Mom gave $ 320 to each girl
<u>Solution:</u>
Given that Lily and Elsa are both college students
Before mom gave them this months allowance lily had $750 and Elsa had &215
<em><u>So amount with Lily and Elsa already is:</u></em>
amount with Lily = $ 750
amount with Elsa = $ 215
After mom gave each girl an equal amount of money for this months allowance, lily had twice as much money as Elsa
Let "a" be the equal amount of money which mom gave to Lily and Elsa
<em><u>So now amount with Lily and Elsa after mom gave equal amount is:</u></em>
amount with Lily = amount with Lily already + a
amount with Lily = 750 + a
amount with Elsa = amount with Elsa already + a
amount with Elsa = 215 + a
<em><u>Now given that lily had twice as much money as Elsa</u></em>
Amount with lily = 2(amount with elsa)
750 + a = 2(215 + a)
750 + a = 430 + 2a
2a - a = 750 - 430
a = 320
Thus mom gave $ 320 to each girl
Answer:
621
629
Step-by-step explanation:
We know that
sin
(
x
+
y
)
=
sin
x
cos
y
+
sin
y
cos
x
If
cos
x
=
8
17
and
sin
y
=
12
37
We can use,
cos
2
x
+
sin
2
x
=
1
and
cos
2
y
+
sin
2
y
=
1
To calculate
sin
x
and
cos
y
sin
2
x
=
1
−
cos
2
x
=
1
−
(
8
17
)
2
=
225
17
2
sin
x
=
15
17
cos
2
y
=
1
−
sin
2
y
=
1
−
(
12
37
)
2
=
1225
37
2
cos
y
=
35
37
so,
sin
(
x
+
y
)
=
15
17
⋅
35
37
+
12
37
⋅
8
17
=
621
629
Answer link
Shwetank Mauria
Nov 22, 2016
sin
(
x
+
y
)
=
621
629
or
−
429
629
depending on the quadrant in which sine and cosine lie.
Explanation:
Before we commence further, it may be mentioned that as
cos
x
=
8
17
,
x
is in
Q
1
or
Q
4
i.e.
sin
x
could be positive or negative and as
sin
y
=
12
37
,
y
is in
Q
1
or
Q
2
i.e.
cos
y
could be positive or negative.
Hence four combinations for
(
x
+
y
)
are there and for
sin
(
x
+
y
)
=
sin
x
cos
y
+
cos
x
sin
y
, there are four possibilities.
Now as
cos
x
=
8
17
,
sin
x
=
√
1
−
(
8
17
)
2
=
√
1
−
64
289
=
√
225
289
=
±
15
17
and
as
sin
y
=
12
37
,
cos
y
=
√
1
−
(
12
37
)
2
=
√
1
−
144
1369
=
√
1225
1369
=
±
35
37
Hence,
(1) when
x
and
y
are in
Q
1
sin
(
x
+
y
)
=
15
17
×
35
37
+
8
17
×
12
37
=
525
+
96
629
=
621
629
(2) when
x
is in
Q
1
and
y
is in
Q
2
sin
(
x
+
y
)
=
15
17
×
−
35
37
+
8
17
×
12
37
=
−
525
+
96
629
=
−
429
629
(3) when
x
is in
Q
4
and
y
is in
Q
2
sin
(
x
+
y
)
=
−
15
17
×
−
35
37
+
8
17
×
12
37
=
525
+
96
629
=
621
629
(4) when
x
is in
Q
4
and
y
is in
Q
1
sin
(
x
+
y
)
=
−
15
17
×
35
37
+
8
17
×
12
37
=
−
525
+
96
629
=
−
429
629
Hence,
sin
(
x
+
y
)
=
621
629
or
−
429
629
Answer:
B
Step-by-step explanation:
This is a power to a power problem. -3 times 2 equals-6. Usually when a number is raised to a negative power, the number is the denominator over 1...with the exponent in the denominator ad well. 5 to the -6 power is 15,605 which is the same as 1/5 to the 6th power....1/15,605
Answer:
1. D 2. B 3. C
Step-by-step explanation:
WARNING: I am not 100% sure about 2.
1. If you simplify the first part of the equation for letter D, you'll realise it is the same equation.
2. It is either B or D. I believe it is B because you would not have to multiply 4 again.
3. The square root of 121 is eleven, the square root of x^2 is x. x=11.
