F(x)=3/5x+1 find f(-15)

Temka [501]

-y=8x
Since slope intercept form is the form: y=mx + b
And -y=8x is basically -y=mx
All you have to do is divide -y by -1 so that the negative of the variable goes away.
Final Answer: y= -8x

3 0

3 years ago

A student is painting a room at a constant rate. She is able to paint 2/5 of a room in 1/2 of an hour. How long does it take to

MrMuchimi

Answer:

75 minutes

Step-by-step explanation:

if it takes 30 minutes to paint 2/5 of the room, then it must take 15 minutes to paint 1/5 of the room.

15 * 5 = 75 minutes or 5/4 hours

7 0

3 years ago

The rate of change of the number of squirrels S(t) that live on the Lehman College campus is directly proportional to 30 − S(t),

pishuonlain [190]

Answer:

S(3)=22

Step-by-step explanation:

The rate of change of the number of squirrels S(t) that live on the Lehman College campus is directly proportional to 30 − S(t).

$\dfrac{dS}{dt}=k(30-S(t))\\ \dfrac{dS}{dt}+kS(t)=30k\\$The integrating factor: e^{\int k dt}=e^{kt}\\$Multiply all through by the integrating factor\\ \dfrac{dS}{dt}e^{kt}+kS(t)e^{kt}=30ke^{kt}$

$(Se^{kt})'=30ke^{kt} dt\\$Integrate both sides\\ Se^{kt}=\dfrac{30ke^{kt}}{k}+C$ (C a constant of integration)\\Se^{kt}=30e^{kt}+C\\$Divide both sides by e^{kt}\\S(t)=30+Ce^{-kt}$

When t=0, S(t)=15

$15=30+Ce^{-k*0}\\C=15-30\\C=-15$

When t = 2, S(t)=20

$20=30-15e^{-2k}\\20-30=-15e^{-2k}\\-10=-15e^{-2k}\\e^{-2k}=\dfrac23\\$Take the natural log of both sides$\\-2k=\ln \dfrac23\\k=-\dfrac{\ln(2/3)}{2}$

Therefore:

$S(t)=30-15e^{\frac{\ln(2/3)}{2}t}\\$When t=3$\\S(t)=30-15e^{\frac{\ln(2/3)}{2} \times 3}\\S(3)=21.8 \approx 22$

8 0

2 years ago

Solving a word problem using a quadratic equation with rationa...

choli [55]

Answer:

length : 8 m

width : 13/2 = 6.5 m

Step-by-step explanation:

area of rectangle = l(ength)×w(idth) = 52

l = 2w - 5

=> (2w - 5)×w = 52

=> 2w² -5w - 52 = 0

we know, when transforming this quadratic equation into a multiplication of two expressions of w, that we need to have 2w and w (to make 2w²), and then which 2 numbers multiply to 52 and add to -5 (when one is multiplied by 2 due to 2w) : -13 and 4

=> (2w - 13)×(w + 4) = 0

=> 2 solutions for w :

2w-13 = 0

2w = 13, w = 13/2

w+4 = 0, w = -4

negative values for a side length of a shape do not make sense, so the only usable solution is w = 13/2

=> l = 2w - 5 = 13 - 5 = 8

8 0

3 years ago

A and B solve please

ASHA 777 [7]

Answer:

a) $7.27344

b) 263.974 hours

Step-by-step explanation:

a)

+) 1 day = 24 hours

+) The cost for 1000 watts each hour is $0.05051 so that each hour use of 1 watt costs: $0.05051 / 1000 = $0.00005051

+) Each hour, each electric heater uses 1200 watts costs: $0.00005051 x 1200 = $0.060612

=> In 24 hours, to heat each electricity heater costs: $0.060612 x 24 = $1.454688

=> In 24 hours, to heat 5 electricity heaters costs: $1.454688 x 5 = $7.27344

So that it costs $7.27344 to heat her house for 1 day

b)

As calculated, the cost to use 1 watt in one hour is $0.00005051

=> The cost to use 75 watts in one hour is: $0.00005051 x 72 = $0.00378825

Assume that the hours of using 72 watts to cost $1 is x (hour)

So that: $0.00378825 * x = $1

=> x = 1/ 0.00378825= 263.974 hours

It takes 263.974 hours for a 75-watt lightbulb to stay on to result in $1 electricity charges

5 0

2 years ago