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3 years ago

Which of the following characteristics best describes the given function of f(x) = 3x - 6?

Mathematics

1 answer:

Trava [24]3 years ago

4 0

Answer:

Step-by-step explanation:

degree 1 ( linear function

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What is the length of CD ? In this diagram ABC EDC ? Please help !!!!

n200080 [17]

Answer:
CD = x = 4 units

Explanation:
We are given that the two triangles are similar. This means that we can set the similarity proportionality as follows:
$\frac{BC}{CD} = \frac{CA}{CE} = \frac{AB}{ED}$

W e have:
BC = 20 - x
AC = 20
CD = x
CE = 5

Substitute in the above proportionality and solve for x as follows:
$\frac{20-x}{x} = \frac{20}{5} = 4$

4x = 20 - x
5x = 20
x = 4

Based on he above:
CD = 4 units
BC = 20 - x = 20 - 4 = 16 units

Hope this helps :)

5 0

3 years ago

Read 2 more answers

A rectangular prism has a length of 714 inches, a width of 612 inches, and a height of 10 inches.

den301095 [7]

Answer:

8 times

Step-by-step explanation:

The volume of the prism:

V = lwh

If each of the dimensions is doubled, then the volume becomes:

V₁ = 2l*2w*2h = 8lwh = 8V

The larger prism has 8 times greater volume

8 0

3 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

1 year ago

When the Breen family left for their vacation the car's odometer read 5,289 miles. Upon their return the car's odometer read 6,0

Mrrafil [7]

The breen family drove 746 miles on their vacation trip

5 0

3 years ago

8(s+3)=72 i need help it is due tomorrow

Montano1993 [528]

Answer:

s = 6

Step-by-step explanation:

8(s+3) = 72

Expand the brackets out:

(8 x s) + (8 x 3) = 72

8s + 24 = 72

Now you get rid of 24 on the left, by taking away 24. But you also have to do the same on the right side so that both sides are equal:

8s + 24 = 72

left(-24) = right (-24)

So that leaves you with:

8s = 48

Now divide both sides by 8 to make them equal and to get s on its own:

8s = 72

left(/8) = right (/8)

Therfore:

s = 6

3 0

3 years ago