Ask question

Ask question

All categories

3 years ago

15

bill wieghs 120 pounds and is gaining ten pounds each month. phil weighs 150 pounds and is gaining 4 pounds each month.how many

months, m, will it take for bill to weigh the same as phil

2 answers:

ale4655 [162]3 years ago

8 0

Bill wieghs 12o and gains 10 per month, his weight can be written as 120 +10m.

Phil's weight can be written as 150 + 4m.

To find the number of months for them to weigh the same, set the equations equal and solve for m.

120 + 10m = 150 +4m

Subtract 4m from each side:

120 + 6m = 150

Subtract 120 from each side:

6m = 30

Divide both sides by 6:

m = 30/6

m = 5

It will take 5 months.

WINSTONCH [101]3 years ago

7 0

Answer:

5 months

Step-by-step explanation:

120 + 10m = 150 + 4m

Subtract 4m from 10m on both sides ( 4m cancels out which leaves 120 + 6m=150)

120 + 6m = 150

Subtract 120 from 150 on both sides (120 cancels out which leaves 6m = 30

6m= 30

Divide 30 by 6 on both sides ( 6 cancels out which leaves 30/6

<u>m=5</u>

You might be interested in

Choose the correct words from the drop-down menu to make a true statement about the system of equations.

Artist 52 [7]

Answer:

C

Step-by-step explanation:

Given the 2 equations

y = $\frac{1}{3}$ x + 2 → (1)

- x + 3y = 6 → (2)

Substitute y = $\frac{1}{3}$ x + 2 into (2)

- x + 3( $\frac{1}{3}$ x + 2) = 6 ← distribute left side

- x + x + 6 = 6, that is

6 = 6 ← True

This statement indicates the system has infinitely many solutions

4 0

3 years ago

Lines I and m are parallel.

tatyana61 [14]

m∠3 = 70°

Solution:

Line l and line m are parallel.

line t and line s are transversals.

<em>Sum of the adjacent angles in a straight line = 180°</em>

50° + (x + 25)° + (2x)° = 180°

50° + x° + 25° + 2x° = 180°

75° + 3x° = 180°

Subtract 75° from both sides, we get

3x° = 105°

Divide by 3 on both sides of the equation.

x° = 35°

x = 35

(2x)° = (2 × 35)° = 70°

(2x)° and ∠3 are alternate interior angles.

<em>If two lines are parallel then alternate interior angles are congruent.</em>

m∠3 = (2x)°

m∠3 = 70°

Hence m∠3 = 70°.

5 0

4 years ago

Using inductive reasoning, what conclusion can you make from the following statement In your study of geometry, you notice that

Lina20 [59]

The answer is: You conclude that most squares are also rectangles.

Hope this helps!

~LENA~

5 0

3 years ago

Read 2 more answers

Write each of the following expressions without using absolute value.

Stels [109]

Answer:

-3+7=4 is the answer if thats what you is looking for

Step-by-step explanation:

7 0

3 years ago

A 1000-liter (L) tank contains 500 L of water with a salt concentration of 10 g/L. Water with a salt concentration of 50 g/L flo

djverab [1.8K]

Answer:

a) $y(t)=50000-49990e^{\frac{-2t}{25}}$

b) $31690.7 g/L$

Step-by-step explanation:

By definition, we have that the change rate of salt in the tank is $\frac{dy}{dt}=R_{i}-R_{o}$ , where $R_{i}$ is the rate of salt entering and $R_{o}$ is the rate of salt going outside.

Then we have, $R_{i}=80\frac{L}{min}*50\frac{g}{L}=4000\frac{g}{min}$ , and

$R_{o}=40\frac{L}{min}*\frac{y}{500} \frac{g}{L}=\frac{2y}{25}\frac{g}{min}$

So we obtain. $\frac{dy}{dt}=4000-\frac{2y}{25}$ , then

$\frac{dy}{dt}+\frac{2y}{25}=4000$ , and using the integrating factor $e^{\int {\frac{2}{25}} \, dt=e^{\frac{2t}{25}$ , therefore $(\frac{dy }{dt}+\frac{2y}{25}}=4000)e^{\frac{2t}{25}$ , we get $\frac{d}{dt}(y*e^{\frac{2t}{25}})= 4000 e^{\frac{2t}{25}$ , after integrating both sides $y*e^{\frac{2t}{25}}= 50000 e^{\frac{2t}{25}}+C$ , therefore $y(t)= 50000 +Ce^{\frac{-2t}{25}}$ , to find $C$ we know that the tank initially contains a salt concentration of 10 g/L, that means the initial conditions $y(0)=10$ , so $10= 50000+Ce^{\frac{-0*2}{25}}$

$10=50000+C\\C=10-50000=-49990$

Finally we can write an expression for the amount of salt in the tank at any time t, it is $y(t)=50000-49990e^{\frac{-2t}{25}}$

b) The tank will overflow due Rin>Rout, at a rate of $80 L/min-40L/min=40L/min$ , due we have 500 L to overflow $\frac{500L}{40L/min} =\frac{25}{2} min=t$ , so we can evualuate the expression of a) $y(25/2)=50000-49990e^{\frac{-2}{25}\frac{25}{2}}=50000-49990e^{-1}=31690.7$ , is the salt concentration when the tank overflows

4 0

4 years ago