All categories

3 years ago

What’s the answer to this problem

Mathematics

1 answer:

Anarel [89]3 years ago

3 0

Answer:

(y+4) (2y+3) is the answer. For more information please check the photo.

You might be interested in

If the Banded Peak school bus travels 2530 km in 10 hours, what unit rate correctly identifies their speed?

prisoha [69]

Answer:

253 km per hour

Step-by-step explanation:

7 0

4 years ago

Read 2 more answers

In the set of real numbers, the first number less than -3 is -4. <br><br> TrueFalse

hodyreva [135]

True because first is 0, -1, -2, -3, and then it is -4 I hope this helps please mark me as brainliest.

3 0

3 years ago

A 500 gallon tank initially contains 200 gallons of water with 5 lbs of salt dissolved in it. Water enters the tank at a rate of

Lapatulllka [165]

Until the concerns I raised in the comments are resolved, you can still set up the differential equation that gives the amount of salt within the tank over time. Call it $A(t)$ .

Then the ODE representing the change in the amount of salt over time is

$\dfrac{\mathrm dA}{\mathrm dt}=\text{rate in}-\text{rate out}$
$\dfrac{\mathrm dA}{\mathrm dt}=\dfrac{2\text{ gal}}{1\text{ hr}}\times\dfrac{\frac15(1+\cos t)\text{ lbs}}{1\text{ gal}}-\dfrac{2\text{ gal}}{1\text{ hr}}\times\dfrac{A(t)\text{ lbs}}{500+(2-2)t}$
$\dfrac{\mathrm dA}{\mathrm dt}=\dfrac25(1+\cos t)-\dfrac1{250}A(t)$

and this with the initial condition $A(0)=5$

You have

$\dfrac{\mathrm dA}{\mathrm dt}+\dfrac1{250}A(t)=\dfrac25(1+\cos t)$
$e^{t/250}\dfrac{\mathrm dA}{\mathrm dt}+\dfrac1{250}e^{t/250}A(t)=\dfrac25e^{t/250}(1+\cos t)$
$\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/250}A(t)\right]=\dfrac25e^{t/250}(1+\cos t)$

Integrating both sides gives

$e^{t/250}A(t)=100e^{t/250}\left(1+\dfrac1{62501}\cos t+\dfrac{250}{62501}\sin t\right)+C$
$A(t)=100\left(1+\dfrac1{62501}\cos t+\dfrac{250}{62501}\sin t\right)+Ce^{-t/250}$

Since $A(0)=5$ , you get

$5=100\left(1+\dfrac1{62501}\right)+C\implies C=-\dfrac{5937695}{62501}$

so the amount of salt at any given time in the tank is

$A(t)=100\left(1+\dfrac1{62501}\cos t+\dfrac{250}{62501}\sin t\right)-\dfrac{5937695}{62501}e^{-t/250}$

The tank will never overflow, since the same amount of solution flows into the tank as it does out of the tank, so with the given conditions it's not possible to answer the question.

However, you can make some observations about end behavior. As $t\to\infty$ , the exponential term vanishes and the amount of salt in the tank will oscillate between a maximum of about 100.4 lbs and a minimum of 99.6 lbs.

5 0

4 years ago

Which equation has a slope: 3/2, y-intercept: –4

ipn [44]

Answer:

The equation of the line that has a slope of 3/2 and a y-intercept of -4 is:

y=3/2x-4.

Step-by-step explanation:

You want to find the equation for a line that has a slope of 3/2 and a y-intercept of -4. First of all, remember what the equation of a line is:

y = mx+b Where: m is the slope, and b is the y-intercept

All you really have to do here is replace m with 3/2, which is the slope you gave, and replace b with -4, the y-intercept you gave, in the equation y=mx+b.

8 0

3 years ago

Which system of equations models this problem? (Image attached)

Leno4ka [110]

Answer:

Your answer would be x+y=531 and y=2x

Step-by-step explanation:

We know that Nancy bought 531 shirts and that some are long sleeved and some are short sleeved. Since x represents the long sleeved shirts and y represents the short sleeved shirts, x+y=531. We also know that there are twice as many short sleeved shirts as long sleeved shirts. So, y=2x.

8 0

3 years ago