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mixas84 [53]
3 years ago
9

Which expression represents the sixth term in the binomial expansion of (5y+3)^10

Mathematics
1 answer:
olga nikolaevna [1]3 years ago
8 0
\bf \textit{the coefficient and values of an expanded term}\\\\
(5y-3)^{10} \qquad \qquad 
\begin{array}{llll}
expansion\\
for\\
6^{th}~term
\end{array} \quad 
\begin{cases}
\stackrel{term}{k}=0..10\\
\stackrel{exponent}{10}\\
-----\\
k=\stackrel{6^{th}~term}{5}\\
n=10
\end{cases}

\bf \stackrel{coefficient}{\left(\frac{n!}{k!(n-k)!}\right)} \qquad \stackrel{\stackrel{first~term}{factor}}{\left( a^{n-k} \right)} \qquad \stackrel{\stackrel{second~term}{factor}}{\left( b^k \right)}

\bf \stackrel{coefficient}{\left(\frac{10!}{5!(10-5)!}\right)} \qquad \stackrel{\stackrel{first~term}{factor}}{\left( (5y)^{10-5} \right)} \qquad \stackrel{\stackrel{second~term}{factor}}{\left( (-3)^5 \right)}
\\\\\\
252(5y)^5(-3)^5\implies 252(5^5y^5)(-3)^5\implies -252(3125y^5)(243)
\\\\\\
-191362500y^5
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The table below represents an exponential function what is the common ratio
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Solution:

Given:

A table representing an exponential function.

The x-values represent the terms, while the y-values represent the numbers.

The common ratio is gotten from the numbers (y-values).

The formula for common ratio is given by;

\begin{gathered} r=\frac{present\text{ term}}{preceed\text{ ing term}} \\  \\ \text{Hence,} \\ r=\frac{108}{36}=\frac{36}{12}=\frac{12}{4}=\frac{4}{1.33\ldots}=\frac{1.33\ldots.}{0.44\ldots} \\ r=3 \end{gathered}

Therefore, the common ratio is 3.

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1 year ago
I NEED HELP PLEASE !!!! ;(
marissa [1.9K]

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The answer is always

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3 years ago
Answer please lot's of points.
Svetlanka [38]

Answer:

t≈8.0927

Step-by-step explanation:

h(t) = -16t^2 + 128t +12

We want to find when h(t) is zero ( or when it hits the ground)

0 =  -16t^2 + 128t +12

Completing the square

Subtract 12 from each side

-12  =  -16t^2 + 128t

Divide each side by -16

-12/-16  =  -16/-16t^2 + 128/-16t

3/4 = t^2 -8t

Take the coefficient of t and divide it by 8

-8/2 = -4

Then square it

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Add 16 to each side

16+3/4 = t^2 -8t+16

64/4 + 3/4= (t-4)^2

67/4 = (t-4)^2

Take the square root of each side

±sqrt(67/4) =sqrt( (t-4)^2)

±1/2sqrt(67) = (t-4)

Add 4 to each side

4 ±1/2sqrt(67) = t

The approximate values for t are

t≈-0.092676

t≈8.0927

The first is before the rocket is launched so the only valid answer is the second one

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Answer:

20x+68

Step-by-step explanation:

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skad [1K]

Since the lines have the same slopes, hence they are parallel lines

<h3>How to determine the relationship between lines</h3>

We can determine the relations by knowing the slopes of the line

For the line with coordinates (9, –5) and (5, –2)

Slope = -2+5/5-9
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For the line with coordinates (–4, –2) and (–8, 1)

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Since the lines have the same slopes, hence they are parallel lines

Learn more on parallel lines here: brainly.com/question/16742265

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