4-(-2))^2}=\sqrt{(-1)^2+(-2)^2}=\sqrt{1+4}=\sqrt5](https://tex.z-dn.net/?f=%7CAD%7C%3D%5Csqrt%7B%281-2%29%5E2%2B%28-4-%28-2%29%29%5E2%7D%3D%5Csqrt%7B%28-1%29%5E2%2B%28-2%29%5E2%7D%3D%5Csqrt%7B1%2B4%7D%3D%5Csqrt5)
The length of MJ:
![|MJ|=\sqrt{(2-4)^2+(-9-(-4))^2}=\sqrt{(-2)^2+(-5)^2}=\sqrt{4+25}=\sqrt{29}](https://tex.z-dn.net/?f=%7CMJ%7C%3D%5Csqrt%7B%282-4%29%5E2%2B%28-9-%28-4%29%29%5E2%7D%3D%5Csqrt%7B%28-2%29%5E2%2B%28-5%29%5E2%7D%3D%5Csqrt%7B4%2B25%7D%3D%5Csqrt%7B29%7D)
![\sqrt{29}\neq2\sqrt5](https://tex.z-dn.net/?f=%5Csqrt%7B29%7D%5Cneq2%5Csqrt5)
Answer:x=4
Step-by-step explanation:
-4 is the answer, because -4^3=-64.
Multiply -4 by itself 3 times:
-4x-4x-4
-4 times -4 is -16.
-16 times -4 is -64.
I hope this helped!