Page 612 - Algebra 1

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The area of a triangle varies jointly with the base and height of the triangle. Given that the area of a triangle is 6 square feet, the base is 3 feet, and the height is 4 feet, find the constant of variation. Express the area of a triangle.
_2_ Multiple Choice Divide 3mn ÷ 9mn .
4m2n 8m3n2
A 2mn B 2mn C 2mn D 27
_2__2_
3m 3n2 3
Travel Times Use the formula _d = t to find how long it takes to travel a distance of
32m3
r
x2 -25milesattherateof x+5milesperhour.
Student A
___
x = -b = -4 = -4 = -2
2a 2(1) 2
_ Student B x=-(-4)= =2
_4 2(1) 2
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Error Analysis Two students tried to find the axis of symmetry for the equation y = x2 - 4x - 3. Which student is correct? Explain the error.
Multi-Step The population of Ireland between the years 1901 and 2006 can be approximated by the function y = 0.000285x2 - 0.0232x + 3.336, where x is the number of years after 1900 and y is the population for that year in millions of people.
a. Justify Tell how you know the function has a minimum rather than a maximum. b. Estimate What was the minimum population and when did it occur? Round to
the nearest year.
c. Predict Use the function to predict the population of Ireland in 2020.
Geometry The equation y = -x2 + 35x gives the area of a rectangle with a fixed perimeter of 70 units, where x is the width of the rectangle. Explain how to use the equation to find the greatest possible area of the rectangle.
C 2-q D 3(2-q) __
3q 3q 3q2 q2 Business Ms. Suarez owns a manufacturing company. Her total profits for one
year are x2 + 44x + 420, where x is the number of units manufactured. Her profits for the spring are x2 + 7x + 100, while her profits for the winter are 17x + 40. Write a simplified expression for the fraction of the total profits that come from the spring and winter seasons.
__ Multiple Choice Simplify 6 - 3q .
9q2 9q2 A _1 B _2
__ _2 Justify When adding 5n + 6p , why multiply the first expression by p and
p2
2
Write Describe the steps in adding and simplifying x2 + 6x + 9 + x + 3 .
2 n4p3 n2p5
the second by _n ? _
2
n_
x
Lesson 90 597