Answer:
The value of Lucys house at the start of 2017 is 231525.
Step-by-step explanation:
It is given that the initial value of Lucys house is 200,000. The at the start of 2017.
The exponential function is defined as
![P=P_0(1+r)^t](https://tex.z-dn.net/?f=P%3DP_0%281%2Br%29%5Et)
Where, P₀ is initial value, r is growth rate, t is time in years.
The value of house is defined by the function
![P=200000(1+0.05)^t](https://tex.z-dn.net/?f=P%3D200000%281%2B0.05%29%5Et)
Where, t is number of years after 2014.
![P=200000(1.05)^t](https://tex.z-dn.net/?f=P%3D200000%281.05%29%5Et)
The difference between 2017 and 2014 is 3 years.
![P=200000(1.05)^3=231525](https://tex.z-dn.net/?f=P%3D200000%281.05%29%5E3%3D231525)
Therefore the value of Lucys house at the start of 2017 is 231525.
Hey there,
Let's say that the first piece is x cm
1st = x
2nd = x + 25%
3rd = x - 25%
100% = 240 cm
1% = 240 / 100
= 2.4cm
x + x + 25 + x - 25 = 100
3x + 25 - 25 = 100
3x = 100 - 25 + 25
3x = 100
3x = 240 cm
x = 240 / 3
= 80 cm
1st piece = 80 cm
2nd piece = 80 + (25% x 80)
= 80 + 20
= 100cm
3rd piece = 80 cm - (25% x 80)
= 80 cm - 20
= 60cm
Hope this helps :))
<em>~Top♥</em>
Answer:
<em>The Graph is shown below</em>
Step-by-step explanation:
<u>The Graph of a Function</u>
Given the function:
![\displaystyle y=g(x)=-\frac{3}{2}(x-2)^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3Dg%28x%29%3D-%5Cfrac%7B3%7D%7B2%7D%28x-2%29%5E2)
It's required to plot the graph of g(x). Let's give x some values:
x={-2,0,2,4,6}
And calculate the values of y:
![\displaystyle y=g(-2)=-\frac{3}{2}(-2-2)^2=-\frac{3}{2}(-4)^2==-\frac{3}{2}*16=-24](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3Dg%28-2%29%3D-%5Cfrac%7B3%7D%7B2%7D%28-2-2%29%5E2%3D-%5Cfrac%7B3%7D%7B2%7D%28-4%29%5E2%3D%3D-%5Cfrac%7B3%7D%7B2%7D%2A16%3D-24)
Point (-2,-24)
![\displaystyle y=g(0)=-\frac{3}{2}(0-2)^2=-\frac{3}{2}(-2)^2=-\frac{3}{2}*4=-6](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3Dg%280%29%3D-%5Cfrac%7B3%7D%7B2%7D%280-2%29%5E2%3D-%5Cfrac%7B3%7D%7B2%7D%28-2%29%5E2%3D-%5Cfrac%7B3%7D%7B2%7D%2A4%3D-6)
Point (0,-6)
![\displaystyle y=g(2)=-\frac{3}{2}(2-2)^2=-\frac{3}{2}(0)^2=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3Dg%282%29%3D-%5Cfrac%7B3%7D%7B2%7D%282-2%29%5E2%3D-%5Cfrac%7B3%7D%7B2%7D%280%29%5E2%3D0)
Point (2,0)
![\displaystyle y=g(4)=-\frac{3}{2}(4-2)^2=-\frac{3}{2}(2)^2=-\frac{3}{2}*4=-6](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3Dg%284%29%3D-%5Cfrac%7B3%7D%7B2%7D%284-2%29%5E2%3D-%5Cfrac%7B3%7D%7B2%7D%282%29%5E2%3D-%5Cfrac%7B3%7D%7B2%7D%2A4%3D-6)
Point (4,-6)
![\displaystyle y=g(6)=-\frac{3}{2}(6-2)^2=-\frac{3}{2}(4)^2=-\frac{3}{2}*16=-24](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3Dg%286%29%3D-%5Cfrac%7B3%7D%7B2%7D%286-2%29%5E2%3D-%5Cfrac%7B3%7D%7B2%7D%284%29%5E2%3D-%5Cfrac%7B3%7D%7B2%7D%2A16%3D-24)
Point (6,-24)
The graph is shown in the image below
<span>Write an equation in the standard form to represent the total rent (y) that Sam has to ... is the y-intercept of the function, and what does this tell you about the car?</span><span>
</span>
Answer:
270°
Step-by-step explanation:
(0, -1) is at the 270° angle. If you do a 360°, you end up back where you started, so the angle is still 270°.