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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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Simplify and write without negative exponents

Inessa05 [86]

$\bf \left( \cfrac{3x^{\frac{3}{2}}y^3}{x^2y^{-\frac{1}{2}}} \right)^{-2}\implies \left( \cfrac{3y^3y^{\frac{1}{2}}}{x^2x^{-\frac{3}{2}}} \right)^{-2}\implies 
\left( \cfrac{3y^{3+\frac{1}{2}}}{x^{2-\frac{3}{2}}} \right)^{-2}\implies \left( \cfrac{3y^{\frac{7}{2}}}{x^{\frac{1}{2}}} \right)^{-2}
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\left( \cfrac{x^{\frac{1}{2}}}{3y^{\frac{7}{2}}} \right)^{+2}\implies \cfrac{x^{\frac{1}{2}\cdot 2}}{3^2y^{\frac{7}{2}\cdot 2}}\implies \cfrac{x^1}{9y^7}\implies \cfrac{x}{9y^7}$

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3 years ago

ILL GIVE YOU BRAINLIST !!!! What is the slope of this table?

VLD [36.1K]

Answer: Slope is m = 2/3

Step-by-step explanation:

-You have exactly four points on a table:

$(3,2) (6,4) (9,6) (12,8)$

-Use the slope formula and use any two points from those four points in order to find the slope:

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

-The two points I use are $(3, 2)$ and $(6,4 )$ for the equation:

$m = \frac{4 - 2}{6-3}$

$m= \frac{2}{3}$

So, the slope of the table is $\frac{2}{3}$ .

8 0

3 years ago

For the order of operations, Group of answer choices Multiplication, division and remainder is performed first Addition and subt

Furkat [3]

Answer: Addition and subtraction is performed after multiplication, division and remainder

Step-by-step explanation:

The correct order of operations is to calculate whatever is in the parenthesis first.

Then calculate multiplication and division depending on which comes first as you move from left to right.

Then addition and subtraction can be performed also depending on which comes first as you move left to right.

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3 years ago

Allison, Buck, Chantal, and Doug compete in a 40-yard dash.

Lena [83]

16 ways. 4 times 4 equals 16.

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3 years ago

The perimeter of a triangle is 19 cm. If the lengh of the longest side is twice

aliya0001 [1]

If the perimeter of a triangle is 19 cm. The lengths of 3 sides is: a = 8, b = 7, c = 4.

<h3>Parimeter</h3>

Let a = longest

Let b= shortest

Let c= third side

a = 2c

a = (b+ c) - 3

a + 3 = b + c

Using three variables to solve the expression for perimeter

Perimeter= 19 cm

a+ b + c = 19

a + (a + 3) = 19

2a + 3 = 19

2a= 16

Divide both side by 2a

a=16/2

a = 8

a = 2c

8 = 2c

c=8/2

c = 4

a + b + c= 19

8 + b + 4 = 19

12 + b = 19

b=19-12

b = 7

Hence,

a = 8, b = 7, c = 4

Therefore If the perimeter of a triangle is 19 cm. The lengths of 3 sides is: a = 8, b = 7, c = 4.

The complete question is:

Perimeter of triangle is 19cm. If the length of the longest side is twice that of the shortest side and 3 less than the sum of the lengths of the 2 sides find lengths of 3 sides.

Learn more about perimeter here:brainly.com/question/19819849

#SPJ1

7 0

2 years ago