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Let’s check out your problem:
Does
(
10
,
6
)
(10,\,6)
(
10
,
6
)
make the inequality 15x + 9y > 8 true?
\newline
Choices:
\newline
(A)yes
\newline
(B)no
View step-by-step help
Home
Math Problems
Algebra 1
Does (x, y) satisfy the inequality?
Full solution
Q.
Does
(
10
,
6
)
(10,\,6)
(
10
,
6
)
make the inequality
15
x
+
9
y
>
8
15x + 9y > 8
15
x
+
9
y
>
8
true?
\newline
Choices:
\newline
(A)yes
\newline
(B)no
Substitute values into inequality:
Substitute the values
(
10
,
6
)
(10, 6)
(
10
,
6
)
into the inequality 15x + 9y > 8. The substituted inequality is 15(10) + 9(6) > 8.
Calculate left side:
Calculate the left side of the inequality
15
(
10
)
+
9
(
6
)
15(10) + 9(6)
15
(
10
)
+
9
(
6
)
. Simplify it to get
150
+
54
150 + 54
150
+
54
.
Add numbers:
Add the two numbers together to get
150
+
54
=
204
150 + 54 = 204
150
+
54
=
204
.
Check if true:
Now we have the inequality 204 > 8. Determine if this is a true statement.
Verify point satisfies inequality:
Since
204
204
204
is indeed greater than
8
8
8
, the point
(
10
,
6
)
(10, 6)
(
10
,
6
)
does make the inequality 15x + 9y > 8 true.
More problems from Does (x, y) satisfy the inequality?
Question
Consider the following problem:
\newline
The total number of subscribers Zhang Wei has for his video page is changing at a rate of
r
(
t
)
=
21
−
2
t
r(t)=21-2 t
r
(
t
)
=
21
−
2
t
subscribers per week (where
t
t
t
is the time in weeks). At time
t
=
8
t=8
t
=
8
weeks, Zhang Wei has
120
120
120
subscribers. How many subscribers does Zhang Wei have by week
20
20
20
?
\newline
Which expression can we use to solve the problem?
\newline
Choose
1
1
1
answer:
\newline
(A)
r
(
20
)
−
r
(
8
)
+
120
r(20)-r(8)+120
r
(
20
)
−
r
(
8
)
+
120
\newline
(B)
∫
20
20
r
(
t
)
d
t
\int_{20}^{20} r(t) d t
∫
20
20
r
(
t
)
d
t
\newline
(C)
∫
8
20
r
(
t
)
d
t
+
120
\int_{8}^{20} r(t) d t+120
∫
8
20
r
(
t
)
d
t
+
120
\newline
(D)
r
(
20
)
r(20)
r
(
20
)
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Posted 9 months ago
Question
Anjali was given this problem:
\newline
A person stands at a distance of
12
12
12
meters east of an intersection and watches a car driving away from the intersection to the north at
4
4
4
meters per second. At a certain instant
t
0
t_{0}
t
0
, the car is at distance
n
(
t
0
)
n\left(t_{0}\right)
n
(
t
0
)
of
9
9
9
meters from the intersection. What is the rate of change of the distance
d
(
t
)
d(t)
d
(
t
)
between the car and the person at that instant?
\newline
Which equation should Anjali use to solve the problem?
\newline
Choose
1
1
1
answer:
\newline
(A)
tan
[
d
(
t
)
]
=
n
(
t
)
12
\tan [d(t)]=\frac{n(t)}{12}
tan
[
d
(
t
)]
=
12
n
(
t
)
\newline
(B)
d
(
t
)
=
12
⋅
n
(
t
)
2
d(t)=\frac{12 \cdot n(t)}{2}
d
(
t
)
=
2
12
⋅
n
(
t
)
\newline
(C)
d
(
t
)
+
12
+
n
(
t
)
=
180
d(t)+12+n(t)=180
d
(
t
)
+
12
+
n
(
t
)
=
180
\newline
(D)
[
d
(
t
)
]
2
=
1
2
2
+
[
n
(
t
)
]
2
[d(t)]^{2}=12^{2}+[n(t)]^{2}
[
d
(
t
)
]
2
=
1
2
2
+
[
n
(
t
)
]
2
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Posted 9 months ago
Question
In one kind of chemical reaction, unconverted reactants change into converted reactants.
\newline
The fraction
a
a
a
of reactants that have been converted increases at a rate proportional to the product of the fraction of converted reactants and the fraction of unconverted reactants.
\newline
Which equation describes this relationship?
\newline
Choose
1
1
1
answer:
\newline
(A)
d
a
d
t
=
k
a
1
−
a
\frac{d a}{d t}=\frac{k a}{1-a}
d
t
d
a
=
1
−
a
ka
\newline
(B)
d
a
d
t
=
k
a
(
1
−
a
)
\frac{d a}{d t}=k a(1-a)
d
t
d
a
=
ka
(
1
−
a
)
\newline
(c)
d
a
d
t
=
k
a
(
1
−
a
)
\frac{d a}{d t}=\frac{k}{a(1-a)}
d
t
d
a
=
a
(
1
−
a
)
k
\newline
(D)
d
a
d
t
=
k
a
2
\frac{d a}{d t}=k a^{2}
d
t
d
a
=
k
a
2
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Posted 9 months ago
Question
Which is the set of integers greater than or equal to
0
0
0
and less than or equal to
6
6
6
?
\newline
Choices:
\newline
(A)
∅
\emptyset
∅
\newline
(B)
{
1
,
2
,
3
,
4
,
5
,
6
}
\{1, 2, 3, 4, 5, 6\}
{
1
,
2
,
3
,
4
,
5
,
6
}
\newline
(C)
{
0
,
1
,
2
,
3
,
4
,
5
,
6
}
\{0, 1, 2, 3, 4, 5, 6\}
{
0
,
1
,
2
,
3
,
4
,
5
,
6
}
\newline
(D)
{
1
,
6
}
\{1, 6\}
{
1
,
6
}
Get tutor help
Posted 8 months ago
Question
The Salem Playhouse wants to make at least
$
6
,
800
\$6,800
$6
,
800
on ticket sales this year. Currently, adults' tickets cost
$
67
\$67
$67
and children's tickets cost
$
16
\$16
$16
.
\newline
Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.
\newline
x
=
x =
x
=
the number of adults' tickets sold
\newline
y
=
y =
y
=
the number of children's tickets sold
\newline
Choices:
\newline
(A)
67
+
x
+
16
+
y
>
6
,
800
67 + x + 16 + y > 6,800
67
+
x
+
16
+
y
>
6
,
800
\newline
(B)
67
x
+
16
y
>
6
,
800
67x + 16y > 6,800
67
x
+
16
y
>
6
,
800
\newline
(C)
67
+
x
+
16
+
y
≥
6
,
800
67 + x + 16 + y \geq 6,800
67
+
x
+
16
+
y
≥
6
,
800
\newline
(D)
67
x
+
16
y
≥
6
,
800
67x + 16y \geq 6,800
67
x
+
16
y
≥
6
,
800
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Posted 8 months ago
Question
An event planner is reserving rooms for a company-wide event. Each ballroom can hold
93
93
93
people and each conference room can hold
23
23
23
people, and together they must hold at least the
841
841
841
people participating.
\newline
Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.
\newline
x
=
x =
x
=
the number of ballrooms
\newline
y
=
y =
y
=
the number of conference rooms
\newline
Choices:
\newline
(A)
23
x
−
93
y
≥
841
23x - 93y \geq 841
23
x
−
93
y
≥
841
\newline
(B)
93
x
+
23
y
≥
841
93x + 23y \geq 841
93
x
+
23
y
≥
841
\newline
(C)
93
x
×
23
y
≥
841
93x \times 23y \geq 841
93
x
×
23
y
≥
841
\newline
(D)
23
x
+
93
y
≥
841
23x + 93y \geq 841
23
x
+
93
y
≥
841
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Posted 8 months ago
Question
Jim is building birdhouses in shop class, and he has a total of
423
423
423
nails on hand. A small birdhouse requires
34
34
34
nails and a large birdhouse requires
41
41
41
nails.
\newline
Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.
\newline
x
=
x =
x
=
the number of small birdhouses
\newline
y
=
y =
y
=
the number of large birdhouses
\newline
Choices:
\newline
(A)
34
x
+
41
y
≤
423
34x + 41y \leq 423
34
x
+
41
y
≤
423
\newline
(B)
41
x
×
34
y
≤
423
41x \times 34y \leq 423
41
x
×
34
y
≤
423
\newline
(C)
41
x
+
34
y
≤
423
41x + 34y \leq 423
41
x
+
34
y
≤
423
\newline
(D)
34
x
×
41
y
≤
423
34x \times 41y \leq 423
34
x
×
41
y
≤
423
Get tutor help
Posted 8 months ago
Question
Craig is building a shelving unit to hold all of his shoes. A pair of work shoes takes up
2
square feet
2\,\text{square feet}
2
square feet
of space, and a pair of boots occupies
5
square feet
5\,\text{square feet}
5
square feet
. The total amount of shelving space taken up by all the shoes can be at most
57
square feet
57\,\text{square feet}
57
square feet
.
\newline
Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.
\newline
x
=
x =
x
=
the number of pairs of shoes
\newline
y
=
y =
y
=
the number of pairs of boots
\newline
Choices:
\newline
(A)
5
x
+
2
y
≤
57
5x + 2y \leq 57
5
x
+
2
y
≤
57
\newline
(B)
2
x
+
5
y
<
57
2x + 5y < 57
2
x
+
5
y
<
57
\newline
(C)
2
x
+
5
y
≤
57
2x + 5y \leq 57
2
x
+
5
y
≤
57
\newline
(D)
5
x
+
2
y
<
57
5x + 2y < 57
5
x
+
2
y
<
57
Get tutor help
Posted 8 months ago
Question
Sasha is knitting baby items to sell at a craft fair. She has a total of
1
,
650
1,650
1
,
650
yards of yarn to use for the items. A pair of booties uses
198
198
198
yards of yarn and a cap uses
201
201
201
yards apiece.
\newline
Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.
\newline
x
=
x =
x
=
the number of pairs of booties Sasha can knit
\newline
y
=
y =
y
=
the number of caps Sasha can knit
\newline
\newline
Choices:
\newline
(A)
198
x
+
201
y
<
1
,
650
198x + 201y < 1,650
198
x
+
201
y
<
1
,
650
\newline
(B)
198
x
−
201
y
<
1
,
650
198x - 201y < 1,650
198
x
−
201
y
<
1
,
650
\newline
(C)
198
x
+
201
y
≤
1
,
650
198x + 201y \leq 1,650
198
x
+
201
y
≤
1
,
650
\newline
(D)
198
x
−
201
y
≤
1
,
650
198x - 201y \leq 1,650
198
x
−
201
y
≤
1
,
650
Get tutor help
Posted 8 months ago
Question
The Middletown High School softball coach is purchasing equipment for her team. She has a budget of at most
$
770
\$770
$770
to purchase bats and softballs. A case of softballs has a price of
$
38
\$38
$38
, and a bat has a price of
$
27
\$27
$27
. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x
=
x =
x
=
the number of cases of softballs
y
=
y =
y
=
the number of bats
\newline
Choices:
\newline
(A)
38
x
−
27
y
<
770
38x - 27y < 770
38
x
−
27
y
<
770
\newline
(B)
38
x
×
27
y
≤
770
38x \times 27y \leq 770
38
x
×
27
y
≤
770
\newline
(C)
38
x
+
27
y
<
770
38x + 27y < 770
38
x
+
27
y
<
770
\newline
(D)
38
x
+
27
y
≤
770
38x + 27y \leq 770
38
x
+
27
y
≤
770
Get tutor help
Posted 8 months ago
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