Answer:
of Example 6
5 and 14
Step-by-step explanation:
IN EXAMPLE 6
Opposite angles are equal so you equate the first one like this
3x + 20 = 10x - 15
15 + 20 = 7x
35/7 = x
x = 5
In next question b
It is a straight line thus it's 180°
so 4n + 22 +8n -10 = 180
12n + 12 = 180
12n = 180 - 12
n =168÷ 12
n = 14
Answer:
a) The car will be worth $8000 after 2.9 years.
b) The car will be worth $6000 after 4.2 years.
c) The car will be worth $1000 after 12.7 years.
Step-by-step explanation:
The value of the car after t years is given by:
![V(t) = 14651(0.81)^{t}](https://tex.z-dn.net/?f=V%28t%29%20%3D%2014651%280.81%29%5E%7Bt%7D)
According to the model, when will the car be worth V(t)?
We have to find t for the given value of V(t). So
![V(t) = 14651(0.81)^{t}](https://tex.z-dn.net/?f=V%28t%29%20%3D%2014651%280.81%29%5E%7Bt%7D)
![(0.81)^t = \frac{V(t)}{14651}](https://tex.z-dn.net/?f=%280.81%29%5Et%20%3D%20%5Cfrac%7BV%28t%29%7D%7B14651%7D)
![\log{(0.81)^{t}} = \log{(\frac{V(t)}{14651})}](https://tex.z-dn.net/?f=%5Clog%7B%280.81%29%5E%7Bt%7D%7D%20%3D%20%5Clog%7B%28%5Cfrac%7BV%28t%29%7D%7B14651%7D%29%7D)
![t\log{(0.81)} = \log{(\frac{V(t)}{14651})}](https://tex.z-dn.net/?f=t%5Clog%7B%280.81%29%7D%20%3D%20%5Clog%7B%28%5Cfrac%7BV%28t%29%7D%7B14651%7D%29%7D)
![t = \frac{\log{(\frac{V(t)}{14651})}}{\log{0.81}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Clog%7B%28%5Cfrac%7BV%28t%29%7D%7B14651%7D%29%7D%7D%7B%5Clog%7B0.81%7D%7D)
(a) $8000
V(t) = 8000
![t = \frac{\log{(\frac{8000}{14651})}}{\log{0.81}} = 2.9](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Clog%7B%28%5Cfrac%7B8000%7D%7B14651%7D%29%7D%7D%7B%5Clog%7B0.81%7D%7D%20%3D%202.9)
The car will be worth $8000 after 2.9 years.
(b) $6000
V(t) = 6000
![t = \frac{\log{(\frac{6000}{14651})}}{\log{0.81}} = 4.2](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Clog%7B%28%5Cfrac%7B6000%7D%7B14651%7D%29%7D%7D%7B%5Clog%7B0.81%7D%7D%20%3D%204.2)
The car will be worth $6000 after 4.2 years.
(c) $1000
V(t) = 1000
![t = \frac{\log{(\frac{1000}{14651})}}{\log{0.81}} = 12.7](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Clog%7B%28%5Cfrac%7B1000%7D%7B14651%7D%29%7D%7D%7B%5Clog%7B0.81%7D%7D%20%3D%2012.7)
The car will be worth $1000 after 12.7 years.
Answer:
5, 9,13,17
Step-by-step explanation:
5 +4 +4+4
Answer:
13. c,
14. a.
Step-by-step explanation:
13. The length of a side PQ with coordinates of
P as (x,y) and Q as (w,z)
is: ![\sqrt{(x-w)^{2} +(y-z)^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%28x-w%29%5E%7B2%7D%20%2B%28y-z%29%5E%7B2%7D%20%7D)
- so, the length of the side AB =
![\sqrt{(5-5)^{2}+(-2+7)^{2} } =\sqrt{0^{2}+5^{2} } =5](https://tex.z-dn.net/?f=%5Csqrt%7B%285-5%29%5E%7B2%7D%2B%28-2%2B7%29%5E%7B2%7D%20%20%7D%20%3D%5Csqrt%7B0%5E%7B2%7D%2B5%5E%7B2%7D%20%20%7D%20%3D5)
![\sqrt{(5-1)^{2}+(-7+2)^{2} } =\sqrt{(4)^{2}+(-5)^{2} } =\sqrt{4^{2}+5^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%285-1%29%5E%7B2%7D%2B%28-7%2B2%29%5E%7B2%7D%20%20%7D%20%3D%5Csqrt%7B%284%29%5E%7B2%7D%2B%28-5%29%5E%7B2%7D%20%20%7D%20%3D%5Csqrt%7B4%5E%7B2%7D%2B5%5E%7B2%7D%20%20%7D)
![\sqrt{(5-1)^{2} +(-2+2)^{2} } =\sqrt{4^{2} } =4](https://tex.z-dn.net/?f=%5Csqrt%7B%285-1%29%5E%7B2%7D%20%2B%28-2%2B2%29%5E%7B2%7D%20%7D%20%3D%5Csqrt%7B4%5E%7B2%7D%20%7D%20%3D4)
now, the easiest one will be when the vertices are on the coordinate axes.
- so, option c will be the most appropriate one.
14. If u see the figure clearly, the lines l and FH are parallel.
the parallel postulate, i.e, the alternate interior angles will always be congruent.
- here, the alternate interior angles are angle1 and angle4.
- therefore to prove this step, he used parallel postulate as a reason.
- so, the correct option is "a"
Answer:
The Answer is: 75.
Step-by-step explanation:
Set up the equation:
45 / 600 = y / 1000
600y = 45 * 1000
600y = 45000
y = 45,000 / 600 = 75.