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dedylja [7]
3 years ago
10

The length of a pool is 3 feet more than twice its width. If the perimeter of the pool is 72 feet, find the dimensions of the po

ol by writing and solving a system of equations.
Mathematics
2 answers:
photoshop1234 [79]3 years ago
8 0
[tex]x-length\\ y-width\\ x=2y+3\\ Perimeter: 2x+2y=72\\\\ System\ of\ equations:\\ \left \{ {{x=2y+3} \atop {2x+2y}} \right. \\ Substituting\ x=2y+3\\ 2(2y+3)+2y=72\\ 4y+6+2y=72\\ 66y=60|:6\\ y=11\\x=2y+3=2*11+3=25[/tex]
lana66690 [7]3 years ago
4 0
A --> length
b --> width
\begin{cases}a=2b+3\\2a+2b=72\end{cases}
\begin{cases}a=2b+3\\2(2b+3)+2b=72\end{cases}
\begin{cases}a=2b+3\\4b+6+2b=72\end{cases}
\begin{cases}a=2b+3\\6b=66|:6\end{cases}
\begin{cases}a=2b+3\\b=11\end{cases}
\begin{cases}a=2*11+3\\b=11\end{cases}
<span>\begin{cases}a=25\\b=11\end{cases}</span>
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2 years ago
Evaluate S5 for 300 + 150 + 75 + … and select the correct answer below. 18.75 93.75 581.25 145.3125
Savatey [412]

we have that

300 + 150 + 75 +...

Let

a1=300\\ a2=150\\ a3=75

we know that

\frac{a2}{a1} =\frac{150}{300} \\\\ \frac{a2}{a1}=0.5 \\ \\ a2=a1*0.50

\frac{a3}{a2} =\frac{75}{150} \\\\ \frac{a3}{a2}=0.5 \\ \\ a3=a2*0.50

so

a(n+1)=an*0.50

Is a geometric sequence

Find the value of a4

a(4)=a3*0.50

a(4)=75*0.50

a(4)=37.5

Find the value of a5

a(5)=a4*0.50

a(5)=37.5*0.50

a(5)=18.75

Find S5

S5=a1+a2+a3+a4+a5\\ S5=300+150+75+37.5+18.75\\ S5=581.25

therefore

the answer is

581.25

Alternative Method

Applying the formula

S_n=\frac{a_1 (1-r^n)}{1-r} \\\\a_1=300 \\ r=\frac{1}{2}\\\\ S_5=\frac{300(1-(\frac{1}{2})^5)}{1-\frac{1}{2}}\\\\=\frac{300(1-\frac{1}{32})}{\frac{1}{2}}\\\\=\frac{300 \times \frac{31}{32}}{\frac{1}{2}}\\\\=\frac{75 \times \frac{31}{8}}{\frac{1}{2}}\\\\=\frac{\frac{2325}{8}}{\frac{1}{2}}\\\\=\frac{2325}{8} \times 2\\\\=\frac{2325}{4}\\\\=581 \frac{1}{4}\\\\=581.25

therefore

the answer is

581.25

6 0
3 years ago
Read 2 more answers
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