Answer:
Part 1) ![10\ months](https://tex.z-dn.net/?f=10%5C%20months)
Part 2) ![\$25,000](https://tex.z-dn.net/?f=%5C%2425%2C000)
Step-by-step explanation:
Let
y ----> the total amount of savings
x ----> the number of months
we know that
The linear equation in slope intercept form is equal to
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where
m is the slope or unit rate
b is the y-intercept or initial value
In this problem we have
<em>Herman</em>
The slope is equal to ![m=\$1,000\ per\ month](https://tex.z-dn.net/?f=m%3D%5C%241%2C000%5C%20per%5C%20month)
The y-intercept is ![b=\$15,000](https://tex.z-dn.net/?f=b%3D%5C%2415%2C000)
substitute
----> equation A
<em>Jackie</em>
The slope is equal to ![m=\$1,300\ per\ month](https://tex.z-dn.net/?f=m%3D%5C%241%2C300%5C%20per%5C%20month)
The y-intercept is ![b=\$12,000](https://tex.z-dn.net/?f=b%3D%5C%2412%2C000)
substitute
----> equation B
Part 1) In how many months will they have the same amount of savings?
equate equation A and equation B
![1,300x+12,000=1,000x+15,000](https://tex.z-dn.net/?f=1%2C300x%2B12%2C000%3D1%2C000x%2B15%2C000)
solve for x
![1,300x-1,000x=15,000-12,000](https://tex.z-dn.net/?f=1%2C300x-1%2C000x%3D15%2C000-12%2C000)
![300x=3,000](https://tex.z-dn.net/?f=300x%3D3%2C000)
![x=10\ months](https://tex.z-dn.net/?f=x%3D10%5C%20months)
Part 2) How much will each of them have saved?
substitute the value of x=10 months in any of the equations
equation A
![y=1,000(10)+15,000=\$25,000](https://tex.z-dn.net/?f=y%3D1%2C000%2810%29%2B15%2C000%3D%5C%2425%2C000)
equation B
![y=1,300(10)+12,000=\$25,000](https://tex.z-dn.net/?f=y%3D1%2C300%2810%29%2B12%2C000%3D%5C%2425%2C000)
Answer:
2 hrs 13 mins
Step-by-step explanation:
If Richard can paint the living room in 4 hrs, then in 1 hour he can paint 1/4 of the living .
If Vanessa can paint the living room in 5 hours, then in one hour, she can paint 1/5 of the living room.
In one hour Richard and Vanessa can paint 1/4 + 1/5 = 1/y
y is the number of hours it will take both Richard and Vanessa to paint the living room. 1/y is how much of the house they can paint in one hour.
1/4 + 1/5 = 1/y
(5 + 4)/20. ( find the LCM)
9/20 = 1/y
9y= 20
y = 20/9
y = 2.22hrs
y = 2 hrs 13 mins
Answer:
![-\frac{26}{2}/ -\sqrt{9}/ 13.5(percent)/ 0/ 13.5](https://tex.z-dn.net/?f=-%5Cfrac%7B26%7D%7B2%7D%2F%20%20-%5Csqrt%7B9%7D%2F%20%2013.5%28percent%29%2F%200%2F%2013.5)
Step-by-step explanation:
Answer:
A.)359.2, B.)2.5 uf
Step-by-step explanation:
E / I = R
208 / 1.04 = 200 ohms
2*pi*f*L = Xl
6.28*400*.143 = 359.2 ohm
1 / (2*pi*f*Xc) = c
1 /(6.28*400*159.2) = 2.5 uf