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sertanlavr [38]
2 years ago
11

At a pond there were 24 ducks swimming. The ratio of ducklings to adult ducks is 5:1. How many ducklings were swimming at the po

nd?
Mathematics
2 answers:
grigory [225]2 years ago
7 0
Twenty ducklings were swimming at the pond
marta [7]2 years ago
3 0

Answer:

20\ ducklings

Step-by-step explanation:

Let

x------> the number of ducklings

y------> the number of adult ducks

we know that

x+y=24 ------> equation A

\frac{x}{y}=\frac{5}{1}

so

x=5y

y=0.20x ------> equation B

Substitute equation B in equation A

x+0.20x=24

1.20x=24

x=20\ ducklings

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2 years ago
186% of what is 56.73
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EXTRA.
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4 0
2 years ago
The first three terms of a geometric sequence are shown below. x+3,-2x2-6x,4x3+12x2,.... What is the eighth term of the sequence
nika2105 [10]
So hmm is a geometric sequence, meaning, the next term is found by multiplying it by "something", namely the "common ratio"

now, if the next term is the product of the common ratio and the previous term, that means, if we divide the previous term by the next term, the quotient will then be the "common ratio", let's do that then

let's divide the 2nd term by the 1st term then

\bf \cfrac{-2x^2-6x}{x+3}\implies \cfrac{-2x\underline{(x+3)}}{\underline{(x+3)}}\implies \boxed{-2x}\impliedby \textit{common ratio}\\\\
-----------------------------\\\\

\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{value of first term}\\
r=\textit{common ratio}\\
----------\\
a_1=x+3\\
n=8\\
r=-2x
\end{cases}
\\\\\\
a_8=(x+3)(-2x)^{8-1}\implies a_8=(x+3)(-2x)^7
\\\\\\
a_8=(x+3)(-2^7x^7)\implies a_8=(x+3)(-128x^7)
\\\\\\
a_8=-128x^8-384x^7
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