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3 years ago

What is the seventh term of a sequence whose first term is 1 and whose common ratio is 3?

1 answer:

7 0

$\bf n^{th}\textit{ term of a geometric sequence}\\\\
a_n=a_1\cdot r^{n-1}\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=1\\
r=3\\
n=7
\end{cases}
\\\\\\
a_7=1\cdot 3^{7-1}\implies a_7=1\cdot 3^6\implies a_7=1\cdot 729\implies a_7=729$

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Find the axis of symmetry of 2x^2 + 12x + 16 Show your work

raketka [301]

The vertex form:

$y=a(x-h)^2+k\\\\(h,\ k)-vertex$

The axis of symetry is x = h.

$y=ax^2+bx+c\to h=\dfrac{-b}{2a}$

We have

$y=2x^2+12x+16\to a=2,\ b=12,\ c=16$

Substitute:

$h=\dfrac{-12}{(2)(2)}=\dfrac{-12}{4}=-3$

<h3>Answer: x = -3</h3>

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goblinko [34]

Answer:

$\frac{m^3}{h}, \frac{cm^3}{h}, \frac{km^3}{h}$

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If you look at the objects thrown as garbage, it's a two- or three-dimensional item that takes up space and also has mass and this is a solid waste.

And the landfill that dumps such garbage is also three-dimensional.

Hence, the volume module, if the object inside is a solid, either would be

$m^3,cm^4,Km^3$

As household numbers rise, landfill space increases.

So,

$household\ number = Proportionality\times landfill\ space$

If H represents the number of household keeps, then it will be a sufficient unit for the purpose of Sophia that is

$\frac{m^3}{h}, \frac{cm^3}{h}, \frac{km^3}{h}$

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2 years ago

2+2=4-1=3 2+4+4+5+6+1+8=

Vinvika [58]

Answer:

Step-by-step explanation:

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2 years ago

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An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so the equa

Setler [38]

Answer:

b=0.5 in

b=2 in

Step-by-step explanation:

we know that

The perimeter of triangle is equal to

$2a+b=15$

Solve for a

$a=\frac{15-b}{2}$ -----> equation A

Applying the Triangle Inequality Theorem

a+a > b

2a > b -----> inequality B

<u>Verify each case</u>

case 1) b=-2 in

This value not make sense, the length side cannot be a negative number

case 2) b=0 in

This value not make sense

case 3) b=0.5 in

substitute the value of b in the equation A and solve for a

$a=\frac{15-0.5}{2}=7.25\ in$

substitute the values of b and a in the inequality B

2a > b

2(7.25) > 0.5

14.50 > 0.5 -----> is true

therefore

b=0.5 in make sense for possible values of b

case 4) b=2 in

substitute the value of b in the equation A and solve for a

$a=\frac{15-2}{2}=6.5\ in$

substitute the values of b and a in the inequality B

2a > b

2(6.5) > 2

13 > 2 -----> is true

therefore

b=2 in make sense for possible values of b

case 5) b=7.9 in

substitute the value of b in the equation A and solve for a

$a=\frac{15-7.9}{2}=3.55\ in$

substitute the values of b and a in the inequality B

2a > b

2(3.55) >7.9

7.1 > 7.9 -----> is not true

therefore

b=7.9 in not make sense for possible values of b

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3 years ago

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mrs_skeptik [129]

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