Nadya has 19 1/4 yards of ribbons she cuts into pieces that each measure 1 3/4 yards. How many pieces of ribbon does Nadya have
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<h3>Answer: -2w^2 + 25w = 25 or -2w^2 + 25w - 25 = 0</h3>
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Explanation:
Refer to the diagram below. The width is w. We have two opposite and parallel sides equal to this. The other two parallel congruent sides are L = 25-2w meters long. We start with the total amount of fencing, and then subtract off the two width values, so 25-w-w = 25-2w.
The area of the rectangle is
Area = length*width
Area = L*W
Area = (25-2w)*w
Area = 25w - 2w^2
Area = -2w^2 + 25w
Set this equal to the desired area (25 square meters) to get
-2w^2 + 25w = 25
and we can subtract 25 from both sides to get everything on one side
-2w^2 + 25w - 25 = 0
side note: The two approximate solutions of this equation are w = 1.0961 and w = 11.4039 (use the quadratic formula or a graphing calculator to find this)
Answer:
In 17th year, his income was $30,700.
Step-by-step explanation:
It is given that the income has been increasing each year by the same dollar amount. It means it is linear function.
Income in first year = $17,900
Income in 4th year = $20,300
Let y be the income at x year.
It means the line passes through the point (1,17900) and (4,20300).
If a line passes through two points and
, then the equation of line is
The equation of line is
Add 17900 on both sides.
The income equation is y=800x+17100.
Substitute y=30,700 in the above equation.
Subtract 17100 from both sides.
Divide both sides by 800.
Therefore, in 17th year his income was $30,700.