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Math Problems
Precalculus
Descartes' Rule of Signs
When Li Juan's auto yard is filled to capacity with only cars, it has
60
60
60
cars. When it is filled to capacity with only vans, it has
50
50
50
vans. Which linear equation models the number of cars,
c
c
c
, and vans,
v
v
v
, that could be in Li Juan's auto yard when it is filled to capacity?
\newline
Choose
1
1
1
answer:
\newline
(A)
c
60
+
v
50
=
1
\frac{c}{60}+\frac{v}{50}=1
60
c
+
50
v
=
1
\newline
(B)
60
c
+
50
v
=
1
60c+50v=1
60
c
+
50
v
=
1
\newline
(C)
c
50
+
v
60
=
1
\frac{c}{50}+\frac{v}{60}=1
50
c
+
60
v
=
1
\newline
(D)
50
c
+
60
v
=
1
50c+60v=1
50
c
+
60
v
=
1
Get tutor help
Divya is solving the following equation for
w
w
w
.
\newline
3
w
−
20
−
5
w
=
2
3 w-\sqrt{20-5 w}=2
3
w
−
20
−
5
w
=
2
\newline
Her first few steps are given below.
\newline
3
w
=
20
−
5
w
+
2
3 w=\sqrt{20-5 w}+2
3
w
=
20
−
5
w
+
2
\newline
3
w
−
2
=
20
−
5
w
3 w-2=\sqrt{20-5 w}
3
w
−
2
=
20
−
5
w
\newline
(
3
w
−
2
)
2
=
(
20
−
5
w
)
2
(3 w-2)^{2}=(\sqrt{20-5 w})^{2}
(
3
w
−
2
)
2
=
(
20
−
5
w
)
2
\newline
9
w
2
−
12
w
+
4
=
20
−
5
w
9 w^{2}-12 w+4=20-5 w
9
w
2
−
12
w
+
4
=
20
−
5
w
\newline
Is it necessary for Divya to check her answers for extraneous solutions?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B)
N
o
\mathrm{No}
No
Get tutor help
www.math.temple.edu
\newline
22
22
22
. Eighteen out of the thirty people who have already come out of a building at the beginning of a lunch break have been women. What are the odds that the next person out is a woman?
\newline
(a)
12
12
12
to
18
18
18
\newline
(b)
18
18
18
to
12
12
12
\newline
(c)
12
12
12
to
30
30
30
\newline
(d)
18
18
18
to
30
30
30
Get tutor help
