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Simplify the expression \(\frac{x+1}{y} \div \frac{2(x+1)}{x}\).
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\(\frac{x}{2y}\) |
Simplify the expression \(\frac{2a-4}{2a} \div \frac{a-2}{3}\).
|
\(\frac{3}{a}\) |
Simplify the expression \(\frac{x^2 + 4x}{3y} \div \frac{x^2 - 16}{12y^2}\).
|
\(\frac{4y(x)}{x - 4}\) |
Simplify the expression \(\frac{p^2 + pq}{p^2 - pr} \div \frac{p^2 - q^2}{p^2 - r^2}\).
|
\(\frac{p(p + q)(p + r)}{(p - q)(p - r)}\) |
Simplify the expression \(\frac{m^2 - 4}{m+1} \div \frac{m+2}{m^2 + 2m + 1}\).
|
\(\frac{(m - 2)(m + 1)}{1}\) |
Simplify the expression \(\frac{x^2 y^2 + 3xy}{4x^2 - 1} \div \frac{xy + 3}{2x + 1}\).
|
\(\frac{xy(2x + 1)}{2x - 1}\) |
Simplify the expression \(\frac{a^2 - 5a}{a^2 - 4a - 5} \div \frac{a^2 - a - 2}{a^2 + 2a + 1}\).
|
\(\frac{a(a + 1)}{(a - 2)(a - 5)}\) |
Simplify the expression \(\frac{x^2 - 8x}{x^2 - 4x - 5} \times \frac{x^2 + 2x + 1}{x^3 - 8x^2} \div \frac{x^2 + 2x - 3}{x - 5}\).
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\(\frac{1}{x(x - 3)}\) |
Solve the equations \(\frac{1}{2}x + \frac{1}{3}y = 20000\) and \(\frac{1}{2}x + \frac{2}{3}y = 30000\) to find separately the amount spent on refreshments and decorations.
|
\(x = 20000\), \(y = 30000\) |
From the square of a certain number, if you subtract twice the number, the result is 15. Find the number.
|
5 or -3 |
The product of two consecutive even integers is 120. Find the two integers.
|
10 and 12 or -12 and -10 |
The length of a rectangular lamina is 3 cm more than the width. If the area is 88 cm\(^2\), find the length and the width of the lamina.
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Length: 11 cm, Width: 8 cm |
A playing field measuring 32 metres by 20 metres has a pathway outside the field all around it, of uniform width. The area of the pathway is 285 square metres. Taking the width of the pathway to be \( x \) metres, set up a quadratic equation in \( x \) to represent the given information.
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\(4x^2 + 104x - 285 = 0\) |
Solve the quadratic equation \(4x^2 + 104x - 285 = 0\) to find the width of the pathway.
|
2.5 metres |
The hypotenuse of a right angled triangle is \( 2x + 1 \) cm. The lengths of the other two sides are \( x \) cm and \( x + 7 \) cm respectively. Solve for \( x \) and find the lengths of all three sides of the triangle.
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\(x = 8\), Sides: 8 cm, 15 cm, 17 cm |
The sum of the first \( n \) terms of the arithmetic progression \( -7, -5, -3, -1, ... \) is 105. Taking \( n \) to be the number of terms we are adding together, set up a quadratic equation in \( n \) for the sum of the first \( n \) terms.
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\(n^2 - 8n - 105 = 0\) |
Solve the quadratic equation \(n^2 - 8n - 105 = 0\) to find the number of terms \( n \) you have added.
|
15 |
When three times a number which is positive is subtracted from the square of that number the answer is 28. Find the number.
|
7 |
The product of two consecutive odd integers is 99. Find the two integers.
|
9 and 11 or -11 and -9 |
In a right angled triangle, the lengths of the two sides containing the right angle are \( 5x \) cm and \( (3x - 1) \) cm. If the area is given as 60 square centimetres, set up a quadratic equation in \( x \) and solve for \( x \). Thereby find the length of each side of the triangle.
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\(x = 3\), Sides: 15 cm, 8 cm, 17 cm |
A man bought a certain number of mangoes for Rs 600. If the price of a mango was one rupee less, then he could have bought 20 more mangoes. Find the number of mangoes he bought.
|
100 |
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