Where to place the lines

Soling two step inequalities<br> d=5v+m, solve for v

Paladinen [302]

Not an inequality but d-m=5v. (d-m)/5=v. Basically just isolate the variable

4 0

2 years ago

steve deposits $1250 in an account paying 3.4% annual interest compounded continously. how long will it take for the account bal

Tomtit [17]

Answer:

It will take 27.19 years

Step-by-step explanation:

Compound continuous interest can be calculated using the formula:

$A=Pe^{rt}$ , where

A = the future value of the investment, including interest
P = the principal investment amount (the initial amount)
r = the interest rate of interest in decimal
t = the time the money is invested for

∵ Steve deposits $1250 in an account

∴ P = 1250

∵ The account paying 3.4% annual interest compounded continuously

∴ r = 3.4%

- Change it to decimal by dividing it by 100

∴ r = 3.4 ÷ 100 = 0.034

∵ The account balance will reach to $3150.5

∴ A = 3150.5

- Substitute The values of A, P and r in the formula above to find t

∵ $3150.5=1250e^{0.034t}$

- Divide both sides by 1250

∴ $2.5204=e^{0.034t}$

- Insert ㏑ to both sides

∴ $ln(2.5204)=ln[e^{0.034t}]$

- Remember that $ln(e^{n})=n$

∵ $ln(e^{0.034t})=0.034t$

∴ ln(2.5204) = 0.034t

- Divide both sides by 0.034

∴ 27.18875 = t

∴ t ≅ 27.19

It will take 27.19 years

3 0

3 years ago

Meredith is 3 times as old as Adam. Six years from now, she will be twice as old as Adam will be then. How old is Adam now

Fantom [35]

Answer:

A=6

Step-by-step explanation:

M=3A

M+6=2(A+6) M+6=2A+12 M=2A+6

System of equations:

M=3A Subtract

M=2A+6

0=A-6

A=6

3 0

2 years ago

The surface are I cannot find

Ilia_Sergeevich [38]

check the picture below.

so the triangular prism is really just 3 rectangles and 2 right-triangles,

now, we know the base of one of the triangles is 2.6, what's its height?

since it's a right-triangle, we can simply use the pythagorean theorem to get "h".

$\bf \textit{using the pythagorean theorem}
\\\\
c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b
\qquad
\begin{cases}
c=\stackrel{hypotenuse}{5.2}\\
a=\stackrel{adjacent}{2.6}\\
b=\stackrel{opposite}{h}\\
\end{cases}
\\\\\\
\sqrt{5.2^2-2.6^2}=h\implies 4.5\approx h$

so, we can now, simply get the area of both of the triangles and the three rectangles and sum them up, and that's the area of the triangular prism.

$\bf \stackrel{two~triangles}{2\left[ \cfrac{1}{2}(2.6)(4.5) \right]}~~+~~\stackrel{rectangle}{(2.6\cdot 4.3)}~~+~~\stackrel{rectangle}{(4.3\cdot 3.9)}~~+~~\stackrel{rectangle}{(4.3\cdot 5.2)}
\\\\\\
11.7+11.18+22.36\implies \blacktriangleright 45.24 \blacktriangleleft$