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Form a quadratic equation in x to represent the information and find the value of x.
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3 partsStep-by-step solution
15 stepsHere are the solutions to the problems.
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Part a· 6 steps
Form a Quadratic equation in to represent the information.
Define variables and set up the initial equation.
Let be the original number of women.
The total amount to be contributed is Sh. 1200.
The original contribution per woman would be .
5 women were unable to contribute, so the number of contributing women became .
The new contribution per woman is .
The problem states that the remaining women contributed Sh. 20 more each.Rearrange the equation to isolate the constant term.
Combine the fractions on the left side using a common denominator .
Multiply both sides by .
Divide both sides by 20.
Rearrange into the standard quadratic form .
The quadratic equation is .
Part b20
Find the value of .
Solve the quadratic equation by factoring.
We need two numbers that multiply to -300 and add to -5. These numbers are -20 and 15.
Determine the possible values for .
Choose the valid value for .
Since represents the number of women, it must be a positive value.
Therefore, .
The value of is .
Part c15
Determine the number of women that contributed the money and the amount each contributed.
Calculate the number of women who contributed.
The original number of women was .
5 women were unable to contribute, so the number of contributing women is .
Number of contributing women women.Calculate the amount each contributing woman paid.
The total amount contributed was Sh. 1200.
Amount each contributed
Amount each contributed Shillings.The number of women that contributed the money is and the amount each contributed is .
:
Write an expression for the area of a triangular ranch in terms of .
Recall the formula for the area of a triangle.
Substitute the given base and height into the formula.
Base km
Height kmExpand the product of the binomials.
Substitute the expanded expression back into the area formula and simplify.
The expression for the area is .
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