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3 years ago

Which expressions are equal to z+(z+6)

Mathematics

2 answers:

kumpel [21]3 years ago

7 0

Answer:

2(z+3)

Step-by-step explanation:

2z+6

take out the 2: 2(z+3)

RideAnS [48]3 years ago

5 0

Answer:

this is your answer

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Imagine a new pasture with grass growing on it. Every day after the seeds have germinated, the number of blades of grass in the

Arisa [49]

Answer:

It took 17 days for the pasture to be one-third covered in grass

Step-by-step explanation:

* Lets explain how to solve the problem

- The number of blades of grass is triple every day

- Consider that there are x blades in the first day

∵ The number of blades of grass is triple every day

∴ The next day the number of blades of grass will be 3x

∴ The formula to find the number of blades of grass after d days is

$x(3)^{d}$

- After 18 days, the entire pasture is completely covered in grass

∵ d = 18

∴ The number of blades of grass = $x(3)^{18}$

- We need to know the the number of days that took for the pasture

to be one-third covered in grass

∵ The number of blades of grass for 1/3 covered = $(\frac{1}{3})x(3)^{18}$

∴ $(\frac{1}{3})x(3)^{18}=x(3)^{d}$

- Remember $\frac{1}{3}=3^{-1}$

∴ $3^{-1}x(3)^{18}=x(3)^{d}$

- Remember we add the power of the same bases when we

multiply them

∴ $x(3)^{-1+18}=x(3)^{d}$ ⇒ divide both sides by x

∴ $(3)^{17}=(3)^{d}$

- Remember if the two bases equal in the equation, then their

powers are equal

∴ d = 17

* It took 17 days for the pasture to be one-third covered in grass

4 0

3 years ago

Which is the graph of g(x) = sqrt x-16

zalisa [80]

Answer:

Step-by-step explanation:

I am not sure if you are asking for the graph of

√(x-16) that has a x intercept at (16,0)

√ x -16 that has a y intercept at (0, -16)

4 0

2 years ago

A recursive formula for the sequence 18,9,4.5,... is

dybincka [34]

Answer:

A1 = 18

A(n) = A (n-1) -2

Step-by-step explanation:

N represents the number in a sequence and the difference in the sequence is -2 since each time the number is listed in the sequence it is divide by 2.

3 0

1 year ago

(5) Find the Laplace transform of the following time functions: (a) f(t) = 20.5 + 10t + t 2 + δ(t), where δ(t) is the unit impul

Aloiza [94]

Answer

(a) $F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

Step-by-step explanation:

(a) $f(t) = 20.5 + 10t + t^2 +$ δ(t)

where δ(t) = unit impulse function

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 f(s)e^{-st} \, dt$

where a = ∞

=> $F(s) = \int\limits^a_0 {(20.5 + 10t + t^2 + d(t))e^{-st} \, dt$

where d(t) = δ(t)

=> $F(s) = \int\limits^a_0 {(20.5e^{-st} + 10te^{-st} + t^2e^{-st} + d(t)e^{-st}) \, dt$

Integrating, we have:

=> $F(s) = (20.5\frac{e^{-st}}{s} - 10\frac{(t + 1)e^{-st}}{s^2} - \frac{(st(st + 2) + 2)e^{-st}}{s^3} )\left \{ {{a} \atop {0}} \right.$

Inputting the boundary conditions t = a = ∞, t = 0:

$F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $f(t) = e^{-t} + 4e^{-4t} + te^{-3t}$

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 (e^{-t} + 4e^{-4t} + te^{-3t} )e^{-st} \, dt$

$F(s) = \int\limits^a_0 (e^{-t}e^{-st} + 4e^{-4t}e^{-st} + te^{-3t}e^{-st} ) \, dt$

$F(s) = \int\limits^a_0 (e^{-t(1 + s)} + 4e^{-t(4 + s)} + te^{-t(3 + s)} ) \, dt$

Integrating, we have:

$F(s) = [\frac{-e^{-(s + 1)t}} {s + 1} - \frac{4e^{-(s + 4)}}{s + 4} - \frac{(3(s + 1)t + 1)e^{-3(s + 1)t})}{9(s + 1)^2}] \left \{ {{a} \atop {0}} \right.$

Inputting the boundary condition, t = a = ∞, t = 0:

$F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

3 0

3 years ago

What is the diameter of if the circumference of 14

Serggg [28]

Answer:

The diameter would be 4.456338407...

Step-by-step explanation:

This is because if the formula for circumference is C= D(pi) , to find the diameter it's the opposite. D= C/pi

3 0

3 years ago