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4 years ago

X+y=40 0.08x+0.03y=1.7

1 answer:

7 0

SOLVING:

$\begin{cases}&x+y=40\quad\Longrightarrow\ Equation\ 1\\&0.08x+0.03y=1.7\quad\Longrightarrow\ Equation\ 2\end{cases}\\ \\ \\y=40-x\\ \\\textbf{Replace\ "y"\ in\ equation\ 2:}\\ \\0.08x+0.03(40-x)=1.7\\ \\0.08x+1.2-0.03x=1.7\\ \\0.05x+1.2=1.7\\ \\0.05x=1.7-1.2\\ \\0.05x=0.5\\ \\x= \dfrac{0.5}{0.05}\\ \\x=10\quad\to\boxed{\boxed{\spadesuit\ First\ answer.\ \spadesuit}}\\ \\ \\y=40-10\\ \\y=30\quad\to\boxed{\boxed{\spadesuit\ Second\ answer.\ \spadesuit}}$

$\textbf{Testing\ in\ first\ equation:}\\10+30=40\\40=40\ \checkmark\\ \\\textbf{Testing\ in\ second\ equation:}\\0.08(10)+0.03(30)=1.7\\0.8+0.9=1.7\\1.7=1.7\ \checkmark\\ \\\textbf{HOPE\ THIS\ HELPS...!!}$

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3 years ago

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3 years ago

in a AP the first term is 8,nth term is 33 and sum to first n terms is 123.Find n and common difference

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I believe there is no such AP...

Recursively, this sequence is supposed to be given by

$\begin{cases}a_1=8\\a_k=a_{k-1}+d&\text{for }k>1\end{cases}$

so that

$a_k=a_{k-1}+d=a_{k-2}+2d=\cdots=a_1+(k-1)d$

$a_n=a_1+(n-1)d$

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$21=(n-1)d$

$n$ has to be an integer, which means there are 4 possible cases.

Case 1: $n-1=1$ and $d=21$ . But

$\displaystyle\sum_{k=1}^2(8+21(k-1))=37\neq123$

Case 2: $n-1=21$ and $d=1$ . But

$\displaystyle\sum_{k=1}^{22}(8+1(k-1))=407\neq123$

Case 3: $n-1=3$ and $d=7$ . But

$\displaystyle\sum_{k=1}^4(8+7(k-1))=74\neq123$

Case 4: $n-1=7$ and $d=3$ . But

$\displaystyle\sum_{k=1}^8(8+3(k-1))=148\neq123$

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3 years ago

Express 100,000 as a power of 10

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2 years ago

Alyssa takes part in the triathlon. She cycles 4/5 of the route, runs 7/8 of the route, and swims the rest of the way. She swims

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Answer:

12 miles

Step-by-step explanation:

Alyssa takes part in the triathlon. She cycles 4/5 of the route, runs 1/8 of the route, and swims the rest of the way. She swims 0.9 miles. Find the total distance of the triathlon route.

Total distance Alyssa cycled and ran =

$\frac{4}{5} + \frac{1}{8}$

$\frac{32 + 5}{40}$ = $\frac{37}{40}$

Distance she swam = 1 - 37/40 = 3/40

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3 years ago