Question 1
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A band must know the dimensions of the stage where they are having a concert. The area of the
rectangular stage is 77 ft2
and the width is x. The length of t
...
Question 1
Selected Answer:
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A band must know the dimensions of the stage where they are having a concert. The area of the
rectangular stage is 77 ft2
and the width is x. The length of the stage is (2x – 3) feet. What is the length of the stage?
49 ft
7 ft
50 ft
11 ft
49 ft
77 = x(2x – 3)
77 = 2x² - 3x Distribute.
For a rectangle, A = lw0 = 2x² - 3x – 77 Set the equation equal to 0, subtract 85 from both
sides.
0 = 2x² - 14x + 11x - 77 Rewrite the trinomial.
0 = (2x² - 14x) + (11x –
77)
Group into a sum of two pairs.
0 = 2x(x – 7) + 11(x – 7) Factor the greatest common factor from both pairs.
0 = (x – 7)(2x + 11) Factor the common binomial from each pair.
x – 7 = 0; 2x + 11 = 0 Use the zero-product property to set each factor
equal to 0.
x = 7; 2x = - 11 Solve each equation separately.
x = 7; x = -11/2 Reject x = -11/2, length must be positive.
Length = 2x – 3; x = 7
= 2(7) – 3
= 14 – 3
= 11
The stage is 11 feet long.
Question 2
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Since 1972 the U.S. Fish and Wildlife Service has kept a list of endangered species in the United
States. For the years 1972 – 1998, the number of species s on the list can be modeled by s =
119.6e
0.0917t where t is the number of years since 1972. Approximately how many species were on
the list in 1993?
820
875
2,752
820
626
To determine t for the year 1993, subtract 1993 – 1972 = 21
s = 119.6e
0.0917t
s = 119.6e
0.0917(21)
= 119.6e
(0.0917 • 21) Group the exponents to make sure the order of
operations is followed.
= 119.6e
1.9257
Minimize rounding errors by keying the entire expression into a calculator.
≈ 820.45
Approximately 820
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