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Tju [1.3M]
4 years ago
15

an artificial lake is in the shape of a rectangle and has an area of 9/20 square mile. the width of the lake is 1/5 the length o

f the lake. what are the dimensions of the lake?
Mathematics
1 answer:
Gnom [1K]4 years ago
7 0
X=length
y=width
Area (rectangle)=length x width
we suggest this system of  equations:
y=x/5
xy=9/20
solve this system of equations by substitution method:
x(x/5)=9/20
x²/5=9/20
Least common multiple=20
4x²=9
x²=9/4
x=⁺₋√(9/4)
we have two solutions:
x₁=-3/2   it does not validate
x₂=3/2    ⇒y=x/5=(3/2)/5=3/10

The dimensions of the lake are:
lengh=3/2 miles
width=3/10 miles

to check:
Area=3/2 miles x 3/10 miles=9/20 miles².
width is 1/5 the length of the lake ⇒  3/10 miles=(3/2) /5 miles

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2 years ago
The first term of an AP is -7 and the ratio of the eight term to the third term is 7:1 calculate the common difference
alukav5142 [94]

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the common difference is 6.

Step-by-step explanation:

Given;

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let the common difference = d

The third term is written as;

T₃ = a + 2d

The eight term is written as;

T₈ = a + 7d

The ratio of the eight term to third term = 7:1

\frac{T_8}{T_3} = \frac{7}{1} = \frac{a+ 7d}{a + 2d} \\\\7 =  \frac{a+ 7d}{a + 2d}\\\\Recall, a = -7\\\\7 =   \frac{-7+ 7d}{-7 + 2d}\\\\7(-7 + 2d) = -7+ 7d\\\\-49 + 14d = -7 + 7d\\\\14d -7d = -7 + 49\\\\7d = 42\\\\d = \frac{42}{7} \\\\d = 6

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4 0
3 years ago
What is the sum of forty-six and ninety-four?
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8 0
3 years ago
Read 2 more answers
The drama club is selling tickets to its play. An adult ticket costs $15 and a student ticket costs $11. The auditorium will sea
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Answer:

83 adult tickets and 217 student tickets.

Step-by-step explanation:

Let number of adult tickets sold = x

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So, number of student tickets = 300 - x

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Given that overall collection = $3630

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Now , collection = $3632

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