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xz_007 [3.2K]
3 years ago
14

What is the largest flag jake can draw

Mathematics
1 answer:
alexgriva [62]3 years ago
5 0
The ratio of length to width is 3/2.  Let's set up equations of ratios using first the 25 cm length of the paper and then the 20 cm width:

 3      25 cm
--- = ----------
 2           x

Solving for x, 3x = 50 cm, and x =16 2/3 cm.  This is possible, since 16 2/3 is less than the paper width 20 cm.

 3       20 cm
--- = -----------
 2         x

Solving for x:  3x = 40 cm; x = 40/3 cm, or  x= 13 1/3 cm.  This is possible, but does not make maximum use of the 20 by 30 cm paper.

Answer:  the largest flag Jake can draw on the paper given is 20 cm (length) by 16 2/3 cm.
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Solve the following system of equations by substitution. Show all steps.
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Answer:

Given system of equations:

\begin{cases}f(x)=-x^2+2x+3\\g(x)=-2x+3\end{cases}

To solve by substitution, equate the equations and solve for x:

\begin{aligned}f(x) & = g(x)\\\implies -x^2+2x+3 & = -2x+3\\-x^2+4x & = 0\\x^2-4x & = 0\\x(x-4) & = 0\\\implies x & = 0\\\implies x-4 & = 0 \implies x=4\end{aligned}

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To find the y-values of the solution, substitute the found values of x into the functions:

f(0)=-(0)^2+2(0)+3=3

g(0)=-2(0)+3=3

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Therefore, the solutions to the given system of equations are:

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2 years ago
Tobias sent a chain letter to his friends, asking them to forward the letter to more friends. The number of people who receive t
malfutka [58]

Answer:

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The number of emails is multiplied by <em>4</em> every <em>9.1 weeks.</em>

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And the exponential function, P(t) will be:

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