How many solutions 4.5z = 4.5z

Tomatoes cost $0.70 per pound. 2 6 8 Weight (lb) Price ($) 1.40 2.10

likoan [24]

Answer: 2, 3, 6, 8 (top) 1.40, 2.10 4.20, 5.60 (bottom)

Step-by-step explanation: If 1 pound = 0.70, then 2*0.70=1.40. 2.10 divided by 0.70=3. 0.70*6=4.20. 0.70*8=5.60.

5 0

1 year ago

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What is the value of x? Enter your answer in the box.

loris [4]

Answer:

35

Step-by-step explanation:

Since all the angles are the same in this triangle, all the sides should be the same too.

Hence, 3x - 5 = 4x - 30

5 + -1x = -30

-1x = -35

x = 35

Hope this helped!

8 0

2 years ago

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The graph models how the temperature of a city has changed since sunrise. Select from the drop-down menu to interpret the positi

Tanya [424]

Answer: The correct answer is the 3rd choice.

5h after sunrise until 15h after sunrise.

Step-by-step explanation: looking at the data, the line intercepts and stays above 0 from 5 to 15. Also I took the test.

4 0

2 years ago

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A tank initially has 300 gallons of a solution that contains 50 lb. of dissolved salt. A brine solution with a concentration of

belka [17]

Let s(t) be the amount of salt in the tank at time t. Then s(0) = 50 lb.

Salt flows into the tank at a rate of

(2 gal/min) (6 lb/gal) = 12 lb/min

and flows out at a rate of

(2 gal/min) (s(t)/300 lb/gal) = s(t)/150 lb/min

so that the net rate at which salt is exchanged through the tank is

ds(t)/dt = 12 - s(t)/150 … (lb/min)

Solve for s(t). The DE is separable, so we have

ds/dt = 12 - s/150

150 ds/dt = 1800 - s

150/(1800 - s) ds = dt

Integrate both sides to get

-150 ln|1800 - s| = t + C

Solve for s :

ln|1800 - s| = -t/150 + C

1800 - s = exp(-t/150 + C )

1800 - s = C exp(-t/150)

s = 1800 - C exp(-t/150)

Now given that s(0) = 50, we solve for C :

50 = 1800 - C exp(-0/150)

50 = 1800 - C

C = 1750

Then the amount of salt in the tank at any time t ≥ 0 is

s(t) = 1800 - 1750 exp(-t/150)

To find the time it takes for the tank to hold 100 lb of salt, solve for t in

100 = 1800 - 1750 exp(-t/150)

1700 = 1750 exp(-t/150)

34/35 = exp(-t/150)

ln(34/35) = -t/150

t = -150 ln(34/35) ≈ 4.348

So it would take approximately 4.348 minutes.

By the way, we didn't have to solve for s(t), we could have instead stopped with

-150 ln|1800 - s| = t + C

Solve for C - this C is not the same as the one we found using the other method. s(0) = 50, so

-150 ln|1800 - 50| = 0 + C

C = -150 ln|1750|

==> t = 150 ln(1750) - 150 ln|1800 - s|

Then s(t) = 100 lb when

t = 150 ln(1750) - 150 ln(1700)

t = 150 ln(1750/1700)

t = 150 ln(35/34)

t ≈ 4.348

5 0

2 years ago

Three points, A, B, and C exists in space such that B is "between" A and C. It is known that AB=7, BC=4, and AC=9. Are points A,

EleoNora [17]

If the points are collinear, then that would mean that the points lie on the same line when joined to each other. In order to confirm this, the distances between the points must sum up to the length of the line.

AB + BC = AC
7 + 4 ? 9
11 ≠ 9

Since they do not sum up, therefore, the points are not collinear.

8 0

2 years ago

How many solutions 4.5z = 4.5z – 6.25 + 6.25