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Law Incorporation [45]

3 years ago

5

Write an equation for each sentence. State whether the equation is true, false, or an on open sentence. 11. Twenty five equals a

number v plus fifteen

1 answer:

lapo4ka [179]3 years ago

5 0

V+15=25. ... The equation is ALMOST always false. It's true only when V=10.

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Emelina wrote the equation of a line in point-slope form as shown below.

Harman [31]

Answer: $y=3x+2$

Step-by-step explanation:

Given: Emelina wrote the equation of a line in point-slope form as shown below.

$(y+4)=3(x+2)$

To write the equation in intercept form, first we multiply 3 inside the bracket values in the right side , we get

$y+4=3x+6$

Now, subtract 4 from both sides , we get

$y=3x+2$

Hence, Emelina’s equation in slope-intercept form : $y=3x+2$

6 0

3 years ago

Read 2 more answers

The diagram shows two campsites on opposite ends of a lake and two triangles formed by intersecting segments from the campsites.

Aleks [24]

Answer:

x=42.3m

Step-by-step explanation:

x/47=82.8/92

92x=3891.6= 42.3m is the distance

6 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Csqrt%7B2%7D%20%5Cfrac%7B7%7D%7B8%7D" id="TexFormula1" title="\sqrt{2} \frac{7}{8}" alt="\sq

quester [9]

Answer:

$\sqrt{2\frac{7}{8} } =\\\sqrt{\frac{25}{8} } =\\\sqrt{\frac{25*2}{16} } =$

±5√2/4

5 0

3 years ago

Write and solve an equation to find the value of x and a missing angle in each triangle below. Use the number bank to help you c

jolli1 [7]

Answer:

1. x = 30

REC = 130

Step-by-step explanation:

2x + 70 = 4x + 10

60 = 2x

x = 30

you try the others

Good luck :D

5 0

2 years ago

A 75-gallon tank is filled with brine (water nearly saturated with salt; used as a preservative) holding 11 pounds of salt in so

Debora [2.8K]

Let $A(t)$ = amount of salt (in pounds) in the tank at time $t$ (in minutes). Then $A(0) = 11$ .

Salt flows in at a rate

$\left(0.6\dfrac{\rm lb}{\rm gal}\right) \left(3\dfrac{\rm gal}{\rm min}\right) = \dfrac95 \dfrac{\rm lb}{\rm min}$

and flows out at a rate

$\left(\dfrac{A(t)\,\rm lb}{75\,\rm gal + \left(3\frac{\rm gal}{\rm min} - 3.25\frac{\rm gal}{\rm min}\right)t}\right) \left(3.25\dfrac{\rm gal}{\rm min}\right) = \dfrac{13A(t)}{300-t} \dfrac{\rm lb}{\rm min}$

where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.

Then the net rate of salt flow is given by the differential equation

$\dfrac{dA}{dt} = \dfrac95 - \dfrac{13A}{300-t}$

which I'll solve with the integrating factor method.

$\dfrac{dA}{dt} + \dfrac{13}{300-t} A = \dfrac95$

$-\dfrac1{(300-t)^{13}} \dfrac{dA}{dt} - \dfrac{13}{(300-t)^{14}} A = -\dfrac9{5(300-t)^{13}}$

$\dfrac d{dt} \left(-\dfrac1{(300-t)^{13}} A\right) = -\dfrac9{5(300-t)^{13}}$

Integrate both sides. By the fundamental theorem of calculus,

$\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac1{(300-t)^{13}} A\bigg|_{t=0} - \frac95 \int_0^t \frac{du}{(300-u)^{13}}$

$\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac{11}{300^{13}} - \frac95 \times \dfrac1{12} \left(\frac1{(300-t)^{12}} - \frac1{300^{12}}\right)$

$\displaystyle -\dfrac1{(300-t)^{13}} A = \dfrac{34}{300^{13}} - \frac3{20}\frac1{(300-t)^{12}}$

$\displaystyle A = \frac3{20} (300-t) - \dfrac{34}{300^{13}}(300-t)^{13}$

$\displaystyle A = 45 \left(1 - \frac t{300}\right) - 34 \left(1 - \frac t{300}\right)^{13}$

After 1 hour = 60 minutes, the tank will contain

$A(60) = 45 \left(1 - \dfrac {60}{300}\right) - 34 \left(1 - \dfrac {60}{300}\right)^{13} = 45\left(\dfrac45\right) - 34 \left(\dfrac45\right)^{13} \approx 34.131$

pounds of salt.

7 0

2 years ago